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THE ORGANS of SPEECH. By Georg Hermann vox MKYKR. OS. XLVIII. FALLACIES. A View of Logic from the Practical Side. By Alfked Siixiwic k. os. London: KEG AN PAUL, TRENCH, & CO., 1 Paternoster Square. The International Scientific Series. VOL. XLVm. FALLACIES A VIEW OF LOGIC FROM THE PM ACTIO AL SIDE ALFEED SIDGWICK B.A. OXOX. BERKELEY FELLOW OF THE OWENS COLLEGE, MANCHESTER LONDON KEGAN PAUL, TREXCH & CO., 1, PATERNOSTER SQUARE 1883 {The riohts of translation and of reinoduction are reserved.) Annex ns PEEFACE, This book is intended, like the others in the Inter- nationcd Scientific Series, mainly for the general reader. That is to say, it requires no previous technical train- ing, and is written as much as possible from the unpro- fessional point of view. Although any treatment of Fallacies must be to a great extent a treatment of methods of Proof, and must therefore demand a certain amount of general logical theory, yet by trying to keep chiefly in view the practical side of the science of Logic, — subordinating to that all other interests or inquiries, — I have been able to neglect the discussion of much debatable matter and to avoid definite adherence to a school. No doubt. Mill and Bain, — and, more remotely, Hume, — are the authors to whom the general substance of the present work is mainly traceable ; but one may, I hope, utilise many of their results without being compelled to accept the whole of their Philosophy. As regards later writers, although vi PREFACE. hints have here and there been taken from various other sources, English and German, the aid so obtained has been, I think (except where expressly mentioned), frag- mentary or indirect. It is impossible fully to acknowledge all the vivct voce help received from friends, but I may at least here express my gratitude to the anonymous Founder of the Berkeley Fellowships at the Owens College. The election to one of these, in 1881, has given me the opportunity of finishing this book (then already designed for this Series) : and has also provided me with the invaluable advice and criticism of Prof Adamson. By the courtesy of the Editor of Mind, sl portion of chapters iii. and iv. (Part I.) is reprinted from that Journal. Manchester, Mau, 1883. CONTENTS. INTEODUCTION. SECTION" PAGE I. Difficulties of Treatment ... ... ... ... ... ... 1 11. The Practical Side of Logic 11 111. Outline of the Work 20 PAET I. PKOOF IN GENEEAL. CHAPTER I. THE MEANING AND AIMS OF PROOF. T. Proof and Ixference ... 31 Importance of the distinction, 31 . Ambiguities of ' Inference,' ' Eeasoning,' etc., 32-34. The problem of Proof always narrower than that of Inference, 35. 11. Proving and Testing 35 Fm-ther ambiguities of 'Proof,' 35-37. Its etymological meaning, 36. Successful resistance to attack, 37, 38. ' Practically ' suflBcient Proof, 38. Value of hostile criti- cism, 39. The discarding of rival theories, 40. viii CONTENTS. • ^ CHAPTER II. THE SUBJECT-IMATTER OF PEOOF : IX GENEEAL. SECTION PAGE I, Real and Unreal Propositions 41 A thesis, what, 41. * Verbal ' and ' Unreal,' 42. Tautology, 43, 44. Self-contradiction, 4i4r-4:7, ' Ultimate beliefs ' and Unreality, 46, Meaningless terms, 47, 48. Propositions apparently, not actually, unreal, 48-51. XL Sibject and Predicate 51 * Things spoken of,' 51, 52. Propositions viewed as stating B, relation, 5S-56. Copula, 54. Starting-point and goal of an assertion, 54, 55. III. Simple and Complex Propositions 56- No sharp line to be drawn between them, 56. An argu- ment, as a whole, is a complex proposition, 58. CHAPTER III. THE SUBJECT-MATTER OF PROOF: MAIN KINDS OF THESIS. I. Indication 59 All propositions assert ' indication,' 59. Indication and im- plication, 60. Special sense of the name, 61, 62. II. Affirmation and Denial 64 III. Abstract and Concrete Propositions 66 The abstract proposition, 66. The concrete proposition, 67, 71. Exceptive denial, and the assertion of difference, 68, 70. Concrete denials, 71. Abstraction and abstract names, 72. Categorical and hypothetical propositions. 73. Respective functions of abstract and concrete pro- positions, 74 ; their interaction, 75-77. ' Overtones ' in a concrete pi-oposition, 77. CONTENTS. ix SECTION PAGE IV. Succession AXD Co-ExiSTEXCE ... 7S 'Plurality' of causes, and their liability to counteraction, 80. Indication seldom absolute, 80-82. ' Chance,' * Tendency,' and ' Law,' 81. Laws incompletely true, 82. CHAPTER IT. THE LAW OF COUXTER-IXDICATIOX 81- The pons asinorum of Logic, 84. ' Presence,' and ' absence,' as sign and signified, 85. Statement of the law, 86. Table illustrating the same, 87. Examples, 87-89. Value of the law, 89-93. The disjunctive proposition, 92, Ap- plication of the law to concrete proposition.s, 95. One precaution necessary, 96. CHAPTER V. THE PROCESS OF PROOF, IX GENERAL. I. The Relation betvteen Thesis and Reason 99" Reason indicates Thesis, 100. Material truth of the Reason, 101, Formal adequacy of the Reason, 102. II. Consistency lOS^ Principles and their 'logical outcome,' 103. Extension to analogous cases, 104. The Maxims of Consistency, 105-107. The use of names, 107-109. The generic and differential elements in the meaning of a name, 108. Analogical and deductive consistency, 110. III. FoRiiAL Adequacy in General Ill The ' Reason given,' and the whole ' rationalisation ' of a thesis, 111. All rationalisation may be expressed syllo- gistically, 111. Proof the counterpart of Explanation, 111, 112. The Principle and the Application, 113. Value of the Syllogism, 113, 114. f CONTENTS. PAET II. THE POSSIBILITIES OF ERROE. SECTION L— BEFORE PROOF. CHAPTER I. PAGE IXTEODUCTOKY 117 CHAPTER II. THE KINDS OF UXEEAL ASSERTION. SECTION L Tautology, or Platitude 120 Causes and results, 120-122. Tautologies sometimes useful as Postulates, 122. Common forms of Tautology, 123. Finer shades, 124-127. 'The' meaning of a word, 124. Bain's view of verbality examined, 125, 126. The special definition, 127. The right to require explanations is practically limited, 128. II. SELF-CONTRADICTION 129 Causes somewhat different from those of Tautology, 129. ' Bulls ' and epigrams, 129. Interval between inconsistent assertions, 130, 131. The more dangerous forms, 131. The Sorites diflficulty, 133-136. Occasional value of vague assertions, 137. III. Meaningless Term 138 Self-contradiction vjithin a term, 138-140. Belief in mysteries, 140. Limits to power of defining, 141. Surn- uium rjenus, 141. Indefinable terms, 142. Ignotum per ignotius, 142. IV. Unreal Assertion : Concluded 143 Recapitulation, 143, 144. Verbal questions, 144-146. De- grces of ' reality,' 146. CONTENTS. XI CHAPTER III. PAGK THE BURDEN OF PROOF 148 The objection 'no evidence,' 148. Self-evident truths, 149, 150. The frustration of disproof, 150. Distinction between denial and doubt, 150. The simple rule, 150, 151. Its extreme cases, 151-154. The sceptical position, 153. The stifling of inquiry, 154, Whately's doctrine examined, I54r-156. How far bound to explain away facts ? 157, 158. The doctrine of ' fair presumptions,' 158-161. Treatment of conflicting facts and awkward questions, 161, 162. Artificial and natui-al laws of discussion, 163. Provisional theories, 164. Presumption of weakness, 165-167. The need and the deruand for Pi'oof, 165. Causes of absence of Proof, 166. SECTION IL—NON SEQUITUR, CHAPTER IV. INTRODUCTORY 168 Non seqidtur co-extensive with failure in formal adequacy of the Reason, 168. A compromise required between Method and Guesswork in detecting fallacies, 169-173. Four meanings of ' Fallacy,' 172, 173. Reductio ad ahsurdu7n, 174. CHAPTER V. THE EMPLOYMENT OF GUESSWORK. SECTION I. General and Special Sources of Fallacy 176 Aristotle's plan of division, 176. Mill's plan similar, 177. The same plan largely adopted in common use, 177. XU CONTEXTS. SECTION PACK II. A List of Gexeeal Objections to any Argument ... 17'^ Four main general objections, 178. These four convenient but overlapping, 178-181. We must limit their meaning by special definition, 182. III. The Objection' Ioxoratio Eleschi 182 Three senses of the term, 182. Dangers of bringing this accusation, 183-185. Logic and Grammar, 183. Use of the Law of Excluded Middle, 185. Snares of language inexhaustible, 186 ; and practically inevitable, 187. Ob- jections that miss the point, 188. Finer shades of the fallacy, 188-191. Change in the meaning of words, 189. Meaning relative to a standard, 191. A broad rale for practice, 192. IV. The Objection P^titio Prixciph 19S Similar difficulty in fixing the meaning, 193-195. The meaning here taken, 195. Means of escape from the accusation, 196, 197. Eesemblance to Platitude, 198. Question-begging names, 198, 199. CHAPTEK YI. THE EMPLOYMENT OF GUESSWORK: CONTINUED. I. The Objection i leading men of science. But in tlie meantime, Logic (as usually understood) can hardly help containing a good deal of elementary matter, and is compelled to take for granted in the learner a power of making very elementary mistakes. It seems that the best Scientific Discovery must always be in advance of Inductive Logic, in much the same way as the best emplopuent of language runs in advance of Grammar. Still, there may be some use in trying to direct and help those Avho are not already scientific, or only in the earlier stages of the pursuit ; nor need the name of Logic compel logicians to claim a dignity beyond their power. One cannot fulfil success- fully the duties of Lord Chancellor and Justice of the Peace at once. As regards Common Sense, it is a little more difficult to avoid coming into conflict here ; since there are plainly two kinds of Common Sense, — one the essence, and the other an undying enemy, of the most perfect use of reason. Ao-ainst near-sio^hted doo-matism, or the self- satisfied refusal to see distinctions, or the habit of slurring" over awkward facts, Logic always intends to carry on a war : but we need not therefore assume that depth or distance of vision, or the practice of splitting hairs or of raising ingenious doubts and difliculties, can never be pushed beyond the limit at which they possess a practical value. The drawing of this line is a standing difficult^^ which cannot be settled off*-hand, but needs the utmost patience : at present, it seems to me, one can only admit the difficulty and remember that the needs of practice IKTROD.] DIFFICULTIES OF TREATMENT. 5 have an older and more final claim than those of curiosity. And, imotatis "iiiiitandis, the same applies to the objections from the side of Art: here, also, two different spirits may be clearly distinguished, one fighting really on our side, though perhaps by other methods, and the other fighting against us indeed, but an enemy deserving little else than contempt from healthy people. But perhaps the special difficulty in the case of Common Sense is that to the simple-minded all things are simple and straightforward. The knowledge of difficulties and of dangers is already an advance beyond mere childish innocence of evil. As Mrs. Farebrother, in Middleniarch, is made to say, " When I was young, Mr. Lydgate, there was never any question about right and wrong. We knew our catechism and that was enough ; we learnt our creed and our duty. Every respectable Church person had the same opinions. But now " — alas ! the reverence for easy-going certainty is lost. So in the kindred question of bodil}^ disease : to our grandfathers, and still more to their grandfathers, diseases were few in number but quite unmistakeable when they came : pre- monitory symptoms were almost things unknown, and degrees of health were only reluctantly admitted possible. And yet the death-rate is decreasing : our ancestors died by thousands of diseases which we are conquering. Very similar is still to a great extent the attitude of Common Sense towards Fallacy. " Did God make men two-legged only, and leave it to Aristotle to make them rational ? " Nothing is harder than to induce short-sight or super- 6 FALLACIES. [Intkoi> ficiality to believe that any extension of view or of insight exists beyond that to which Common Sense i.s- accustomed : although the actual telescope and the microscope cannot now be treated as mere toys, yet out- side the realm of material objects the telescopic and the microscopic spirit is still, by many, considered almost worse than useless. The general reader has, in fact, a rooted belief that Logic is a highly unpractical body of doctrine : unpractical perhaps not only through short- comings of its own, but from the supposed fact that no one but an absolute fool can ever commit a fallacy. Is not the light of Nature worth more than all the reason-, •ings of all the logicians that ever lived ? Such an appeal to idleness is always sure to win a large amount of ready applause. The view here taken, on the contrary, is that many things are believed in the name of Common Sense which a higher Common Sense would condemn, and that no one who is merely human can avoid fallacy altogether for a day. Another fact moreover which operates to prevent any widespread interest in Logic is, no doubt, its barrenness in surprises. In all the physical sciences, Common Sense is being constantly forced to acknowledge that its. methods are not so infallible as our fathers fondly supposed. Even the question " Am I not to believe my own eyes ? " carries no longer the same conclusiveness as- formerly, while every day some new portion of firmly held popular faith is shown to have been delusive or in- complete. Nor is it only in what are commonly called INTROD.] DIFFICULTIES OF TREATMENT. 7 the Phj'sical Sciences that this is the case. Political Economy, though it depends so largely on mere careful- ness and consistency of thought, is rich in unsuspected facts. In Mental Science, and perhaps in Ethics, a harvest of surprises is ripening. But in Logic the case is different. The central practical doctrines of Logic have been so long ago made common property that to a great extent they have passed into commonplace : which is much the same as saying that they commonly command verbal assent too readily for real assent to be strong. They lose the strong support that comes from conquered doubt, and through supposed familiarity pass into real oblivion. Hence it is chiefly in generalising what is already known, and so preserving it in a shape more easy to remember and apply, that the value of Logic consists. And therefore it is difficult to prevent its doctrines being tedious or exasperating, even where they may be most required. There are one or two minor objections to the study of Logic, — even practical Logic — which may be just mentioned here as possible stumbling-blocks. One some- times hears, for instance, that there are so many systems of Logic all at variance with each other that the puzzled inquirer cannot tell which to accept. On this it seems sufficient in the first place to remark that Logic does not claim to be a sort of revelation, which any one is requested to ' accept ' at all, but rather a labour-saving apparatus which each may usefully alter somewhat to suit his own particular needs. Again, it is hardly too much to say that 8 FALLACIES. [Ixtrod. whether the inquirer thinks for himself, or accepts the system of any one logician or of all, the result for 2)ractical purposes will be precisely the same, except perhaps as to speed in learning. In all that is essential to practice there is not only no difference of opinion but room for none. The disputed ground of Logic lies wholly outside that science when viewed as a machine for combating Fallacy. The disputed points refer, without exception, either to the question of the proper province of the science, or its convenient arrangement, or to the adja- cent subjects of Metaphysics, Psychology, Rhetoric, or Grammar. Another objection, only to be mentioned as unim- portant, is that the study of Fallacies belongs altogether to Rhetoric rather than to Logic, and to Rhetoric in a degraded form. The effect of a study of Fallacy, it seems to be sometimes feared, must be to make us tricky, or at least to lead to wordiness and mere ingenuity of repartee. But let us at any rate meet part of this objection by our- selves refusing to let a harmless word offend. If the name Rhetoric be preferred let us accept that name without hesitation. And as to the question of fact, of the actual effect of a study of Fallacies, that of course is a matter on which there is ample room for difference of opinion, and I firmly believe that such study has on the whole a depressing and disarming effect on the power of being successfully sophistic, even where the will to deceive is present. For really effective sophistry nothing is so vitally requisite as semi-innocence. Just so far as the Introd.] difficulties OF TREATMENT. 9 epigram holds true that unconscious hypocrites are the greatest hypocrites of all, so may we say that the self- deceiver is the most successful sophist. Of course, by definition, Fallacy and Sophism are distinct, — the latter is clever deception, the former only honest error ; but the line between them is in real life so dim and wavering that the distinction is practically useless for most purposes except that of giving our neighbour an un- complimentary name. Witness the case of the highly respectable, and even honourable, man who late in life begins to find cherished theories unstable. By the hypothesis his defence of them can be considered pure fallacy no longer, and yet would it not be cruelly unfair to class him with conscious sophists ? Efi*ective sophistry of the more conscious kind can only take place either where the audience are immensely beneath the sophist in acuteness or where they are positively eager to be deceived. And these may, from a general point of view, be regarded as exceptional cases. We are mostly subject to the criticism of our equals, and the real belief is widely held that, after all, truth so far as attainable is an end to be desired. Another objection sometimes heard is that there is danger in tampering with mother-wit by substituting for it the highly abstract, narrow, inelastic rules of Logic. Real life, it is said, is large and complex and many- sided. To deal with actual problems successfully, a quickness and breadth of perception are needed, which must be largely unconscious, under pain of being in- 10 FALLACIES. [Intkoi.. complete. Much in the same ^vslj as the hard rules of srammar are vexatious to those who know their mother- tono-ue, or as a deliberate effort to remember how to spell a word is apt to raise needless doubts and difficul- ties, so, it is sometimes held, does highly conscious- reasoning produce more evil than it conquers. This objection has some real force, and in our last chapter there will be occasion to speak of it again. At the present stage it may be sufficient to remark that although, no doubt, a little knowledge is a dangerous thing, yet rightly understood that fact is, in ordinary circum- stances, merely an argument for trying to attain as much knowledge as possible. The fact of the danger once recognised too, it becomes to a great extent disarmed. The amount of knowledge required to get beyond the dangerous stage in Logic is easily attained : and with or without that knowledge the application of Logic is mainly dependent on practice rather than on theory. All that theory can expect to do in the matter is to clear the way, and so to economise a great deal of time at the beginning. No book on Logic can be used as a vade- onecum, — carried in the pocket and consulted when in doubt whether to take a cab or not, and in other daily difficulties of the kind. If any reader is inclined ta expect such aid he will certainly be "disappointed. The point of view and the. expectations must be altered^ or there will be little good to be got from any book. Nothing can be a complete guarantee against all fallacy ; nor can Logic be made an instrument for testing or IXTEOD.] THE PRACTICAL SIDE OF LOGIC. 11 judging off-hand the truth of all possible propositions- put forward. II. The Practical Side of Logic. We are, then, not here properly or directly concerned mth any of the disputed questions of Logic : we need not even discuss the nature of that science or the limits of its province. And yet the matters we shall have ta treat constitute in themselves the main thread which runs through all logical doctrine, and the final object for which it has been developed. By making the practical purpose of Logic the central point of interest, we help to gather up and bind together its disconnected parts. Logic may in fact be viewed as a machine for combating Fallacy. Like all machines, too, it is itself capable of much improvement in the certainty, the pace, and the fineness with which it performs its work. But unlike machines of lifeless material, its final purpose is in constant danger of being forgotten for other interests,, as men sometimes lose sight of their main intention, take means for ends, and become misers or enthusiasts. Logic is rather a living organism than purely mechanical, and it is full of rudimentary organs which have historical and explanatory interest, but not all of which are now any longer useful for performing work or preserving the life of the science. The Logic required for examinations, is thickl}^ over-grown with disputed questions properly belonging to other departments of inquiry : and though, 12 FALLACIES. [Introd. many of these discussions are of great value in them- selves, and some perhaps also for developing still further the theory of Logic ; though no one can consider himself a thorough student of the science until he knows, at least in broad outline, the history of these disputed questions, yet there are points of A^ew from which we may use- fully neglect them, may avoid all doubtful matters, fix attention solely on the practical means of fighting fallacy, and, as preliminary, sum up the admitted doctrines which bear dkectly on that purpose, to the exclusion of all the rest. We shall neglect, therefore, all inquiry into the proper ' province ' of Logic. If any reader prefers any other name for the doctrines here treated, no objec- tion will be raised. It is our business to inquire what the doctrines bearing on the above-mentioned purpose are, not what they may best be called. If through the employment of a wrong name any discoverable error should arise at any point, that point will present a con- venient opportunity for correcting our definition. Pro- visionall}', however, and with this apology, we may use the name of Logic. Next, we shall neglect, as said above, all ' ultimate ' questions ; all questions of purely metaphysical interest. And here it seems necessary to remove a possible miscon- ception. There is an active hostility to Metaphysics which has exasperated some metaphysicians into declaring that we cannot do without them. Metaphysics of some sort, they tell us, there must be. The only alternative is between good metaphysics and the cheap substitute INTROD.] THE PEACTICAL SIDE OF LOGIC. 13 that Positivism provides. Without stopping to inquire whether possibly other alternatives might be discovered, I may remark that what is here meant by neglecting metaphysical discussions is simply leaving the decision of the question which system of metaphysics is, on the whole, the best, until some occasion when the pressure of more immediate practical needs has been relieved. The most ardent metaphysician would hardly contend that an unexceptionable system of metaphysics is a necessary of daily life ; and it is entirely with explana- tion and prediction regarded from an everyday point of view that we are here concerned. Having satisfied more immediate needs, readers can proceed for themselves afterwards to the more remote. The attempt to begin with Metaphysics, however natural it may be, is rather too much like attempting to write a flowing hand while we ought to be practising pothooks. It is a fair descrip- tion of the ' practical ' spirit in Logic, to say that it consists chiefly in the intentional neglect of these deepest difficulties. We start at any rate with all assumptions on which the meaning and use of language depends; and with those which are necessar}^ in order that explanation and prediction (for practical purposes) should be possible. We assume, for instance, that the distinction between the subjective and objective Universe has a real value ; and also that the whole Universe may be usefully parcelled off" into definite 'nameable things,' — objects qualities, events, and classes of these, — which, for all l-t FALLACIES. [Introd. practical purposes, may be viewed as consistently break- ing its continuity. As corollaries to the second of these assumptions, or as an amplification of it, we may accept the formulae known as the 'Axioms of Con- sistency,'* — the Laws of Identity, Contradiction, and Excluded Middle. Secondly, as regards the Metaphysics of Causation, we avoid the ultimate difficulties simply by stopping short before they are reached, and by con- fining our attention to what may be called a lower point of view. "We assume the existence of uniformities in Nature, — natural laws ; the narrowing down of these into exactitude being the endless problem of discovery, and the completest knowledge of them already attained at any period being, for that period, the basis of all explanation, prediction, and proof. The difficulty of keeping the discussion of Fallacy clear of psychological questions will be obvious to all readers of Mr. Sully's recent work on Illusions ; but the •scientific treatment there given, a treatment of the subject directly from the psychological point of view, helps to absolve us here from attempting to deal with its difficulties. Logic is always in some danger of en- tanglement with Psychology, but by keeping the practical purpose prominently in view, we probably avoid, better than in any other way, confusion between the two distinct sets of questions. It is only with the regulative laws of thought that Logic has any direct concern. What- ■ever psychological doctrines may be here occasionally * More properly ' Postulates.' Also called ' Maxims : ' cf. infra, p. 105. IsTROD.] THE PRACTICAL SIDE OF LOGIC. 15 appealed to, must accordingly be considered as of quite secondary importance. Aofainst confusion with Rhetoric we shall find it more difficult to guard. The connexion between Practical Logic and Rhetoric is extremely close, and for those whose interest lies in accurately mapping out the boundaries of either science, must no doubt be very puzzling. Rhetoric is commonly considered as the science of Persuasion (and possibly also of Pleasing) by means of language, — persuasion whether to true or to false conclusions; and since Persuasion partly depends on showing the person to be persuaded an appearance, whether real or counterfeit, of truth — of absence of fallacy, — the importance to it of a thorough familiarity with Logic is obvious. Rhetoric can hardly exist, in its most powerful shape at least, without a considerable knowledge of the difference between sound and unsound reasoning. It may, in fact, on its argumentative side, be viewed as an embodiment of Practical Logic, used by one person upon another or others, and applied in- differently either in aid of the purposes for which Logic properly exists, or in antagonism to them. But though Rhetoric cannot exist without Logic, the latter science can, it seems to me, exist apart from the former. As Mill expressed it, if there were but one rational being in the universe, that being might be a perfect logician ; Logic, in this sense, is in fact simpler than Rhetoric, and preliminary to it. The connexion between Logic and Grammar is per- 16 FALLACIES. [Ixtkod. haps not quite so confusing, though still not altogether easy to avoid. Both Logic and Grammar sit in judgment on the 'meaning of assertions made. Both are con- cerned with the use of language, and both lay down rules for its correct employment. In one sense, there- fore. Logic may be regarded as only a wider Grammar ; not indeed as presuming to dictate the absolute meaning of any given set of words, but as legislating unmistakably in certain cases on the combined meaning of any two or more separable assertions Avhen their separate meaning- is already agreed upon or declared. AVhile Grammar, for instance, tells us that two negatives make an affirma- tive. Logic takes a Avider view and says in effect " Use whatever words and phrases you please (however ungram- matical) so long only as their meaning is clearly 'agreed upon ; but having agreed on the meaning of your terms and your propositions, two contradictories fill a Universe, and to deny the one is to assert the other." The main difference, perhaps, is that while Grammar is solely con- cerned with enforcing the prevailing /as/r/o7i in language, and thus with preventing solecism. Logic cares not at all what the fashion may be, insisting solely that meaning shall be in the first place agreed uj^on, and then con- sistently preserved. In Logic, a largeness of interpre- tation is needed, which is quite unknown to Grammar ; for its sole concern is, through preventing inconsistency, to strike at the root of Fallacy. At the same time it is not always quite easy in practice to keep the two purposes wholly distinct, since Logic finds gTeat con- Intkod.] the PKACTICAL SIDE OF LOGIC. 17 venience and great economy of time, in making some use of accepted Grammar. A certain amount of Grammar, as also a certain amount of Psychology, is one of the necessary foundations for any effective study of Logic. Accordingly, while we shall have occasion sometimes to neglect side-questions interesting in themselves, but whose interest is of grammatical rather than logical importance, yet from our point of view language is a necessary instrument, and the accepted rules of its em- ployment are of high convenience ; and hence it may no doubt be found sometimes a little difficult to separate the two interests of Logic and Grammar. In short, so far as any question, whether commonly treated as a logical one or not, has a direct and obvious bearing on the methods of combating Fallacy, to that extent it will deserve our consideration: so far as its bearing on our main purpose either cannot be traced, or is too remote and lengthy for satisfactory treatment, to that extent we shall simplify our work by avoiding it. The practical purpose of Logic being, then, the guidance of our reasoning as safely as possible through the dangers to which it is exposed, it remains to explain and to limit this purpose more particularly. ' Guidance ' is slightly ambiguous, since a set of hints and rules aimed purely at increasing our powers of discovery, might fairly be held by some to come under this designation. But it is entirely with proof that we shall be concerned : with the reflection on our inferences, not with inference or discovery itself directly. Indirectly, of course, the c 18 FALLACIES. [Ixtrod. methods of proof are auxiliary to discovery, but it is of great importance to keep the two purposes distinct. For proof there must always be in the first place a proposition to be proved, or thesis; while, in inference, this is the final goal of which we are in search, and which is then rightly called the conclusion. Roughly speaking, every thesis is of course itself an inference, but an inference (or conclusion) does not becomes a thesis for proof until we reflect upon our reasoning, and desire to examine the strength of our grounds for the belief. Guidance, there- fore, must here be taken to mean not the first vague hints that may set us on the track of a fruitful inference, but the methods for conducting an impartial trial upon conclusions ah'eady somehow reached. The methods of Logic cannot be employed for the direct purpose of enabling us to reason, but only for that of enabling us to know whether in a given case we have reasoned correctly, or at least to discern where the weak point in our certainty must lie. 'Reasoning' too demands explanation. By some {e.g. Whately and Hamilton) an attempt has been made to restrict the name to the process of unfolding our conceptions, syllogising, or concluding from generals to particulars ; errors in reasoning being taken to mean simply failures in consistency. In this sense of the term, a child who had once been scalded through putting his hand into a basin of hot water, might be said to reason correctly in dreading a basin of cold water on the next occasion ; but he would then " reason correctly " IxTKOD.] THE PKACTICAL SIDE OF LOGIC. 19 by means of a premiss materially false, — that premiss being of course some such universal as 'All water in a, basin will scald,' or some such application as ' This is hot water.' In another of its senses, to reason is, as Mill puts it, simply to infer (whether provisionally or reflectively) any assertion from assertions already admitted. And since Mill's definition is perhaps most in accordance with ordinary usage, and further since it enables us to bring under consideration the dangers in Inductive or Empirical Proof, it is in this sense that we shall here understand the term, adding however that it is against errors in reflective reasoning only that Logic can at all undertake to guard, Methods of guidance might be discussed either from the positive side or the negative, — as supplying marks by which to recognise either valid evidence or invalid. The latter plan, as the name chosen for the book will have already shown, is adopted here. Not only is Fallacy in many ways more interesting than correct reasoning, but this view of the subject seems to me to keep before us, more distinctly than could otherwise be done, the negative character of practical Logic. The application of Logic is on the whole rather restrictive than forward-moving. As already said, it does not discover, but it proves, or tests, discoveries which claim to be already made. Moreover, in proportion as this negative or questioning spirit becomes habitual, our chance grows stronger of avoiding the character of an advocate, and attaining the judicial frame of mind. The 20 FALLACIES. [Inteod. first condition of all for avoiding fallacy, must surel}' be, as Mr. Spencer expresses it, " the calmness that is ready to recognise or to infer one truth as readily as another." But besides this possible disciplinary ad- vantage, and on the whole more important than it, the fact should be remembered that it is as the enemy of Fallacy that Logic must always find its application to real life : Fallacy occupies much the same position in regard to the science of Proof that disease occupies in reofard to the science of Medicine. In speaking of the negative character of Logic as a practical science, we must not however imagine that its action on belief is purely repressive. Rather, by repressing the natural tendency to undue belief, we earn the right to be doubly secure in those beliefs that stand the trial well. Of all unpractical habits of mind, the purely sceptical habit, so far as it can exist, is perhaps the least satisfactory ; and if Logic really led no further than this, there would be strong practical reasons for determining to blind ourselves to its truths. But perhaps it may be found possible to keep the dangers of Proof in view, while still remembering the central purpose for which this is done ; namely, not in order to discard as much pretended evidence as possible, but to win security in our beliefs, through taking care. IIL Outline of the Work.> The war against Fallacy is, I am afraid, far too large an enterprise to be undertaken by any one book. INTROD.] OUTLIXE OF THE WORK. 21 or indeed by any one author. Whether or no it was possible long ago, to survey the whole field of knowledge, both in general and in detail, laying down the law for all men, and marking out the line between truth and falsehood in all departments, nothing of the kind is possible now : no one at the present time, — unless abso- lutely unaware of the modern developments of Science, and its innumerable fields of special research, — will presume to ofier to his readers, a set of infallible methods for keeping free from error. There would be great danger, it is felt, of providing something not much more practical than Dr. Watts' rules 'for the right use of Reason.' But there are certain broad laws (which may with sufficient accuracy -be called Laws of Evidence in general) Avhich are perfectly universal in their stringency, and which it concerns every one to have at his fingers' ends. Properly speaking these are laws, not of evidence itself, but preliminary to the operation to which the name 'judgment of evidence ' is most commonly applied, — laws of interpretation (in a wide sense of that term), or, more exactly, laws of the implication of one assertion by another or others, whether the process of the given material inference be from the general to the particular, or vice versa. The law here called that of 'Counter- indication ' * may be mentioned as a typical example of what is meant; or the Maxims of Consistency, above referred to ; or again, the law that all Proof, to be really * Cf. infra, p. 84. 22 FALLACIES. [Lvteod. Proof, requires a reference to some wider generality* than the thesis. The knowledge of such laws is not by itself a sufficient safeguard against all possibility of error, but only a prior condition of attaining any safety in judging, even with the best possible special knowledge, or after the longest ' experience.' Such laws, though in reality extremely few and simple, — some even almost ludicrously self-evident, — present sufficient difficulties, in their application, to render the study of them, in regard to such application, a subject well worth careful attention : and a part of this task is what lies before us here. It is evident that several different purposes in study- ing Fallacies may be distinguished. There is, for instance, the purely scientific or theoretical interest,, whether as regards the Psychology of error, or merely with the view of obtaining an exhaustive list, and a clear tabular arrangement, of its varieties. Or on the other hand there is the practical interest (wliich may of course also be in the best sense scientific), leading to a survey of the methods of combating Fallacy in the shapes in which it actually occurs. And under this second head certain quite distinct purposes must further be noticed as possible. The methods of combating Fal- lacy admit broadly of three quite separable developments : there may be methods for (1) simply detecting fallacies already committed by ourselves or others ; or (2) for con- victing others of such errors when found ; or (3) methods aiming at the attainment of the completest infallibility * Cf. infra, pp. 112, 213, 320. Introd.] OUTLIXE of THE WOEK. 23 possible. Or, as we might more briefly express the same division, methods of diagnosis, cure and prevention. Of these various subjects, our purpose here will be to neglect (as said above) the Psychology of error, and to aim at obtaining only such classification of the various possible forms of Fallacy as shall be of use for one or more of the three practical purposes above mentioned. Next it may be remarked that, of these three, the last would be a truly desirable accomplishment, but that the total avoidance of Fallacy being a comprehensive subject, it seems better to attack it piecemeal, and by degrees. The second demands a combination of logical and rhetorical considerations for which neither Logic nor Rhetoric can be said to be as yet at all prepared : this subject, if less comprehensive than the last, presents at any rate a dangerously complex problem. Even the first question (the detection of Fallacy), if it is to be treated in any thorough manner, ofiers practical difficulties which might well render us content with a less ambitious aim : but since this first question is really preliminary either to success in controversy, or to the avoiding of Fallacy, the most efiectual course appears to be to inquire in the first instance what can be done towards the accomplish- ment of this simpler purpose. The power of detection is in fact the first stage towards avoidance ; which follows gradually, as detection becomes habitual. We shall find, however, that this purpose itself admits of being divided further. Some only of its elements, as preliminary to the whole problem of the detection of 24 FALLACIES. [Inteod. Fallacy, will constitute the matters for our consideration. As already said, we shall be concerned mainly with the methods of Proof and Disproof, and with the points at which any case of attempted Proof or Disproof is liable to break down. In this way, at least, a rough ground- work will be laid, from which any of the practical questions may afterwards be approached. The mere laying of such foundations should of itself help materially in the detection and avoidance of Fallacy, — though it can of course contribute nothing to their exposure so far as this lies beyond and outside detection. Shortly, then, the work before us is to survey, classify, explain, and illustrate the possible objections which can be brought against any belief, so soon as it is definite enough to take shape in language, and thereby to become a thesis for proof An exhaustive review of possible objections once taken, the formation of methods for detecting and avoiding Fallacies becomes less difficult ; and, accordingly, some suggestions are incidentally made for carrying on the work towards this goal. Since any pretended assertion may be : — 1. Meaningless : 2. Mere unsupported assertion : 3. Insecurely supported : this will constitute our main primary division. In the first case, of course, cadit qiicestio as to the truth of the assertion. In the second case we have to reckon with the Burden of Proof And finally, if a reason be given for belief, our judgment of its force must depend pri- INTROD.] OUTLINE OF THE WORK. 25 marily on the extent and soundness of our knowledge of the methods of proof; afterwards, on our knowledge of the special subject in question. " People talk about evidence," it has been said, " as if it could really be weighed in scales by a blind justice. No man can judge what is good evidence on any par- ticular subject, unless he knows that subject well." This is perfectly true : knowledge of the special subject is required before we can judge of the material truth of all that our reasons formally imply. But so long as igno- rance of these formal implications themselves exists, the methods of Logic have useful work to do. It is just in making clear what these formal implications are, — in making us aware of the full extent of our assertion when we bring forward any reason in support of any thesis, — that the central practical interest of Logic consists. Beyond this, in fact, it cannot go : in Logic as in Law Ignorantia facti excusat, ignormitia juris non excusat. It may be added, however, that there is no immediate danger of Logic's occupation coming to an end. People still commit purely logical blunders, quite apart from any ignorance of the special subject. Next, whatever reason is given in support of an assertion made may fail to prove it in either of two ways. It may be : — (1) Materially false, even if sufficient : (2) Formally insufficient, even if true : With the truth of the Reason given we have nothing to do in Logic. That is to say, we can only call for its 26 FALLACIES. [Introp. supports, for the supports of these again, and so on until we reach some ground sufficiently firm. Accordingly, a knowledge of the requirements of formal adequacy (apart from the question of material truth) is not only all that any science of Reasoning can pro^dde, but so far as complete, would be a safeguard against all discoverable error. The point at which logical doctrine ])ev se falls short of this complete success, has been above vaguely in- dicated. Later we shall be in a better position for seeing more definitely how far the help of Logic alone can carry us. Finally, the reason or reasons given in support of an assertion either include in themselves the oneaning of that assertion or do not. In the former case the question as to their material truth becomes at once all-important ; in the latter case the central operation of Logic begins. For if the Reason given does not already include the Thesis in its meaning, some other assertion is required to complete its binding force : and it is in the adding of this further assertion that all the danger lurks. The theory of Proof in general will guarantee our supplying the further assertion correctly ; while it is the question of the material truth of such further assertion that often depends in great measure on our knowledge of the special subject. Our work, therefore, will consist first of all in a pre- liminary survey of the nature of Proof in general, iti^ subject-matter and its process. Having cleared tlie ground in this manner, we shall proceed to take in detail the objections which can possibly be brought against INTROD,] OUTLINE OF THE WORK. 27 any assertion, dealing first with those objections which arise before Proof begins, and afterwards with the various points at which any case of attempted Proof is liable to frustration. Under this last head will be found, in one sense, the main difficulty; since here we shall have to consider to some extent the different dangers introduced by the different varieties of Proof It is hoped, however, that these minor distinctions will not unduly obscure our more general view. In cdl cases where real (as op- posed to verbal — Cf. p. 204) reasons are brought forward in support of an assertion, the operation of Logic consists in forcing into explicitness whatever is imphed beyond that which directly appears. The central point of in- terest throughout is the accurate determination of the further assertion implied in giving any Reason in support of any Thesis. PART I. PROOF IN GENEBAL. CHAPTER I. THE MEANIXa AND AIMS OF PEOOF. I. Proof axd Ixferexce. One of the distinctions which it is most difficult, and at the same time most important, to keep in view, is that between Proof and Inference. In any treatment of Logic, confusion of these two separate processes is likely to lead to much obscurity; and for us such confusion would be certainly fatal, since our main object is to sim- plify as far as possible the highly complex problem which the avoidance of Fallacy presents, attacking in the first place the most preliminary difficulties : and, as wiU pre- sently become evident, the detection of Fallacy is closely bound up with the whole question of the needs and danofers of Proof, while the attainment of methods for rendering our inferences secure corresponds more nearly to the wider and deeper problem of avoiding Fallacy altogether. Nor will it be sufficient for us to rest content with the brief and easy-going dismissal of the difficulty which is sometimes accepted. It may be perfectly true, as S2 FALLACIES. [Part I. Whately (e.g.) says, that ''Reasoning comprehends I'ii- ferring and Proving, which are not two different things^ but the same thing regarded in two difterent points of view : like the road from London to York, and the road from York to London ;" but if London happens to be the place we want to reach, it becomes a matter of some im- portance to distinguish carefully between the two dif- ferent directions. It will not suit us to find ourselves eventually either in York, or wandering for ever between Grantham and Peterborough. For neither of these results shall we derive much consolation from reflecting that it is " the same road, only regarded from two difierent points of view." 'Inference' is, in fact, a highly ambiguous word, capable of being applied to Proof as well as to Discovery ; and all round the question lie a number of further verbal ambiguities. When we infer one fact from another or others, we believe that fact ' by reason of ' our belief in those others ; and when we prove one fact by means of another, exactly the same expression is commonly used. In both cases there is ' reasoning,' and accordingly both that from which the inference is drawn and that on which the proof is based are indiscriminately called, in popular language, the ' reason.' We reason when we proceed from premisses to conclusion, arriving at new truths by means of old ones ; and we reason when, having already a thesis (an assertion) before us, we produce arguments to support it, even if such arguments be then for the first time thought of Again, ' premisses ' is some- Chap. I.] THE MEANING AND AIMS OF PROOF. 33 times used for the grounds of Proof, and sometimes for the data of Inference : ' conclusion ' sometimes means that which is discovered; and sometimes that which is proved. These ambiguities are probably one great source of confusion in the matter ; but besides the merely verbal connexion between Proof and Inference, and per- haps in fact a cause of it, there is also a deeper and real connexion to which still more of the difficulty may be traced. Before we can infer safely, we must prove ; but before we can prove, there must be some belief set up for proof, and belief (at least in its more definite forms) always draws a large part of its life from prior beliefs, and is therefore already an inference. There are, in fact, ' inferences ' and ' inferences,' — our first vague guesses, and the last assured results of careful inquiry and copious hostile criticism. Again, in some cases and to some extent, the reasons to which we appeal as proof of a given belief are exactly those which in fact led us to the belief in question. This is indeed far. from being always the case, since in very many instances the causes of a belief are too numerous or too shadowy to be remem- bered in detail, or even to be summed up in any concise expression. We need not base this assertion on any reference to the more physiological causes of belief : quite apart from the uncertainty of these, and even assuming the causes of belief to be purely intellectual, who can tell exactly why he believes his neighbour worthy or unworthy of confidence ? Or who can sum up satisfac- torily the multitude of indefinite observations that go to D 34 FALLACIES. [Part I. support the judgment, ' That is a well-dressed woman/ or ' This is a windy sky : ' what are the signs, exactly, by which we recognise a friend's step, or feel the pulse of an audience, or judge some work of art ? In these and many other cases only a small part of the real cause can ever be given as a reason. Nevertheless, the causes of our belief may often be appealed to, if we can remember them, as a reason for believing : the same facts may be grounds of Inference and of Proof As a preliminary step, then, we may find some advan- tage in correcting these ambiguities by the employment of two different names. Althouo-h 'Inference' might no doubt fairly be taken as having both a forward and a backward reference, thus covering both fields — Discovery and Proof, — there will be great convenience in restricting it as far as possible to the former of these two meanings ; * and also in keeping the expres- sions ' a conclusion ' ' drawn from ' (or 'following from') its 'premisses' (or 'data') for the case of Inference, and using for the case of Proof the expressions ' a thesis ' ' guaranteed by' its 'reasons' (or ' resting upon ' its 'grounds'). By the name Inference we denote the process of reaching a belief: by Proof we mean the process of establishing it on a firm foundation after it is already somehow reached. The inferred belief, before reflection on its validity begins, is not yet a thesis with reasons given : * Chiefly because 'Discovery' — the only other name which seems at all applicable —is apt to fix attention rather on the result than oh the process. €hap. I.] THE MEANING AND AIMS OF PROOF. 35 these only come into existence when we begin to test the foundations of a belief put forward as secure. The problem of Proof is thus always narrower and more definite than that of Inference. Instead of asking ^t large ' What conclusion may be drawn ? ' Proof asks ' Is such and such a given conclusion warranted ? ' In- stead of ' What is the cause, or efiect, or nature, of A ? ' or ' What is the law involved ? ' Proof asks ' Does X stand to A in this relation ? ' 'Is such and such a law the true one ? ' Instead of having, for answer, to choose amongst all the letters of an indefinitely long alphabet, Proof has only to decide between the two alternatives,— Yes, or No. II. Proving and Testing. It must not, however, be supposed that by thus con- trasting Proof with Inference all has been done that is necessary to bring out its full meaning and to avoid all ambiguity. Is Proof the finding of guarantees, or their examination when already found? Is it the attempt to establish a given belief, or the attempt to break it down, or neither of these exactly ? In this matter also popular usage is not consistent, though on the whole it leans rather to the meaning that makes Proof consist in the finding of guarantees. If the view here taken be correct, there is a possible reconcilia- tion between these apparently opposite meanings, and ^either by itself is merely incomplete. For some purposes, no doubt, it may be sufficient to say that proving a belief 3G FALLACIES. [Part I. consists in establishing its truth, but this definition after all carries us only a very short way. Nor will it suffice, when asked further how a truth is to be established, to- answer that the process consists in 'stating a valid reason' for the belief in question. This, too, is true as far as it goes : to prove an alibi, for instance, or to prove the defendant's guilt, means to establish the truth of the assertion that the defendant was elsewhere, or is guilty : and no doubt the process always consists in showing a valid reason why the assertion should deserve belief So- again, to prove that the angles at the base of an isosceles triangle are equal to one another, means to establish the truth of that proposition ; and the manner of performing the process certainly is by showing a valid reason, or a set of valid reasons, why we should believe it to be true. But there is an important fact about the meaning of Proof which this explanation tends to make us overlook. The word Proof, like so many other words, has under- gone a change of meaning in the course of its history. In old times, to prove anything meant simply to test it, to see what strain it would bear or what fault could be found with it. ISTothing was implied, one way or the other, as to the result of the inquiry : the thing to be proved might pass the examination with honours, or might fail ignominiously, but in either case the proof took place. Thus, " the exception proves the rule " meant simply that the exception tries, or strains, the riile : " I have bought five yoke of oxen and must needs go and prove them " referred merely to the need of frying the €hap. I.] THE MEANING AND AIMS OF PROOF. 37 oxen, or testing their working power. And to some -extent this old meaning may, perhaps, be said still to remain in use; to take a thing 'on probation' still allows us to contemplate the possibility of discarding it later as useless, to 'probe' is a confessedly tentative pursuit, and a lover may ' prove untrue.' It is, of course, often misleading to attempt to find the modern meaning of a word by tracing its history. In very many cases any attempt to bind words down to their ancient meaning would lead to serious error. And yet if the historical inquiry be properly guarded, it may >sometimes serve to throw a light on the modern meaning which would otherwise be lost or overlooked. We must certainly avoid supposing that to prove an assertion means nowadays simply to subject it to tests, but at the same time by remembering this ancient sense we learn some facts about the meaning and aims of Proof which are really inseparable from it, and which the modern employment of the word rather too much tends to hide. Be this, however, as it may, for our purposes at any rate it is in attack rather than in establishment that the interest lies ; or at least only in such establishment as may be won in open battle. Our concern with Proof differs from that of the advocate in that we are not interested in the finding of evidence to support a thesis, but only with the judging of evidence already put forward; or, on the other hand, dismissal of the case when all evidence is wanting or when no definite issue can be joined. Viewing Proof as essentially consisting in successful 38 FALLACIES. [Part I, resistance to attack, we in the first place keep before our minds the limit of dogmatism be^'ond which no real proof can carry us. It is true that assertions which have been tested so far as our tests can go, stand in a better position as regards trustworthiness than assertions which have not been tested ; and since in multitudes of cases the tests applied are amply sufficient for all practical purposes, Proof has come in course of time to mean chiefly establishment on a sound basis. Even the com- pletest establishment of a truth is, no doubt, limited by our very finite power of applying tests to it ; but this we easily, and for the most part wisely, forget in the pre- sence of the plain and fruitful fact that our power of testing belief is in so many cases practically sufficient. It would be pedantic and absurd to be always re- membering that our tests may after all be incomplete. When we, or those whom we accept as sufficient authority, have tested the assertion that the earth is round, or that matter gravitates, it will be found on the whole more useful to act on all occasions precisely as if those assertions were absolutel}^ true. Having arrived at Melbourne by way of Suez, we should hardly, through modesty as to the limits of human knowledge, hesitate to sail for Europe again in an easterly" direction. The belief that the earth is round is certainly only proved — only tested and not yet found Avanting, — but we get from our tests, in that case and in many others, a kind of certainty which on the whole it is wiser not to doubt. Fallible though we are, and incomplete though CiiAP. I.] THE MEAXING AND AIMS OF PROOF. 39 our methods of proof or testing may be, yet there are strong practical reasons for considering our knowled^-e in some cases perfectly secure, certain kinds of proof sufficiently complete. Although, then, simply testing is in this way the root-idea, or original intention, of the word Proof, the full meaning we shall understand by it is establishment by means of tests ; or, more fully, establishment in the face of hostile criticism. Not until both sides of a case are heard can the verdict claim to be of real value; and if we accept a conclusion without considering how far the facts will support an opposite one, we do so at our peril. Thus, in fixing the meaning* of a name, the point of practical importance is where to draw the line, or how to distinguish the thing in question from other things ; in establishing an explanation, a law of nature, or a pre- diction not yet verifiable by the event, the important point is to exclude all alternative theories. We know, for instance, what ' work ' is, roughly, and we use words like ' civilisation ' or ' honourable ' — and even terms aiming at greater definiteness, as ' animal,' ' vegetable/ 'man,' and 'beast' — with the utmost glibness, and with a fair amount of sense : but the whole difficulty of fixing their definitions, or settling their exact meaning, begins when we attempt to draw the line dividing them from their opposites ; when, in fact, we try to justify our exclusion of certain candidates for the title. We must know clearly what is not work, if we are to find the * See also pp. 93, 106, 133, inf. ■ 40 FALLACIES. [Part L stricter applications of the word ; we must determine (if possible) where civilisation ends and its opposite begins, or what are the exact points of difference which separate animal from vegetable, man from beast. Again, before we can consider any theory proved, whether such theory be a sweeping law, like that of gravitation, or an explanation or prediction of some one actual event, we must have sound reasons for excluding every possible rival theory. This, at least, would constitute complete Proof, if such could ever be attained : so far as it falls short of this, our proof is weak. The exhaustive examination of alterna- tive theories is of course an ideal which we cannot com- pletely reach; but the nearer we approach to it, the more thorough is our proof, the less assailable our cer- tainty. Thus assertions stand on a varying scale of credibility: which is only another way of saying that evidence varies in strength. In proportion as the attacks resisted represent all possible attacks, Proof is complete. Hence the importance of our central question, — On what grounds can any asser- tion be attacked ? And first we need a general view of the nature and varieties of assertion ; a classification of the questions that may arise for Proof CHAPTER II. THE SUBJECT-MATTER OF PROOF: IN GENERAL. I. Real and Unreal Propositions. Having sketched tlius in outline tlie distinction between Proof and Inference (the only other process with which Proof is liable to be confounded), the next point of preliminary interest appears to be the subject-matter on which Proof is employed. I say of preliminary interest, because on the plan to be here adopted, we need in this place attempt to treat only a very smaU group selected out of all the complicated questions, so important and so fundamental in the higher study of Logic, centering in the doctrine of Proposition, or Assertion, or Judg- ment. For we are not concerned in any direct way with the Psychology of either Perception, Thought, Judgment, or Inference : Proof is concerned with ready-made Asser- tion only. At present we have only to notice certain broad distinctions in kinds of Assertion, with especial reference to the bearing of these distinctions on the question of Proof A judgment is a Thesis only when 42 FALLACIES. [Paut L capable of expression in intelligible language, and whiU- the need for Proof is felt. First in importance for us is tlie distinction between Beal and what may be called Unreal propositions. The latter of these are insusceptible of Proof : the former are its subject-matter. The name 'Unreal' as here applied to proj)Ositions^ is somewhat mder than what is usually meant b}' 'verbal.' Usually the distinction between real and verbal is taken to correspond precisely to that between ' accidental ' * and ' essential ' propositions ; verbal pro- positions being restricted to mean such only as are tautologous or identical, — those in which the Subject f already contains, as a part, at least, of its meaning, that which is asserted of it in the remainder of the proposi- tion. Thus, ' A triangle is a three-sided figure ' is com- monly given as a typical example of the verbal proposition. But for our purposes we need some name to express indis- criminately all kinds of assertion which are insusceptible of Proof ; and in order to avoid ambiguities I propose to call these ' unreal,' rather than verbal. In itself the name ' verbal ' might certainly be held to designate very appro- priately every proposition which is merely a string of words, fulfilling, it may be, all grammatical requirements, but without conveying sense, — mere empty sound so far * Or, as the corresponding ' Judgments ' are termed (by Hamilton and others), ' Ampliative ' and ' Explicative,' or (by Kant) ' Synthetical' and ' Analytical.' t ' Subject' we may define provisionally as ' that which is primarily spoken of.' There "will be more to say about it presently. CilAP. II.] SUBJECT-MATTER OF PROOF : IX GENERAL. 43 as possibility of interpretation is concerned ; but ' verbal ' is a name already in use for a more restricted purpose. At this stage it is not necessary to face the question as to the means of distinguishing in practice unreal pro- positions from real. Such inquiry belongs to a later place in our scheme, and will there be to some extent discussed.* At present, we have only to register the fact that unreal propositions are to be met with, — empty shells of assertion without a kernel, — and to set out the heads under which these may be conveniently divided. In the first place, then, comes the case, already spoken of, where the assertion is already made as soon as the meaning of the 'Subject' is understood, — tautologous, or essential, or identical propositions. It is easy to see that where that which is said of a thing is that which is known already, or rather that which is already told as soon as the Subject is enunciated, the proposition (for in form it may still of course be a proposition, containing nominative case and verb) lacks, if not raison cVetre, at least capacity for proof. The mere attempt to prove any such proposition involves a vicious circle in our thoughts. We have prejudged alread}^, by hypothesis, the question of its truth, and inquiry can lead but to one result — a result which might have been reached without the labour. If, for example, a coroner s jury were to give it as their solemn opinion, that 'deceased came to his death by extinction of the vital forces,' it would require no gTeat efibrt to see that this supposed piece of inform a- * See pp. 120-147. 44 FALLACIES. [Part L tion leaves us exactly where we w^ere before. This, however, is rather an extreme instance. Perhaps the commonest case of all is where, in some shape or other, a proposition laboriously informs us that excess is not advisable, — as (in a discussion on local legislation in one of the Channel Islands, — I quote from a newspaper report) " The Bailiff said, it was essential that no measure should be unnecessarily adopted. On the other hand, everything necessary must be done." Or again, " I should not advise too great hurry," or ''Growing lads and women should not attempt too much at a time." If ' too much ' means anything at all, it means that on the whole the amount spoken of is not advisable, and in all such cases no real information is given until the speaker pro- ceeds to say Jioiu much is considered by him excessive.* These instances are purposely chosen as being almost self-evident and indisputable. Later on,t we shall have occasion to notice some of the real difficulties in the matter. In the second place come the cases where the asser- tion made is already denied in the meaning of the Subject — self-contradictory, or suicidal propositions. These, of * It must bo here remarked, however, that in many cases such asser- tions are merely blundering expressions, or grammatical solecisms, rather than absolutely without a meaning, — the speaker and his audience both having some actual amount dimly in view. There are also, no doubt, a few cases where ' too much ' does not really intend to sum up the total question of advisability, but refers to some other standard, as in the sentence, ' It is better to have too much luggage on a journey, than too little.' t See p. 124, inf. Chap. II.] SUBJECT-MATTER OF PROOF : IX GENERAL. 45 course, stand essentially on the same footing as the class just mentioned. The question of their truth is prejudged already, only the reverse way. Perspicuous examples which are really faulty are less common here however, since the explanation of their actual employment is not so frequently as in the case of tautology a slipshod, do-nothing, easily satisfied habit of thought, but rather a youthful, reckless, revolutionary spirit, making use of poetical license in expression, or aiming at strong- rhetorical effect. There is usually more life in self- contradictory assertions than in platitude, even if it be life of a rather uncurbed nature, and often these are used to convey in a forcible, epigrammatic manner, real truths which may indeed be paradoxical (in the sense of being- contradictory to received opinion), but which are none the less worth knowing : still, as they stand, such propo- sitions take their place outside the realm of Proof, since in Logic we are necessarily limited by language, what- ever its faults may be. Luckily, however, an epigram / ^^^^-^^ c^-^^X-, that is worth anything may generally be translated into ^ .u..^^^ a real proposition if we can be content to sacrifice its '"'"^ ' merely artistic qualities ; and since the practical value of these can only be for stirring up our sluggish attention, when this object is once accomplished we may safely relapse into a cooler state of mind. Where harm is done by self-contradictory propositions is not so much in the field of positive assertion as in that of doubt ; where, for instance, doubts are nominally raised, by means of language, about something which language itself postu- 46 FALLACIES. [Pakt I. lates as a starting-point, — as {e.g.) " Can one individual be at the same time another individual ? " Or, '' By successive additions of nothing, can something be at last developed ? " Xo question here can exist for Proof, as we shall understand that term, since the answer is given abeady in the postulates of language (otherwise known as the ' Maxims of Consistency ' or the ' Laws of Thought'*), and language is needed in order to state the question. This remark leads us to the outskirts of a very thorn}^ subject, — namely the position of ' Ultimate beliefs ' in reo'ard to unreality. It may be said at once that they do not come within the subject-matter of Proof as here understood. Without attempting to determine, even approximately, the number or the nature of these ulti- mate beliefs, or to say anything further about them, it will suffice to acknowledge (if required to do so) that such there must be. Pushing back the examination of reasons for any belief we must of course either ultimately come to a basis of mere assumption, or go on questioning for ever. It seems best, therefore, at once to admit the existence of beliefs which may stand above, and not below, the possibilit}^ of 'Proof;' and then to relegate all discussion of such beliefs and their validity to those who feel desirous of examining them, and competent to undertake the inquiry. For us, in the mere capacity of logicians, and not metaphysicians, language limits thought ; and we therefore start at least with the Postu- * See also pp. 14, 105. Chap. II.] SUBJECT-MATTER OF PROOF : IX GENERAL. 47 lates on which the meaning of language depends, dispens- ing with all attempts to climb outside or above them. Only so far then as a real meaning can be found in the answer Yes or No to any question, — a meaning expressible in consistent language and translatable, if need be, into terms of practice, — will such question come within our subject-matter. Wherever to doubt any belief, — e.g. that 'whatever is, is;' or that 'it is impossible for the same thing at once to be and not to be ' — would nullify the postulated meaning of the language used, such belief (if it can be called a belief at all ; but this may be conceded for the sake of peace) we will consider to lie above the possibility of proof And wherever this does not appear to be the case then the grounds of the belief will be open to our examination, even if for the purpose of ,saving time or trouble it may be also open to us to dis- pense with such inquiry. The view appears a tenable one, and has been stated at some length by Mr. Spencer,* that certain supposed questions, commonly believed to be of metaphysical interest, cannot be strictly called ques- tions at all, in any fruitful sense of that term : but since controversy is not here an object, it seems simpler to say that we choose to limit our own inquiry as above. Thirdly comes the case where any term used in a proposition fails, whether through self-contradiction t or otherwise, to convey intelligible meaning. There is, so far as I am aware, no special name in use for this kind of * Principles of Psychology, pt. vii. ch. iii. t i.e. ivithin the term, not between the two terms. 48 FALLACIES. [Part I. unreal assertions as a class, although certain forms of them have (very properly) earned the name of mysteries. These too, from the nature of the case, may safely sing in presence of the robber Doubt. So far as they are consist- ently incomprehensible, so far the question of their truth or falsity can clearly not be raised, except in words. Their acceptance, indeed, as a formula, may show a willing and tractable spirit, and they may to that extent have a value : but such acceptance differs of course from belief in being admittedly a voluntary act, and not a mere im- meritorious and reluctant yielding to the brute weight of evidence. Here too it is somewhat difficult to find examples which shall be universally perspicuous, — unless we take such questions as were sometimes discussed by the Scholastics, — as whether two glorified bodies can occupy the same portion of space at once, or whether God knows more than He is conscious of: or the doctrines of the Cabbala, — that all souls pre-existed in Adam, that the human is united to the Divine mind as the radius of a circle to its centre, or that existence is infinitely distant from non-entity. Besides assertions which are thus completely insus- ceptible of Proof, there are also many cases where Proof may airpear to be inapplicable; which cases however must be carefully distinguished from unreal propositions. Such, for example, is the case where, though the belief i& real enough, and quite possibly sound, proof is unattain- able owing to the multitude or the intangible nature of the grounds of belief, or owing to the shortness of the Chap. II.] SUBJECT-MATTER OF PEOOF : IX GENERAL. 49 time available for their examination — as where we take a violent liking or dislike to a person at first sight, or have to decide in a hurry upon some complicated course of action. In such cases the incapacity for proof — if there be real incapacity — cannot be discovered by mere inspection of the thesis, but needs to be shown by ex- ternal evidence. And unless and until this is shown in the given case, we have clearly no reason to treat it differently from any other real assertion. Under the head of propositions insusceptible of exact proof it may be well also to notice that immense class of assertions, very commonly in use, whose essential nature is to be vao'ue. Such assertions as that on the whole the ordinary meaning of a word is so and so, or that there is a growing tendency among civilised people to do this or the other ; or, still more, the finer shades of suggestive, tentative assertion conveyed in poetry, jest, or innuendo : these afford, from the nature of the case, an insecure footing for the fruitful application of logical method. But these, too, stand on a very different level from unreal propositions, since the reduction of them to definiteness is not in any way precluded by their ow^n postulates, but only difficult perhaps, or at any rate inconvenient on some ground or other. When we meet with one of these assertions, two courses are open: either to treat it in a spirit of generosity or carelessness, accepting it as claiming only a lower degree of assertive force, and as fulfilling its own purpose if not exactly ours ; or else, if exactitude be for any reason really important, expending E 50 FALLACIES. [Pai:t L the trouble necessary to render it as far as possible definite. Until this is done there is of course room for misinterpretation, and therefore no security for strict sifting of the question raised. Lastly, it is obvious that many assertions which migJd be proved, do not in fact stand in need of it. There are a vast number of cases in which Proof is practically never demanded. That ' Socrates is mortal,' for example, or that 'Queen Anne is dead ;' that ' some coins are metallic,' or some logical examples rather absurd ; these are assertions which, for all practical purposes, may now be considered sufficiently safe against serious attack. Here, too, no general rule can be given for distinguishing propositions which have been sufficiently proved already from those which still stand in need of proof. This is one of the matters which fall quite outside the scope of Logic, and must always be decided between the assertor and his audience by special agreement. It is, in fact, merely pre- liminary to Logic, and in no way connected with the actual methods of Proof To claim for a proposition, the truth of which is still highly doubtful, the advantage which belongs to one that has successfully resisted all attacks, is no doubt a common enough rhetorical device. So, on the other hand, is the attempt to obstruct an argument by raising unnecessary difficulties. But Logic cannot undertake to judge of motives. Later on, in speaking of the Burden of Proof, we shall have occasion to notice this difficulty more fully.* At present it is * See pp. 151-167, inf., also pp. 128, 171. €iiAP. II.] SUBJECT-MATTER OF PROOF : IX GENERAL. 51 important to pass on to the discussion of Eeal Assertion, its nature in general; and to a broad classification of the kinds of Real Assertion that may be proposed for Proof. II. Subject and Predicate. It is on all hands admitted that every proposition, as soon as understood, may be divided into two parts — the subject, or name of the 'thing' primarily spoken of, and the remainder of the sentence, or the words expressing the whole assertion made about such Subject. If we de- note the Subject, as is usual for shortness, by the letter S, we may denote the remainder of the proposition by the letter J — the Judgment made about the S. In so general a science as Logic — or since the province of Logic is not yet clearly marked out, let us say in so general a science as that of Evidence, or Proof — we find , indeed, it is possible to avoid ambiguity, but since the symbol must have a name we camiot altogether escape the use of language, and can only strive while using it to avoid any misleading associations. For the purpose of dealing with the dangers of Proof, — including thereunder all dangers to which a thesis, or asserted judgment, is liable, — the most important fact about propositions seems to be the power which they give us (when their truth is believed) of passing from the known to the unknown. There are two distinct ways in which they may do this, one of which may be called ' implication,' * and the other ' material indica- tion;' the former being the case where by merely analysing the meaning of a name or proposition we either arrive at or guarantee certain of its less obvious consequences; while 'indication' (in general) includes this case and also the commoner one where we obtain the same power, not by mere analysis of the meaning, but by viewing one fact as material evidence for another, — evidence asserted as strong enough to stand against all hostile criticism. The proposition ' Man is fallible ' might be an instance of either of these modes of indica- * C/. Mr. H. MacColI, in J/uid, No. xyii. p. 45. The difference between Mr. Mac Coil's view and. mine appears to me far less important than the resemblance ; and I trace much of my own view (and especially the 'law of counter-indication') jointly to the article quoted, and to Wundt's recent work (Logik, vol. i. Erlcenntnisslehre). Chap. III.] MAIN KIXDS OF THESIS. Gl tion, according as the notion ' fallibility ' did or did not enter into the special meaning postulated for the name ' man.' If we pass to ' new knowledge ' * by analysing the old, we do not reach a new theory, but the applica- tion of an old one : while the attempt to prove by way of implication is, of course, either to argue in a circle or to appeal ad hominem. Material indication is the sole means of really passing from unknown to 'theorised,' or from theorised to known, — so far as knowledge is capable of being guaranteed. The chief difficulty about the name 'indication' consists in stretching it to cover the assertion of both Law and Fact; or, as such assertions will here be called. Abstract and Concrete propositions. It is easy enough to see how every Laiv asserted may be viewed as an indication, since the primary purpose of every law is, of course, to be in- terpreted, or applied : hence the S of every abstract pro- position is expressed either directly as a ' general name ' (simple or complex), or else, — and especially where such S is itself a proposition — is generalised by means of an ' if,' or ' where,' or ' when,' etc. But when we come to speak of concrete propositions, the word ' indicates ' draws us at once into clumsiness of expression. This case of * The question whether, by analysis merely, vre can " increase our knowledge " is as ambiguous as the question whether by digestion we can " increase " the food we swallow. We do not increase its sum, or weight : we do increase its utility. We get a new and firmer grasp of old material. Though we may, of course, add to our power of applying knowledge, by analysing accepted truths, this merely points to the thoughtlessness with which we habitually bolt our axioms whole. 62 FALLACIES. [Pakt I. death, no doubt, may indicate (or point to) poison, or my pulse at the present moment may indicate (or show) the absence of fever, or yesterday's panic in the city may indicate (or foreshadow) a future increase of bankruptcy ; but it is undoubtedly clumsy to say that Bavius ' indicates the qualities of ' a fool : we habitually condense those four words into the one word ' is.' Nevertheless, with this apology, I propose to use the name ' indicates ' in default of a better to fit all cases. Much of the difficulty may be removed by remembering that it is only in abstract propositions that S is really a sign, in the ordinary sense of the term : it is only there at least, that it is intended to be used as a sign, or mark, or label, bearing a recognised meaning. The essential characteristic of concrete propositions is that their S cannot be said, in general {i.e. universally) to indicate the ^, except by virtue of all the special circumstances bound up along with the thing most prominently denoted there as 'S.' It may, indeed, be on general grounds only that we believe this or that concrete proposition, — as, that ' the panic will increase the number of failures : ' but this does not appear in the statement. In the con- crete proposition we distinctly assert the possession of something over and above mere general grounds, namely a full review of all the special circumstances. In spite of any hidden facts, w^e assert our judgment as deserving of belief. The assertions which are thus to be included under the symbol — > (which may be read 'indicates') are €hap. III.] MAIX KIXDS OF THESIS. 63 accordingly those of Dependence * (whether causal or logical) and of Classification. By an assertion of causal dependence is meant an assertion that two ' things,' — usually events, but sometimes objects or qualities, — are causally connected so that one of them is to some extent an indication of the other, whether a sign in the strict sense, or merely a symptom. Some ' things ' in nature are found, or supposed, to be marks or signs of others, as a falling barometer indicates a coming storm, or as breathing indicates that life is not extinct, or as every existing human being indicates the prior existence of a pair of human parents. The statement of these indica- tions may accordingly be written: 'Falling barometer — > coming storm,' ' Breathing — > presence of life' and 'Human being — > prior human parents.' By an assertion of logical dependence is meant an asser- tion that the truth of one proposition ' follows from ' that of another, or that the meaning of one name is included in that of another. Most names and propositions are intended to bear a meaning, — that is, to mark or signify notions or facts, — and some propositions are intentionally put forward as guaranteeing the truth of others. Thus the name 'Intolerance' may be in- tended to include the notion ' active hostility ; ' or the assertion ' He is coming,' the fact ' He is not here ; ' or again, the assertion ' He is a man ' may be employed to guarantee the truth of the assertion ' He is fallible.' And these may respectively be written 'Intolerance — > * Cf. Wundt. Logik : Erl-enntnisslehrc, pp. 179-186, 277, 281, etc. 64 FALLACIES. [Part I. active hostilit}^' ' He is coming — > he is not here ' (but of this the usual grammatical form would be ' If. or since, he is coming he is not here/) and ' He is a man — > he is fallible' (or 'He is a man, and therefore he is fallible ; ' or ' He is fallible, for he is a man.') By an assertion of Classification is meant the extremely frequent cases where a ' thing ' is said to deserve a certain name, or to bear ' essential resemblance ' to another thing, or to belong to a certain class, or to possess a certain quality, or to have another thing ' coexisting ' with it ; as in *Gold is an elementary substance,' or 'belongs to the class elements,' or ' The State essentially resembles a family,' or ' Every rose has its thorn ' (or ' With every rose a thorn co-exists ') ; which may accordingly be written ' Gold — > Element,' ' State — > Family,* 'Eose — > Thorn.' II. Affirmation and Denial. Indication may be either affirmed or denied. Certain propositions, instead of committing the assertor to any definite statement of the relation between S and ^, are content to say merely that some definite assertion, taken as already made about them, is untrue. These will be called Denials : all others will be caUed positive Assertions, or ' Affirmations.' It is a matter of some difficulty to mention any special grammatical form as fairly representative of the denial, since even sentences containing the negative particle 'not,' in close connexion with the verb, or the Chap. III.] MAIN KINDS OF THESIS. 65 quantification ' no ' before a noun, or a ' negative name ' as P (or ^), are very frequently used to express a posi- tive assertion as here defined. Thus we may say, ' That is not bad,' or 'jSTo pen can attempt to describe the scene,' or ' He is unskilful, worthless, disagreeable, incom- petent, etc.,' without at all attempting to confine our- selves to bare denial of something either actually or only presumably said before. The grammatical form of the proposition, though often useful as a hint towards the meaning in this respect, is at best an uncertain guide ; nor can even the whole context be taken as in every case complete evidence of the real intention. The two distinct intentions do, however, exist, and are to some extent inferrible from the words employed. Where the intention is doubtful, there is nothing to fall back upon except an express declaration by the speaker as to the sense in which the proposition is put forward. At present, however, we are not concerned with the means of arriving at the intention, but only with classifying those distinguishable meanings which have importance for the doctrine of Proof Of these the most important is the distinction between positive assertion and bare denial. And having called attention to this fact, we may proceed at once to examine more in detail the manner in which this distinction runs across the others. CO FALLACIES. [Part I. III. Abstract and Coxcrete Propositions. Next in importance is the opposition between Law and Fact asserted; or, as it may be otherwise called, between Abstract and Concrete propositions.* The abstract proposition may be expressed indiffer- ently in any one of various grammatical forms, of which perhaps the commonest are those familiar types (denoted under the traditional scheme by the letters A and E) whose S is the name of the members of a class, ' All ' or ' None ' of whom ' are ' P. Thus, ' All men are fallible ' (A), or ' No men are secure against fallacy ' (E), are simple, straightforward examples of the asser- tive abstract proposition. In both cases the attribute ' humanity,' wherever found, is said to indicate the attribute ' liability to error.' Another common form which the abstract proposition takes, is where the S con- sists of what is sometimes loosely called an 'abstract name,' as ' honesty ' or ' theft.' Thus, we might assert that ' Honesty is the best policy,' or that ' Theft cannot prosper long ; ' meaning, in the two cases respectivel}^, something rather more clumsily expressible by ' Honest actions, in general, indicate success as likely to follow,' and ' Dishonest actions, in general, indicate that (in spite, it may be, of temporary success) ultimate failure is probable.' Of course, these and similar sentences may contain other meanings also — may even be used * Cf. also "■ noticral "' and " real " propositions in Newman's Grammar of Assent, p. 7- CuAP. III.] MAIX KINDS OF THESIS. 67 ironically, — but in so far as they are used to express the meaning explained, to that extent they are what we here call assertive (or affirmative) abstract proposi- tions. Again, the adverbs ' always ' and ' never ' are very largely used to express the copula of assertive abstract indication, as in 'Bread always falls upon the buttered side,' or ' A story never loses by re-telling.' And again, another still commoner grammatical form in use is the conditional or hypothetical sentence, beginning ■with ' if,' or ' when,' or ' where,' or ' while,' etc. ; as in ' If it rains in Ceylon, it pours,' or ' When poverty comes in at the door, love flies out of the window,' or ' Where there is smoke there is fire,' or ' While there is life, there is hope : ' in each of these cases the purpose of the proposition may be to assert of one 'thing' that it universally indicates another, whether in the past, present, or future, relatively to itself We need not at present follow these grammatical variations into further •detail : enough has been said to illustrate them in a rough preliminary manner. The concrete proposition, on the other hand, contents itself with a less (apparently) sweeping assertion. It says, not that S wherever found indicates ^, but that in this particular instance it does so. Looking at all the cir- , and for assertions of difference the symbol <^. As to exceptive denials, perhaps the most frequent grammatical form which these take is that known under the traditional arrangement as the ' particular ' * pro- * Cf. Symbolic Logic, chap. vii. p. 161. The particular proposition, as actually employed, no donbt serves several other purposes also, notably that of registering our first vague grounds of Inference, as contrasted with anything deserving the name of grounds of Proof. Finding two ' things ' frequently or even occasionally conjoined, we often begin to get upon the track of some law, and eventually we may rise thereby to Chap. III.] MAIX KINDS OF THESIS. 69 position (I or O) : e.g. ' Some negroes are fairly intelli- trent/ or ' Some Mexicans are not habitual liars.' Ao-ain, the adverbs ' sometimes ' or ' sometimes not ' are fre- quently used in exceptive denials ; and again the expres- sions * ^ is quite compatible with S/ or ' S is by no means necessarily ^ ; ' and again, the expression ' all . . . are not/ as in 'All that glitters is not gold/ and various other forms, such as, for example, 'There are lawyers and lawyers.' Here also no form of words is by itself perfectly unambiguous : we need something else to show whether the proposition is really intended as asser- tive or as a bare denial. But on the whole, and roughly, the particular proposition may be taken as most nearly typical of this class. No useful distribution of any proposition into its component parts, it must be remem- bered, can ever be made until the real intention of the speaker is clear. As to ' assertions of difference,' there is some difficulty, as the name chosen may help to show, in placing them quite clearly in the class of mere denials. The justification for doing so lies, however, in the fact that without some supposed belief that, for the purpose in hand, no difference exists {i.e. that S — > ^) the asser- tion of difference is too trivial to have any practical value, since points of difference may always be found between two things, however nearly alike. Hence the the power of making, and perhaps proving, some abstract assertion regarding them. But, regarded as positive assertion, this is too vague to be called a * thesis.' 70 FALLACIES. [Part I. essential purpose of these assertions is to contradict some- thing ah^eady supposed to be believed. The sole practical use of the assertion of difference is either to break down a supposed analogy or to deny the applicability of a name, i.e. the right of a ' thing ' to belong to a certain class ; and this whether the proposition be abstract or concrete. Thus we might say ' National Government is a different thing from family government' (abstract), or 'Whales are not fishes ' (abstract), or ' The Kilmainham arrange- ment was not a compact ' (concrete), or ' The case of ]\Ii\ A. is different from that of Mr. B.' (concrete). These propositions merely say that S differs from §. For further examples of this form of denial we may take such expressions as ' Seeing is a very different thing from believing,' or 'Liberty is one thing and License quite another,' or even perhaps ' Force is no remedy ' ; though this last phrase has no doubt been more often used to- express a vague law that ' Force — > probable continu- ance of the evil' than merely to deny an assertion to the contrary or to correct the use of a name. As this last example may serve to show, there is sometimes a difficulty in deciding whether a given sentence is really an asser- tion that S indicates the absence of something (as ice, for instance, indicates the absence of a certain degree of heat)^ or a mere assertion of difference between S and ^. But this is a difficulty which cannot be remedied by simply refusing to notice it. The possibility of misunderstand- ing the real intention of a given set of Avords, is one that can hardly too often be brought to mind. CuAP. III.] MAIN KINDS OF THESIS. 71 Corresponding to concrete assertions there are con- crete denials ; and of these again two kinds. We have ah'eady spoken, just above, of the concrete assertion of difference, and after what has been said of assertions of difference in general, the nature of the first kind of con- crete denial will be sufficiently clear. Nor is there much difficulty as to the other kind of concrete denial. It follows from the nature of concrete assertion that these cannot be at all described as ' exceptive/ since there is no law to which they directly take exception. Perhaps the best name for them is ' Simple denials.' These also are found in various gTammatical forms, but the commonest is, no doubt, where 'not' is added to the verb, as in ' This was not due to drink,' ' The crisis will not be fol- lowed by any important change,' ' It is not accompanied by much danger, after all,' etc. Also in this sense a nega- tive name as ^ may be sometimes used, though perhaps rarely. Thus in saying 'The door is unfastened,' we might conceivably intend merely to deny the opposite assertion, but more probably the intention would be to convey a positive assertion of our own. \Yhen once the distinction between concrete and abstract propositions is clearly kept in view it becomes sufficiently easy to recog- nize the simple concrete denial. The abstract proposition is, then, the assertion or denial of any general law in Nature, of however narrow sweep or insecure stability : the concrete proposition is the assertion or denial of a single fact. The con- crete proposition takes a concrete S, ' this man,' ' these 72 FALLACIES. [Part I. instances/ ' my lecture yesterday,' ' your hope of suc- cess ' and tells us what these ' indicate/ forwards in time, or backwards, or contemporaneously. And here must be noticed an objection which may possibly be raised at first sight to this use of the word ' concrete/ A man, it may be said, is clearly concrete enough, and so perhaps is an instance ; but a lecture, is not that dangerously near the abstract ? And ' Hope,' ' Success/ are not these purely abstract terms ? The answer is that no word (when used in a proposition — and it is only when so used that we are here concerned with words) is in itself either abstract or concrete, but its context makes it so. Any word may be either, according to the purposes of our assertion. We may speak of ' man ' or of ' men ' in the abstract, in spite of the solid flesh belonging to each individual ; and on the other hand, by hedging in a so- called ' abstract name,' with the help of a demonstrative pronoun, or in whatever way the resources of language will allow us to apply such name to some actual concrete case, we destroy for the time its abstract nature, and the pro- position as a whole becomes concrete. If I make an assertion regarding the ' truth ' of some particular story, I state no law, and deny no law, but confine my remarks to one particular concrete fact. The underlying meaning of ' abstract ' is always ' detached from special circum- stances,' or ' generalised ; ' and so long ago as Berkeley's time our limitations in conceiving (or having a definite idea of) anything in the abstract have been clearly shown. We cannot conceive things in the abstract, but Chap. Ill] MAIX KIXDS OF THESIS. 73 we can make abstract assertions regarding them; — can sometimes say, that is, how they will behave or how they should be explained or designated under all cir- cumstances indifferently ; and where we speak of this man, your hope, etc., we include special circumstances which ' man ' and ' hope ' by themselves would lack. In the concrete proposition we sum up the total circum- stances, taking (or rather professing to take) all the indi- vidual peculiarities of the case into consideration before pronouncing judgment. Whether or not 'hope' in the abstract may tell flattering tales habitually, we say that taking all the present circumstances into account it does so here. The S of a concrete proposition differs from that of the corresponding abstract one in being saddled with all the individual peculiarities of the given case. And on this account the concrete assertion differs from the abstract one in being less easy to disprove ; since the ' circumstances ' are nearly always wide enough to contain something that even science fails to reckon. It must now be sufficiently evident also that so long- as the meaning is clear, the gTammatical form of the sentence — categorical or hypothetical, simple or com- plex, A or E, etc. — is not of the slightest importance. The proposition, for instance, 'Murder will out,' is, for purposes of proof, the same whether expressed in this fashion or in the shape 'All murders are eventually discovered,' or 'No murders remain undiscovered,' or "Murder always comes to light,' or 'Murders never remain hidden,' or ' When (or if) murder is committed, 74 FALLACIES. [Pakt I.. detection is sure to follow,' or in Avliatever wa}^ it may suggest itself to rhetorical ingenuity to clothe the same meaning. At the root of all abstract propositions lies; the formula — S (universally) — > ^ and this whether ^ be past, present, or future relatively to S and whether the name of either be positive or negative. In each case S (in general) is said to be a sign, or mark, of ^, whether in the past, j)resent, or future, relatively to itself Where S is found, ^ (it- is asserted) may be looked for. Abstract propositions play an important part in proof, — whether proof of other abstract propositions or of concrete ones. They summarise, in a compact and convenient form, whatever general knowledge of nature we have already obtained, and serve as tests to which to bring any new assertion propounded for proof. The establishment of these is of course the centre of interest for science. It is through the existence of such 'de- pendences ' that all explanation and prediction become possible, and our consistent recognition of them consti- tutes the main difference between our conception of Nature as a network of uniformities, and the earlier notion, so inevitable to savages, of a world governed by caprice or luck. Concrete propositions, on the other hand, although constituting in one sense the foundation for science, find their main interest, as subject-matter for proof, in a less exalted region. Although in common life also the truth Chap. III.] MAIN KINDS OF THESIS. 75 of general laws (inore or less vague perhaps in theii* statement) may to no small extent be debated, yet the bulk of the questions arising there for settlement are of a concrete character; and, roughly speaking, the com- moner the life the more relatively frequent are the concrete assertions put forward. Whether this or that thing, person, or definite group, did act in such and such a manner, or does possess such and such qualities ; whether this or that individual action, event, or ' acci- dent' was due to such and such causes, or will have such and such results ; these are the most frequent ques- tions about which in daily life doubt arises, and which press for settlement and proof Every one of these is concrete, — an assertion directly regarding individual fact, not general law, — and as such is marked off by a chasm as wide as any that can be made in Logic, from the propositions above defined as abstract. Between concrete and abstract knowledge, however, with respect to their attainment and growth, there has been mutual aid and mutual criticism so far back as can be traced at all. No doubt, in one sense, concrete knowledge (or some- thing separated from ' knowledge ' only by imperceptible degrees) is earlier in time, just as common life is earlier than Science. But in both there are now innumerable shades of development or completeness. It may be safe to say, perhaps, that from crude concrete perceptions the first predisposition for abstract knowledge arose, and that by means of such predisposition, aided by language^ or signs, the first crude abstract guesses were formed. / FALLACIES. [Part I. But tlie history of knowledge, from the earliest evidence attainable, is a record of the alternate and mutual pro- duction, correction, and illumination, of one kind of judgment by the other. At the present stage of pro- gress, as will be seen in speaking of the kinds of Proof, there are thus in operation two somewhat conflicting methods of testing truth, — two methods which, though often opposed as rivals, and either of which may at times become unimportant or inapplicable, are yet to a great extent capable of being employed in one and the same investigation. Our theories require to be grounded on facts, and also to be confronted with them: but to see our facts in the light of theor}^, though a dangerous habit, is in some ways a useful one. No practical mind can desire wholly to dispense with the formulated results of all past observation. Nor, perhaps, could such a desire be reall}^ satisfied : it is difficult to find a single case of observation that is quite free from the influence of our general knowledge. Whatever may be true of the earliest concrete assertions, at the present time every concrete assertion put forward as a thesis carries with it a remote and indirect reference to numerous ' laws ' assumed. By implication it declares the posses- sion not only of some one piece of abstract knowledge but of many; it professes the knowledge not only of a law but of conflicting tendencies, by means of which the special circumstances can be allowed for and 'a total balance struck. Thus the concrete proposition (when ■so far developed as to become a thesis for proof) is Chap. III.] MAIN KINDS OF THESIS. 7/ always full of abstract propositions unexpressed. Some- what as the trained ear can detect the overtones in a musical sound, the logical mind detects the hidden as- sumptions in a concrete proposition. The abstract pro- position also certainly professes an acquaintance with concrete facts, but not quite in the same manner as the concrete proposition professes a knowledge of the laws of Nature as bearing on the special circumstances of the case under consideration ; for since the abstract propo- sition expressly avoids saying anything about special circumstances, the assertion made is almost infinitely simpler. Practically, of course, the ' overtones ' in a con- crete proposition are mostly overlooked, but it is their existence that constitutes the chief weakness of un- aided common-sense. What seems to common sense more indisputable than that this given action is a case of ' firmness ' or ' streno^th of character,' or ' courao-e ? ' Perhaps a deeper insight Avould show that among the special circumstances must be included ignorance of con- flicting claims, or ignorance of danger. There still remains to be noticed that very common form of proposition which, when two concrete things are already given as having occurred or as existing successively or simultaneously, asserts causal connexion between them. When we say, for instance, 'Your hasty speech was the cause of all the disturbance,' or, ' It is this pillar that supports the building,' is the assertion properly abstract, as implying some law, or concrete, inasmuch as it speaks directly and expressly 78 FALLACIES. [Part I. of individual facts ? Such propositions, I hold, may be used for either purpose, or for both together. It is diffi- cult to say for which they are most often applied, or even which is most often their primary meaning. On the whole one would perhaps be inclined to call their concrete meaning primary, and to say that the abstract meaning was rather insinuated, or implied, than directly intended as an assertion. But in practice it will be found that these assertions are largely used for appa- rently^ confirming, by means of facts experienced, causal laivs already more than half believed. And since the abstract meaning has a wider importance, and since moreover if the assertions be true in the concrete there must also be some true abstract assertion behind them, it seems best to view them as capable of both a concrete and an abstract meaning, the disproval of either of which would disprove both. For convenience, then, we may speak of these as Abstract- Concrete propositions, if it be clearly . understood that they form no new distinction in kinds of meaning, nor interfere with the division already made (of meanings, not of forms of words) into abstract and concrete. At the end of the book (Appendix E) will be found a table (I.) of the divisions thus far made. IV. Succession and Co-existence. There are not many minor distinctions of meaning in propositions that call for notice here. We are not in Chap. III.] MAIN KINDS OF THESIS. 79 search of all the varieties that can possibly be distin- guished, nor even of such as may be on the whole the most important for general purposes, but only of such as have special interest for the purpose of discussing the methods and the dangers of Proof. It seems necessary, however, to mention briefly the distinction between propositions asserting succession (whether backwards or forwards in time) and those asserting co-existence ; or, as they are more commonly called, assertions regarding Causation, or Causal sequence, and assertions which merely name, or classify, the S, or which state some of its constant concomitants without necessarily attempting to trace them to a parent cause. Such importance as the distinction has, for us, flows from the fact that according to the nature of the asser- tion in this respect is to some extent its liability to special dangers. Wherever indication is asserted, whether in abstract or in concrete propositions, all importance turns, of course, on the deo^ree of trustworthiness of the si^n : * some signs being more certain than others, but even a vague symptom being better than none at all. And according as the assertion points backwards or forwards in time (S a sequent of ^, as in 'Valleys — > prior denudation;' or S an antecedent of ^, as in ' Deficient education — > future increase of crime ') is it to some extent open to * We must here use ' sign ' in an extended meaning also, to corre- spond to ' indication : ' so as to say that in every proposition, abstract ■ftr concrete, S is the ' sign,' and S' the thing signified, or ' signification.' 80 FALLACIES. [Part L special and different dangers : propositions pointing backwards being liable to the danger of overlooking 'Plurality* of Causes;' and propositions pointing for- wards, to that of overlooking tlie liability of one cause to be counteracted by another. Thus, to take first Abstract assertions : it is seldom we can say that any given S invariably indicates the past existence of any given §, — unless, indeed, the ^ employed be so vaguely defined as to be of very little practical service. Every event (S) we may no doubt assert, within the widest empirical limits, indicates the past occurrence of soone other event, the essential part of which recurring, S will recur : true, but we do not often find this doubted. The point of practical importance is, ivJiat prior events does S indicate. Or, again, every existing human being has certainly had (i.e. indicates the prior existence of) a human grandfather: this also is too axiomatic to convey practical information, though we ma}^ want to know the name or the special character- istics of the grandfather in question. Almost, but not quite, equally rare is it to find complete invariability of sequence asserted, except thus vaguely, when the refer- * Mr. Carveth Eead's term, ' Vicariousness ' of Causes, though less ambigcous, I only do not use because the name * Plurality ' appears to be so firmly established, and need not really mislead. The reader to -whom the phrase is unfamiliar must notice that what is meant is the possibility of any one of several causes having produced the ' same *' effect, as where ' one kind ' of death may be due to heart-disease, or to a fever, or to yet other alternatives ; the name has nothing to do with the combination of causes, as where a death is due to mental anxiety, ]phi.s insufficient food, x>lvs an illness not otherwise necessarily fatal. Chap. III.] MAIN KINDS OF THESIS. 81 ence is forward in time. A shot through the heart or brain is perhaps invariably followed by death, and if there were interval enough between the two events we should say the former indicates the latter as sure to happen : but favourable seed-time does not necessaril}- indicate abundant harvest, since in the interval some unforeseen counteraction may arise, or at the seed-time itself along with certain favourable conditions there may have been an unsuspected enemy sowing tares. So again, we may often predict too vaguely to be of much real service. Sunshine, we know, for instance, always follows rain, and may be expected sooner or later ; but what we most want to know is ivlien to hope for it, or under what exact conditions, if within our power to compass. Accordingly, abstract assertions of succession are commonly made with a large margin for the incalculable. We feel fairly contented in obtaining any hint of ' law ' — any knowledge, that is, which may form a basis for even imperfectly secure inference and proof The only alternative to ' Chance ' * is often ' Tendency,' and in our gladness to escape from Chance we dignify this as ' Law.' An abstract assertion pointing backwards has, then, to deduct from the trustworthiness of its asserted indication in order to allow for the possibility of ' other causes producing the same effect ; ' and this even where * By ' chance ' is meant in this connexion no more than the con- tradictory opposite of 'known, law.' Some law there is nowadays always assumed to be, but that the conjunction is due to chance means really that no amount of limitation of S or of 5 will give us a known law between the two things so designated. See also Appendix D. G 82 FALLACIES. [Part I. we possess a real ' Causal Law.' It is a real law, for example, that prolonged starvation invariably causes death. But still we are very far from being able to say that death, wherever found, indicates prolonged starva- tion. And in like manner every abstract assertion pointing forwards in time has, almost in proportion to its definiteness and consequent practical value, to allow for possible antidotes or counteraction. In abstract assertions of co-existence, we can often attain greater certainty of indication (for practical pur- poses, at least, and within narrow fields), but even here large use is made gratefully of incomplete laws — indica- tions only roughly trustworthy, true only on unexpressed conditions. We may know, for instance, that boys ' as a rule,' delight in mischief, and we may make real use of the knowledge, without being at all able to gene- ralise the exceptions so as to state a quite invariable law. If we could truly say, e.g. 'AH boys except those who are physically deformed are mischievous,' our indi- cation would be of far greater value than while we can only say 'the majority,' or ' many,' or 'the average boy,' or any other vague limitation. In the concrete proposition, on the other hand (except, as will be presently seen, in the case where S is said to deserve the name ^), there can be no talk of the asser- tion being roughly true. The given S was either as a fact preceded by ^ or not ; ^ either will or wiU~ not be among its consequents in time. Here, accordingly, it becomes still more important to recognise the Plurality €hap. in.] MAIN KIXDS OF THESIS. 83 of Causes and their liability to counteraction ; and hence the purpose of distinguishing the two kinds of assertion, namely those with a backward and those with a forward reference, — assertions explanatory or detective, and those Avhich predict. As regards the descriptive or classifying proposition (where S is said to deserve the name g^) here a little more latitude seems inevitable. Names are altogether so loosely applied — their correct meaning varies habitually within such wide limits, — that in giving S a name not already assumed to belong to it of right, we may well be content, in many cases, to come somewhere near the mark. Is this man civilized, intel- ligent, learned, unsteady, idle, brave ? Even when we judge his character accurately uifact, very many of such questions might admit of the double answer, Yes and No.* As, then, in the case of explanatory or detective pro- positions the main difficulty flows from the Plurality of Causes, and in predictive propositions from the liabilit}^ of one cause to be ' counteracted ' by others ; so in pro- positions of co-existence the danger is that of taking for " essential ' something that is ' accidental ' merely, — i.e. of believing ' always ' when the real truth is ' some- times.' For if the proposition be concrete (as, 'This man is a fool ') it still professes abstract knowledge,— knowledge of the essential qualities which go to form the meaning of the predicate in question. Tables II. and III., in Appendix E, show concisely the results of this section. * See also pp. 124, 133, 184, 189, inf. CHAPTER lY. THE LAW OF COUNTER-mDICATIOK As the presence of one thing may indicate the presence of another, so may presence indicate absence, or absence indicate presence, or absence indicate absence. All these are, of course, equally assertions of indication. Thus a negro's coloured skin may be asserted to indicate the presence of a cheerful temperament, or the absence of some other qualities ; and the absence of pain, in certain cases, to indicate the presence of paralysis, or the absence of inflammation. On any view of Logic, the real 2^ons asinoruon is the group of facts here to be generalised under the one 'Law of Counter-indication.'* This law may be said to lie directly at the root of the ordinary doctrines of conversion and contraposition, and also to contain an explanation of the whole syllogistic process. Difficult * Mr. MacColl, who formulates essentially the same law, adopts for it the name contraposition. But contraposition, in its usual -meaning, seems never to have had quite so wide an application, and therefore I prefer ' counter-indication ' as less likely to mislead. Cf. also Pro f Croom Robertson's remarks, in Mind, No. i. p. 148. Chap. IV.] THE LAW OF COUNTER-INDICATION. 8 a though it is to state the law in perspicuous language, and intricate though some of its consequences may be, the principle itself is really extremely simple, and, once grasped, can hardly be forgotten afterwards. It needs, however, some special definition in order to overcome in the first place the difficulties of statement. The words ' presence ' and ' absence ' are until further explained, hardly general enough to express all that is intended, and are only chosen because no other, more comprehensive, names appear to be available. The pre- sence or the existence of a thing or quality, the happen- ing of an event, the truth of an assertion, stand on one side of the opposition intended, as contrasted with the absence or the non-existence of a thing or quality, the non-happening of an event, the untruth of an assertion. And for brevity and our own convenience merely, I wish to extend the use of the two terms chosen, in order to cover these diverse meanings. Accordingly such assertions as that ' human beings — > human parents,' or that 'the existence of discontent in India — > bad government,' or that 'the falling of a stone — > the force of gravity,' or, 'If he is well he will certainly go,' etc., are all cases of ' presence ' indicating 'presence' in the sense intended. And so with the indication of absence by presence, and of presence or absence by absence. The two words are not to be under- stood as strictly limited to their ordinary sense, but as stretched to include the wider meaning postulated as above for the sake of simplifying the expression. 86 FALLACIES. [Part I, Now, since we mean by S the whole of that ' thing ' which constitutes the sign or datum, and by §b the whole of that which the sio^n sio^nifies, it is clear that if we employ symbols to express respectively that thing the presence or absence of which may indicate ^, and that thing the presence or absence of which may be indicated by S, we cannot use S and ^ themselves for such a purpose without incurring misinterpretations. Instead of them it would be better, where necessary, to use the corresponding small letters s and S. Thus, if the presence of a steady pulse — > absence of fever, ' steady pulse ' and ' fever ' are respectively s and S, ' the presence of a steady pulse ' is S, and ' the absence of fever ' is ^. Finally, if we call that S or ^ which expresses the 'presence' of s or S, a ijositive one; and that which expresses their ' absence ' a negative one ; and if we call their positiveness or negativeness their quality ; and the change from positive to negative, or from negative to positive, a change of quality ; the law may be stated as follows : — All indication of ^ by S {affirinecl or denied) is ex- pressible as indication of S by ^ (affirmed or denied^, if, and only if the quality of both S and ^ be changed. Let us trace the operation of this law, first symboli- cally and afterwards by means of examples. And for the symbolical expression let S and ^ stand for the positive forms, and non-S and non-^ for the negative ones. Then the sole equivalent of Chap. IV.] THE LAW OF COUNTER-INDICATION. 87 (1) s-> ^ is non-^-^ non-S (cf. contraposition of A).* (2) S — ^ non-^ }y & —^ non-S (c/. simple conversion of E).* (3) (4) non-S — > ^ )) non-^ — > S {cf. exclusive disjunction).* non-S — > non-S) ,y ^^ s (cf. No. 1, above). and the sole equivalent of (5) s+> ^ is non-^-f^ non-S (cf. contraposition of 0).* (6) S -+^ non-^ >> ^-|-> non-S (cf. simple conversion of I) .* (7) non-S -H^ ^ „; non-&+> S (cf No. 3, above). (8) non-S -f-^ non-^ ^4^ S (cf. No. 5, above). But examples will perhaps show the process more clearly. Take first the assertion that "every corrupt tree bringeth forth evil fruit " (i.e. presence of corruption in the tree — > ditto in the fruit) ; then the equivalent form of this, and the sole indication implied, would be * absence of corruption in the fruit — > absence of cor- ruption in the tree ' (i.e. ' if the fruit is sound, the tree is sound '). What the proposition does not tell us, but what may perhaps be known to be true from other sources, is, either that corruption in the fruit indicates corruption in the tree {i.e. " every tree that bringeth forth evil fruit is corrupt"), — which would be the ' simple converse ' of the original proposition, — or that * These names refer to some of the ordinary technicalities of Logic. They are well explained in all the text-books; e.g. Bain's Deduction, pp. 113-116, 122. 88 FALLACIES, [Part I. soundness in the tree indicates soundness in the fruit — which would be the 'reciprocal.' From the original proposition, we can indeed get the denial of any such law, as that corruption in the fruit indicates soundness in the tree (i.e. ' Some corrupt fruit is the offspring of a corrupt tree;' the 'converse per accidens') ; but this, being a denial, is not itself a statement of indication : the sole indication is that which in the A and propositions is usually called the ' contrapositive,' in the I and E propositions the ' simple converse,' and which in all propositions is here called the counter-equivalent. Or take (2) the assertion that ' no quakers are dis- honest' (quaker tenets — > absence of dishonesty.) Of this the formal equivalent would be that dishonesty — > absence of quaker tenets (' No thieves are quakers '). Here will at once be recognised the ordinarj^ simple con- verse of E, our rule differing, in fact, from such conver- sion only in being applicable more generally, so as to include all grammatical forms of proposition, so long as they express the indication of non-^. Thus from the conditional sentence, 'If it be true that he has come, then it must be false that he has broken his leg;' we get by counter-indication, 'If it be true that he has broken his leg, then it must be false that he has arrived.' Again, from (3) " He that is not with us is against us " (or * Everyone is either with us or against us,' or 'All except our party are unfriendly') we get by counter- indication some proposition meaning that all except the plainly hostile are on our side ; and if the proposition €hap. IV.] THE LAW OF COUNTER-INDICATION. 89 should prove untrue in one of its aspects it must be untrue in the other also. This form of proposition de- serves more attention in Logic than it sometimes obtains, and we shall presently (p. 92) have to devote a few words of special notice to it. It is perhaps more liable to misinterpretation in respect of its legitimate counter, than any of the other forms.* The importance of the Law of Counter-indication is far-reaching in Logic. But so far as relates to the in- terpretation merely of the meaning of assertions it may be shortly stated. A certain proportion of indications there are — a comparatively small proportion, however — which really ' cut both ways/ or, as it is technically called, allow of the ' reciprocal ' f assertion also. Thus, * As examples of the remaining forms may be given : from (4) ' with, oat trouble there can be no success,' ' the attainment of success shows that trouble has been taken : ' from (5) ' typhoid fever does not neces- sarily show that there has been defective drainage,' 'proper drainage is no complete safeguard against typhoid fever : ' from (6) " the presence of the attribute ' habitual tendency to drunkenness ' does not neces- sarily show the absence of (or 'is compatible with') a fair amount of industry " ' the presence of a fair amount of industry does not neces- sarily show the absence of a tendency to drunkenness' (or, from 'some habitual drunkards are fairly industrious ' ' some fairly industrious men are habitual drunkards ') : from (7) ' absence of the power of discrimi- nation does not necessarily mean presence of the power to generalise,' * absence of the power to generalise does not necessarily indicate pre- sence of the power to discriminate : ' from (8) ' illness does not necessarily mean weakness,' ' strength does not necessarily mean health.' t The name ' reciprocal ' will be here slightly extended beyond the ordinary usage, and employed to mean not only what Prof. Bain calls {Logic, vol. i. p. Ill) the " material obverse," but also the illegitimate converse of any indication (aflSrmed or denied) ; i.e. the converse formed without changing the quality of S and =S. Thus, both 'non-S -^ non-S ' 90 FALLACIES. [Pakt 1. evil fruit does perhaps, as a fact, indicate an evil tree. So again, while a certain label on a bottle shows that it came from a certain firm (S indicates ^), we are also often told, in the same breath, that " without such label, none are genuine " (non-S indicates non-^) ; and while equilateral triangles are equiangular, equiangular triangles are equilateral. From these and similar occasional cases a certain looseness has affected our application of all words expressing indication (the word ' indication ' itself seems to me least ambiguous of any) through which its essential one-sidedness comes into frequent danger of being forgotten. The law of counter-indication helps to remind us that sign and signification are not quite identical. Here should be noticed further a fact which interferes largely with what may be called the positive utility of the law, — the fact, namely, that s is so often a mark whose presence or absence is much easier to recognise than that of S. When Darwin finds, for example, that white cats, with blue eyes, are always deaf, the counter equivalent (absence of deafness, in cats, — > non-white- ness of fur or non-blueness of eyes) is hardly likely ever to be %ised as a direct indication. If we want to discover the colour of a given cat's eyes, we should probably use our own, by way of direct observation, rather than employ a series of experiments upon the cat's power of and ' S> -^ S' would be forms of tbe 'reciprocal' of ' S — > 5.' See also Wundt's remarks on 'one-sided' and 'mntual' dependence in general; Logik (ErTcenntnisslehre) , pp. 214. 245, 317, etc. CiiAP. IV.] THE LAW OF COUXTER-IXDICATIOX. 91 hearing. And so in many other cases. The chief value of the law is rather restrictive than inferential, — namely to prevent our supposing the reciprocal necessarily true. Readiness to accept the reciprocal as equivalent, is one of the strongest tendencies in uninstructed human nature. Recognising, for instance, the rough truth of the law that stupid people are conservative, the superficial reasoner is apt to overlook the difference between this assertion, and that ' to be conservative — > stupidity ; ' assuming that success in examinations is a good indi- cation of hard work and high talents, common sense supposes that this assertion reall}^ means that failure in examinations is a good indication of idleness or incom- petence ; only with great difficulty can the illogical mind be made to see that other causes of such failure can possibly exist besides the one or two most superficial or striking ; and when the plurality of causes is at last recognised here, it seems to shake some people's faith in the positive indication also. Professor Jevons, speaking with a wide knowledge of students' capabilities, tells precisely the same tale. "A man," he says, "who is very ready at integration begins to hesitate and flounder when he is asked such a simple question as the follow- ing: 'If all triangles are plane figures, what informa- tion, if any, does this proposition give us concerning things which are not triangles ? '" To some extent also, and chiefly where symbols are employed, no doubt the error flows from a mere thoughtless inclination for balance, or antithesis, or symmetry. Those who are just 02 FALLACIES. [Part I. beginning the study of Logic are perhaps especially apt to be slaves to this inclination. De Morgan notices (and Jevons endorses the opinion) that the average beginner, when asked what follows from 'Every A is B,' invariably and promptly answers, 'Every B is A of course' One cannot help feeling that the cause is in such cases probably not very deep; the schoolboy who, being told that the three sides of a certain triangle were equal, triumphantly inferred that the fourth side must be equal too, hardly supplies a better instance of simple want of thought. Most of all, perhaps, in interpreting the thoroughly ' disjunctive ' proposition (where absence is asserted to indicate presence), this spirit of superficiality may be seen in harmful operation. That is to say, a disjunction is relied upon as exhaustive while it is thought sufficient to prove the mere assertion of difference. Thus 'Con- servative' and 'Liberal' are certainly different, but it does not follow that they are the only two alternatives. The counter-equivalent of ' non-S — > ^ ' is, as shown above, ' non-^ — > S,' but what is thus wi'ongly taken as equivalent is ' g:) — > non-S,' — a proposition almost always far easier to prove. For when we say that " If not s, then % ' we make a large assertion. We divide, in fact, the whole universe into two classes, s and S, and boldly assert that nothing else but these exists,— that whatever is not in the one class must be in the other. Now^, to do this w^ith s and not-s. or with S and not-S, is a matter of common occurrence ; Chap. IV.] THE LAW OF COUXTER-IXDICATIOX. 93 SO common, in fact, that whenever we use a general name we tacitly accept thus much responsibility. But in such cases the only difficulty is as to the position of the dividinor line, not as to the outer limits of the field that may lie beyond it : ' not-.s,' or ' not-S ' does not bind us to specify otherwise than quite vaguely the things that lie outside our defining fortification. When, however, we go further and say, ' I know a positive name for the whole class, not-s {e.g. 'not-con- servative '), and that name is S,' {e.g. ' liberal ') we really profess to have looked out from the citadel s, and to have scanned the universe therefrom. Of course there are cases where, owing to special circumstances {e.g. artificial limitation of the ' universe,' * or again, the case where s occupies a larger extent than not-s) this is prac- tically possible. It needs little courage to assert that all the contents of my pocket are either letters or po.st- cards, or that if a man does not believe the earth is round, he must be slightly crazy. But there are many more cases where we are apt mistakenly to suppose the universe scanned ; and this danger is immensely increased if we are careless enough to suppose that it is ' the same thing' (or even 'practically' the same thing) to prove the reciprocal. * De Morgan was, I believe, the fii'st to observe that behind most assertions there is an unexpressed limitation of the range of their extent. There is a ' universe of Discourse ' beyond which the assertion is not intended to apply. ' Not-white,' for example, is predicable solely within the universe 'colour;' and 'Nonconformist' excludes, by custom, heathens and atheists, as well as those who conform. 94 FALLACIES. [Part I. But mere thoughtlessness is, no doubt, not the only explanation of the tendency in question. The deepest source of it seems to be the fact that provisional belief in the reciprocity of indications is so often fruitful as reo'ards the earliest o-uesses at unknown truth : for O CD ' though ^ (or non-S) may not exactly indicate S (or non-^), it is often so closely connected with it by causa- tion that in finding where such indication fails we hit upon the real law. Corruption in the fruit, for example, may except in certain assignable cases indicate corruption in the tree. Nevertheless, in Proof as distinct from Discovery, the tendency is fatal, and needs to be held in severest check. It is unsafe even to suppose, as seems so natural, that mutual indication is the rule, and one-sided indication the exception. Probably the pre- vailing attitude among the illogical is best expressed as the belief that any law, in the absence of proof to the contrary, involves a 'fair presumption,' at least, that the reciprocal is true; Avhile fair presumption is not worth distinguishing from ' practical certainty : ' the real fact being that the most an abstract indication ever involves is a fair presumption (and that not alwa^^s) that the re- ciprocal is worth the labour of investigation. But it seems unnecessary to say more about the practical value of the law of counter-indication : it merely binds up into one scheme rules whose utility is already well-known. This is the case, at least, as regards the universal affirma- tive and the particular negative : perhaps, however, the ease with which the disjunctive proposition is liable to Chap. IV.] THE LAW OF COUNTER-INDICATION. 95 be taken for the mere assertion of difference, may be a less familiar fact. It remains to ask how far the law is applicable to concrete propositions. The answer seems to be that, though formally implied, the counter- equivalent is in concrete propositions never directly needed. This is in fact the extreme case of what was noticed in the example of the blue-eyed cats. If s be a concrete ' thing/ we have other marks, more readily applicable than non-^, by which to prove its absence : it is in fact known to us mainly by means of its attendant circumstances as a whole ; and % is only one of these, and (by hypothesis) not the most familiar. We can, indeed, apply counter- indication to concrete matter in some such way as this : suppose the concrete proposition to be ' This murder — > greed of gold ; ' if we are certain of this, and also of the fact that in a given prisoner's case the greed of gold was absent (non-§b), we no doubt may infer that this murder was not (non-S) committed by him. But here, of course, it is not ' this murder ' whose existence we get denied, but the truth of the theory that it indicates the prisoner as its cause : it seems that the result is obtained circuitously, by means of the abstract indi- cation involved, — namely ' Any one who committed this murder must have had a greed of gold,' or ' The abstract possibility of this murder — > such motive,' and this motive was absent in the case before us : hence, in the case before us ' this murder ' was absent too. This is better viewed as a case of highly elliptical syllogism than of Immediate Inference. 06 FALLACIES. [Part I. There is one further precaution to be observed in using the law ) a precaution, however, which is probably too simple to require notice except so far as symbols are employed. And perhaps the reader already recognises * that half the mental confusion that exists is really due to the use of symbols, — whether such symbols are imposed upon us by the real need for abbreviation (as e.g. in the case of general names), or by what may appear to be the wanton pedantry of logicians. It is easy enough, for instance, to see that the proposition 'Every man is an animal ' does not imply that every animal is a man, though possibly some people might be less clear about it if A and B were substituted for Man and Animal. Latet dolus in generalihus. But here the source of con- fusion to which I wish to draw attention is that due to the time-elem.ent in indications. Where propositions of co-existence are in question, no difficulty can possibly arise, but in the case of succession it may be worth while to notice that where S indicates (or fails to indicate) future ^, non-^ indicates (or fails to indicate) jyctst non- ^, and where S indicates (or fails to indicate) 2^<^st ^, non-^ indicates (or fails to indicate) future non-^. The examples, given above, of the connexion between labour and success, or between typhoid fever and the drainage,! were chosen with the view of showing this necessity. Practically, where actual examples are employed the danger is not likely to arise ; but in the absence of an * With Mr. Kejjies;Mind, No. xv. p. 366. t See note on p. 89 : examples (4) and (5). Chap. IV.] THE LAW OF COUNTER-IXDICATIOX. 97 express caution there might perhaps be a tendency to suppose that ' S — > future ^ ' is equivalent to ' non-^ — > future non-S/ with which indication (as would be seen at once when translated into full language) it has really nothing to do. Less important does it seem to mention that mere puns form no exception to the law. No reader, I hope, wall be puzzled by the fact, for example, that while the presence of courage clearly indicates 'presence of mind,' it by no means follows that ' absence of mind ' indicates anything approaching to cowardice. Logic presents ad- mirable opportunities for those who find amusement in punning, — a fact largely recognised some two thousand years ago. But at present we are not concerned with any difficulties due to merely verbal quibbles. There remains little more to be said here about the subject-matter of Proof, except to admit as unmistakably as possible that the view of propositions here taken, and the classification here made, is far simpler than would be required for almost any purpose other than ours. For Psychology certainly, and also for the doctrine of In- ference in general (as contrasted with reflective Inference, or Proof) very much more would be needed. But in Proof we start always with some co'inpleted Judgment, some Judgment developed so far as to be expressed, reflected upon, and its validity called in question : hence the growth or formation of the Judgment from its earUest traceable stages is of no direct concern to us. Many of the varieties of grammatical structure correspond roughly H <)8 FALLACIES. [Pakt 1. to shades of meaning which vary both in definiteness and strength of assertion, and in richness of implication. These are in themselves of high importance : but before the interest in these arises we need to keep perfectly clear the first broad distinction between proven and not- proven. For such a purpose the plan which commends itself alike to common sense and to Logic, is that of treating the proposition as something put before us in an already formed condition; put forward, that is, as conveying intelligible meaning and deserving intelligent belief By considering it a pretender to these qualities and then proceeding to inquire how far it actually falls short of attaining them, we best arrive at some notion of its real position on the long scale between worth and worthlessness. It is on this account that we choose, as being of directest interest, the task of considering in detail the series of possible objections that can be brought against any thesis set up as worthy of belief. CHAPTER V. THE PEOCESS OF PKOOF, IN GENEEAL. I. The Relation between Thesis and Reason. What is the relation between a thesis, as such, and any reason given for it ? What is really said in saying, ' the proposition T* is true, because the proposition R* is true ' ? This question lies at the root of the doctrine of logical sequence. To prove an assertion, it was said in Chap. I., is to establish it in full view of hostile criticism : the function of the advocate being to find and bring forward reasons for belief or disbelief, and the function of the judge being to weigh the evidence brought forward, balancing the arguments for and against. Our concern, it has been also explained, is entirely with the latter of these functions, and accordingly we may dispense with all con- sideration of the finding of the arguments. But suppose an argument already found and pro- duced — suppose, that is, not only a thesis brought for- * For convenience, T and R will, thronghout, be occasionally used for * Thesis ' and ' Reason ' respectively. 100 FALLACIES. [Part I. ward, but also a reason or reasons in support of it ; * by what means are we to judge of the binding force of such argument, how test the validity of the reasons given, or the strength of the evidence adduced ? The answer to so large a question cannot be given briefly and directly, except in words too general to render real assistance in the special cases. But it may be worth while first to take the broad and distant view. Clearly the most preliminary requisite is that no mistake should be possible as to the full relation between Reason and Thesis, as proposition guaranteeing and proposition guaranteed. We elected also (p. 73) to neglect the distinction be- tween categorical and hypothetical propositions, as stand- ing outside our interest; and to treat all propositions, whatever their grammatical form, as alike in stating a relation between two terms. But in order to do this it was necessary to explain that the terms of a proposition, so understood, are sometimes themselves propositions, — as in the familiar case of the ordinary h^q^othetical. Now every argument may be viewed as a proposition of this character, with subordinate propositions as its terms. Every argument states that the truth of E indicates the truth of T. Every argument, that is (to apply the law of counter-indication), whatever else it says, makes an assertion expressible in the formula : — E -> T, and non-T — > non-R : * Eeasons for any thesis are, of course, reasons against the opposite one ; and the expression may therefore be safely generalised as in the text. Chap. V.] THE PROCESS OF PROOF, IX GENERAL. 101 whicli is the symbolic expression for " Grant E, and T follows, and Deny T and the denial of R follows." Or, since in every argument the truth of the Reason is asserted to guarantee that of the Thesis, every argument also asserts that unless the Thesis were true, the Reason would be false. But this is not all that an argument, as such, asserts. There is another element in every case of attempted proof; * namely, the assertion of the onaterial truth of the Reason. Without this, the relation asserted would of course fail in relevance to the matter in hand. Unless the reason brought forward for believing a thesis be itself asserted to be true in fact, the argument as a whole would clearly be devoid of all meaning. It is no argument to say that if some false or doubtful proposition were true, the thesis would be true: to support {e.g.) the thesis "England is on the verge of ruin " by declaring " I could appeal to statistics if only they were different," or even by means of the reason "Because ]possihly statistics would show." t In other words, failure in material truth * Cf. Mr. H. :\IacColl. Mind, xvii. 55. " The statement ' a, there- fore & ' is stronger than the conditional statement ' a implies &,' and implies the latter. The former asserts that h is true because a is true ; the latter asserts that h is true provided a be true." t The mere mention of so trivial a fact as this second element in the full meaning of an argument, seems to need some apology ; and the present is a good opportunity for remarking that wherever self- evident truths are enunciated in discussing the underlying principles of Logic, the purpose is by no means to convey new information, but rather to go through the duty — irksome alike to reader and writer — of formally X02 FALLACIES. [Part I. of the Eeason is one danger which every argument must avoid ; the sole other danger being that of failure in the formal adequacy of such Eeason, — i.e. the material un- truth of the asserted relation between R and T. Any argument, in short, is liable to frustration in twc^ ways : — (1.) If R be in fact untrue : (as, perhaps, where England's impending bank- ruptcy is appealed to in proof of the disastrous effects of Free Trade.) (2.) If R can be true while T is false : (as where the Sun's movement round the earth was the Thesis, and the facts of 'rising' and ' setting ' were the Reason given.) As to the first of these two possible attacks on Proof, it is clear that when once the question is raised whether R be true or not, R becomes itself a new Thesis, and must either be accepted without further inquiry or submit in turn to have its o^vn grounds produced for examination : the same difficulty recurring until a basis of accepted truth is reached. It is therefore sufficient for Logic, as such, to carry the analysis of the methods of Proof up to the point where the formal adequacy of the reason given is secured, thus guarding against the second of the two attacks : for the first of them leads to a mere repetition of these methods, only on new subject-matter. Can then registering such facts, merely to prevent possible misunderstandings, and for convenience in afterwards referring to them. CriAP. v.] THE PROCESS OF PROOF, IN GENERAL. 103 the highly generalised statement, given above, of the nature and needs of formal adequacy be translated into a shape somewhat more convenient for application to actual arguments ? This question will need a rather circuitous answer. II. Consistency. Probably there is no meaning more universally asso- ciated with the epithet ' logical ' than that of pushing to the extrevie. That is to say, a man is popularly said to be logical (whether as a term of admiration or of the reverse) in proportion as he shows a tendency to push accepted principles to their legitimate outcome. The logical person is, as a rule, uneasy under any system which, while refusing expressly to modify inconsistent principles, tosses them together and takes the mean result. In his simplicity he supposes that whatever is asserted as true must be intended as strictly true, — true even in its extreme case : a principle false in a single instance becomes to him fallible altogether. Hence he is apt to lack that quality which may be flatteringly called the delicate tact and skill required for handling political or ethical fictions with advantage, or for utilising to the full certain ancient structures thickly coated over with anomaly. The English Constitution, English Law, the English Church, present to such a person continual diffi- culties. He demands a clear understanding or no pretence of it, codification or else anarchy, absolute submission to authority or else absolute freedom from it. In this sense 104 FALLACIES. [Part I. it is that the French are called in every newspaper a logical nation, while the English (with the exception perhaps of a portion of the reforming party) have in many quarters quite an opposite reputation. But this is not all. Besides reading the remoter consequences of principles which are ready-made, the logical person is apt to generalise principles, on his own account, out of isolated facts. Besides being tenax propositi, he is eager for justice to be dealt. Not con- tent with demanding that an actually asserted principle (a 'universal' or 'abstract' assertion) shall be true in its extreme cases, he is inevitably inclined to take even purely concrete or individual assertions as covertly asserting a principle, — any disclaimers on the part of the assertor notwithstanding. Thus, if the ' logical ' Legis- lator finds some individual, or some class, in possession of a certain right or subject to a certain duty, he is always under strong inclination to extend such right or duty to analogous cases : if householders and lodgers in a borough have a vote, he is apt to view them as members of a wider class including (at least) householders and lodgers elsewhere : he resists a Permissive Bill on the ground that it is 'illogical' to allow the sale of liquor in one district while prohibiting it in another, — if alchohol is pernicious at all, he argues, it is pernicious everywhere ; or if the ratepayers are to have this prohibitory power they must ' logically' be allowed the like power in other cases, until there might be nothing left of individual liberty. So again, he considers it indefensible to protect €iiAP. v.] THE PROCESS OF PROOF, IX GENERAL. 105 one branch of industry without protecting all. In a word, behind apparently simple individual facts, he has a keen eye for possible principles involved. In appealing in this way to what is after all only a loose and popular meaning of the word, I must not be understood as laying more stress on such meaning than it deserves. Popular usage is often, of course, as misleading as etymology, when the purpose is to find the most accurate sense of a term at the present day. But as already explained, such purpose lies altogether outside our interests, our only desire at present being to gather in from any source available the broadest preliminary notions. And while the loosest custom is ever the most widely spread, the widest custom has the best chance of indicating, however vaguely, the more permanent founda- tions of meaninof. The two correlative ' logical ' tendencies just noticed have, it is true, only a remote and indirect connexion with the needs of formal adequacy ; but their recognition may serve very well to bring us a stage nearer to the actual point. If to be logical is, mainly, to be consistent, perhaps a glimpse at the nature of consistency will afford a closer view of the point in question. The Maxims * of Consistency (also often called the "Laws of Thought") are commonly given as three in number, — The Laws of (1) Identity,— A is A ; (2) Con- tradiction, — A is not not-A; and (3) Excluded Middle, — A is either B or not-B. Whenever we use a name, we * Bain : Logic, i. Introd. sect. 22. 106 FALLACIES. [Part I. use by implication the whole meaning belonging to that name, both (1) positively, and (2) negatively: and (3) every ' thing ' either deserves any suggested name or does not. By the first Law, for example, 'a man's a man/ whatever else he may also be. And by the second, we must take care that our defining-line is clearly drawn. What is outside A must not be confused with that which is within the range of its meaning. A name may be qualified, i.e. may have other (compatible) meanings added to it, as wlien we speak of ' a strong man, armed ; ' but incompatible meanings cannot* be joined to it with- out reducing its employment to absurditj^ by taking away the meaning already given ; so long as two contra- dictory meanings are supposed to remean in force, each neutralises the other, leaving the total name a blank. A straight line which is also, in the same plane, a curved line, is no line imaginable by us at all. Trivial though these twof Laws may appear Avhen viewed either as Postulates of Lano-uao-e or as statements of psychological fact, j^et as practical maxims for ensuring the consistent use of names they are evaded or violated by everybody every day; and though it may well be held that absolute obedience to them is, in the present state of language at least, practically impossible, it cannot be denied that as ideals they have a certain use. At * Except as hereafter explained, see p. 139. t The third law, (excluded middle), deducible from the other two, first comes into importance when we deal with the subject of misinter- pretation. For the present it may be left aside. CuAP. Y.] THE PROCESS OF PKOOF, IX GENERAL. 107 present, however, our sole purpose is to connect them with the needs of formal adequacy in general. We seem to have made perhaps rather an abrupt leap, from speaking of holding to Principles, and of rational- ising our isolated beliefs by bringing them under Prin- ciples, to the question of abiding by the postulated meaning of names. But there is no great leap after all. A general name may be viewed either as something to be applied (and thus, in effect, a Principle) or as something to be defined (and thus to be brought under a wider Generality).* The use of a general name is twofold always, — to be given to a ' thing,' and to signify certain supposed facts about that thing. Names, in fact, so far as used at all, can only be used as terms in a proposition, whether as S or ^ : every general name is applicable to something: nameable, and sig-nifies some other nameable O ^ CD thing or things. ' Man ' denotes (as Mill phrased it) the individual men, and connotes the attributes essential to the class. Accordingly the process of attempting to abide by the meaning of our names is, at bottom, iden- tical with that of attempting to abide by our assertions : and in speaking of one we speak of the other. Every name, then, that has a meaning, b}" virtue of that meaning refers the object named to its place in a system of wider and narrower classes : to state the fall meaning of any name -f* (or as it is technically called, to * If N stand for ' general name,' then we may symbolise the use of names as S — ^ N — ^ 5. t Otherwise than by merely giving a synonymous term. 108 FALLACIES. [Paet I. define tlie corresponding notion), in eveiy case without exception consists in mentioning some wider class {genus) of which the things designated form a part, and also mentioning the marks {difference) by which the part in question may be distinguished from the whole remainder of the wider class. Thus ' city ' might be defined as ' a large to^vn {genus) possessing a cathedral' {difference). And if, accepting this definition, we make the assertion ' Manchester is a city/ we state really ti'JO things about Manchester, — (1) that it is a large town, and (2) that it possesses a cathedral. Either of these two elements of the meaning of every significant {i.e. 'general') name, — the generic or the differential element — may from various causes become obscured or sink out of sight. One set of minds find a standing difficulty in seeing the wood for the trees, another set habitually fail to see the trees for the wood : the former, fixing their attention mainly on the points of difference, forget the common link that binds the members of a class together ; while the latter stop at the broad resemblance, disdaining, or dreading, or simply not per- ceiving, the obscurer diff"erences of detail. The term * city '' of course, being quoted here specially on account of its simplicity of meaning, does not well exemplify either difiaculty : but the majority of general names do exemplify it, more or less. A negro, for instance, is 'man,' with a diff'erence, and perhaps the disputed question whether he is a ' man and a brother ' will supply an example of what is here meant — some people, through Chap. V.] THE PEOCESS OF PROOF, IX GENERAL. 109 seeing clearly that he is not a ' brother/ being inclined to treat him as hardly human ; while others, through the obvious fact of his humanity, have perhaps rather over- looked his differential qualities. It is not always, then, so simple a matter as it might seem at first, to take care that A means really A, and not at all not-A ; and what is worse, owing to the unavoidable faults of language it is only possible within somewhat narrow limits to " call things by the same names as other people." But here it is sufficient to notice in the first place that it is the Law of Identity which (viewed as a practical maxim) bids us recoo'nise the o-eneric element in the meaning of a name, while the Law of Contradiction draws our attention to the differential line. Names, then, are employed in Proof as tickets, or marks, or signs. Every general name is a significant label, intended to make a two-sided assertion about the thing that bears it. And consistency demands that whenever we apply a name we shall be prepared to face all consequences and abide by the full meaning of such name : to fail in doing so, is to be inconsistent, and thereby to destroy the value of our own assertion. This demand, it will be seen at once, corresponds to the first of the two logical tendencies noted above, namely the holding to our Principles. A Principle, in the sense there used, is nothing more than a universal or abstract assertion. To bring any case under a law or principle is precisely the same operation as to bring any S within the range of a name : the purpose in both cases being to 110 FALLACIES. [Part L make use of generalised knowledge already supposed to be true. On the other hand the second logical tendency — extension to analogous cases — is a much more com- plicated affair, being partly mere deductive * consistency iind partly a process far more difficult to guard from error. The main feature in the second case is in fact not merely the application of abstract assertions, but also their formation, — a process which has often to be carried on with dangerous speed and without the aid of fully outspoken statement. Here too, however, exactly the same two fundamental dangers are present, — namely on the one hand that of overlooking points of difference (between the cases supposed to be analogous) and thus generalising too widely; on the other hand that of neglecting points of resemblance, and thereby not ex- tending the principle far enough. In both kinds of Con- sistency (accepting for the moment the popular name) all turns upon our accurate appreciation of the points of difference and resemblance : but in Deductive Consistency we are concerned with the differences and resemblances generalised and acknowledged already in the names employed, while in Analogical Consistency the point of primary importance is the nature of the things them- * As this is the first occasion where the name ' deductive ' has to toe here employed, it may be well to explain, for those to wh-om the term is unfamiliar, that deduction, whether used in Inference or in Proof, is always the process of interpreting a law in its details, or applying it to the particular cases which it is intended to cover. This may be easily remembered by viewing the process (Deduction) as a downward one, — law being * higher ' than fact. Chap. V.] THE PROCESS OF PROOF, IN GENERAL. Ill selves, and the extent and kind of difference and re- semblance really existing between them. III. Formal Adequacy in general. By failure in formal adequacy of the Reason, is meant, it was said, every case where E, can be true while T is false. It now becomes important to look more closely at the nature of E, in general, inquiring what (if anything) is universally characteristic of such assertions as are capable of supporting a Thesis. Since by R we mean only the reason actually given or expressed, it must be admitted that there is no universal property of R, as such, except those already mentioned, — namely such as are involved in the mere relation between any Reason and any Thesis. But if instead of the ' Reason given ' merely, we speak of the whole 'rationalisation' of the Thesis, — the reason, if any, implied, as well as the reason expressed — the case becomes very different. For two elements, express or implied, are required for all rationalisation : (1) a Principle or abstract indication (an assertion that a certain sign is trustworthy) ; (2) an Application of such Principle, or an assertion that the sign is present in the case or cases contemplated by the T : in other words, all rationalisa- tion may be represented syllogistically. Proof is thus, in an important sense, the counterpart of Explanation. The two go hand in hand, and each is only possible in presence of the other. Just as explan- 112 FALLACIES. [Pakt L ation always demands a reference to some wider Gener- ality than that which is to be explained, so Proof always demands a reference to some wider Generality than that which is to be proved. To explain, and to prove, consist essentially in this.* Both are forms of ' rationalisation.' It must not indeed be supposed that such ' wider gener- ality' is always in the fii'st place formulated ^ even in thought, — much less in language. The kind of evidence called circumstantial, for instance, and still more the argument from analogy (or 'parallel cases') are by nature averse from any such restrictive procedure, preferring rather to keep their principles as dim and intangible as possible. But none the less is some principle, how^ever limited (so only that it be wider than the thesis itself), required before any test can be applied; and the main business of Logic, as a practical science, is to force, in every case, such principle into explicitness, in order to see whether or no it and its apj^lication can bear the daylight, or stand the strain of stubborn fact. An argument, like a chain, must of course be tested by its weakest part: and while either the principle or its application, or both, may be unwarranted by fact, it is the principle itself which presents at least the largest target for attack, and which is therefore oftenest the centre of logical interest. Behind every reasoned belief there is at least one abstract proposition more or less * We have seen above (p. 108), how in the case of explaining the meaning of a name, the process (Definition) always refers the thing named to some higher genus. Chap. V.] THE PROCESS OF PROOF, IX GENERAL. 113 vaguely implied : and the most potent engine of disproof, — and through disproof, of proof, — is the process that brings to light these underlying abstract propositions, in order that their validity may be called in question. The rationalisation of knowledge is its reference to principles sufficiently secure from criticism ; and it is the Syllogism which helps us to force these principles into explicitness in any given case, and so enables us to inquu^e into the foundation on which the thesis rests. In all complete rationalisation of a thesis, then, there is always, implicitly at least, one indication used as an indication, and therefore abstract. This we shall call the Law or Principle. And there is also, implicitly at least, a claim that the case or cases spoken of in the thesis come under such law. Whether this (the 'minor premiss ') be itself an abstract or a concrete proposition, it is equally called the Application. The doctrine of the Syllogism, whatever other value it may possess, is mainly useful, as regards the rationalisation of a thesis, for drawing attention to any links that may be missing from the chain of complete demonstration. The present is not however the best opportunity for discussing the details of this operation. In this first general view of Proof, it is sufficient to register the assertion (afterwards more fully justified ; see pp. 212, 300) that Syllogism, so far as the said purpose is concerned, is perfectly general in its operation, — applies to all Proof Avhatever, and is not, as the beginner is apt to think it, an engine to be used in ' Deductive Inference ' merely. I 11^ FALLACIES. [Part L As regards Proof, then, the uses of the Syllogism are chiefly two : — (1) When a person has akeady admitted the truth of a principle and its application, to bind him down to every particle of assertion thereby made. In this use (as we shall see later) it is an argumentv/ni ad Jtominem. (2) When any thesis, with its reason, is put forward, to enable us to supply whatever is wanting to complete the Demonstration. We thus apply our knowledge of the syllogistic needs, either in order to determine the general law under which the special case in question is supposed by the assertor to come, and from which the thesis is supposed to derive its cogency, — and this with the intention of inquiring into the truth of such under- lying assumptions : or else (where no principle has yet been formulated) in order to force the assertor to see what must still be done in order to stop all gaps in conclusive reasoning. The mode of these operations will be more fully developed in the sequel. PART II. THE POSSIBILITIES OF EBROB. SECTION I.— BEFOEE PEOOF. CHAPTER I. INTRODUCTORY. Having thus sketched in outline the main facts regarding Assertion and Proof which are of preliminary importance, we are now at liberty to begin to trace the actual bearing of these on the detection of Fallacy, by examining in detail the openings at which error may creep in. When an assertion is &st enunciated, the Possibility of Error is at its maximum, and we have now to exhibit the process by which, step by step, this possibility may be reduced. We are only concerned, of course, with its reduction to the lowest minimum attainable, not at all with the question how nearly the goal may absolutely be reached. There will be no harm therefore in con- ceding that after Logic has done its utmost, human falli- bility remains : only let us protest against the view that since the moon is out of reach there is no sense in trying to cultivate the earth. It must be remembered further, that since the 118 FALLACIES. [Part IL detection, rather than the total avoidance, of Fallacy- is the chief object of our present inquiry, this method of diminishing the chances of error is only intended to be used for making sure that such and such a fallacy is absent. By trying which of the series of possible attacks a given assertion or argument can fairly meet, we at the same time discover its point of weakness. If it should pass our whole examination, we discover, not that it is absolutely free from all possibility of error, but merely that such possibility must be of the more remote kind which for practical purposes we are accustomed to accept and disregard. In the Introduction, the possible objections to any assertion were broadly divided under three heads : — (1) The objection to its reality as an assertion, its capacity for Proof or Disproof; an objection which seeks to condemn the Thesis as such, and without even in- quiring what its grounds may be, as containing a mere empty shell of assertion, without a meaning : (2) The objection that the Thesis is a mere assertion; standing entirely alone and without even attempted support ; or in other words that nothing has been done to remove the burden of proof : and (3) That though 'real' reasons are brought forward in support of a ' real ' assertion, such reasons are inauffi- cient; which objection is commonly condensed into the two words, Non Seqiiihtr. The plan here followed then will be to take each of these objections in turn, to discuss them by the help of CuAP. I] INTKODUCTORY. 119 examples, and also to connect them with the broad principles of Logic. And first in order comes the charge of Unreality. In a former chapter* unreal propositions were divided under three heads : — (1) Tautologous, or ' essential/ or ' identical ' proposi- tions, or 'Platitudes': (Jf already enunciated in the meaning of S). (2) Self-contradictory, or suicidal, propositions: (J already contradicted by the meaning of S). (3) The case where any term used in a proposition is, from any cause, devoid of meaning. In each case, then, it is clear that the meaning of the terms employed is the important matter, and that it is only so far as such meaning is wanting in clearness of conception that this particular fallacy can occur. Defini- tion of the terms is accordingly the direction in which to look both for means of detecting the fallacy and for safeguards against the first of the main objections. * See pp. 43-48. t Symbol first employed on p. 51. CHAPTER II. THE KINDS OF UNHEAL ASSERTION. I. Tautology, or Platitude. Taking in order tlie three heads — Tautology, Self-con- tradiction, and Meaningless Term, — it may be of service first of aU briefly to enlarge the explanation above given of their nature, — their causes, varieties and results. First, then, as regards Tautology. Its causes and results are essentially the same as those of the Fallacy known as Petit lo Pvincvpii, or begging the question. The assertion itself revolves smoothly in a circle, just as, in the latter case, that more complex kind of assertion known as an ' argument ' may be seen to do.* We render the assertion unassailable, by simply postulating ah initio (in the definition of its terms) that it shall not be assailed. Psychologically, indeed, it may be true that in most cases of apparent tautology pure and simple, there is really a fluctuation between two assertions (closely similar, .per- haps, in form), — one real but highly insecure, and the other verbal and thereby safe against all attack on the * Cf . infra, p. 193 ff. Ohap. II.] THE KINDS OF UNREAL ASSERTION. 121 score of truth ; and that we use the former when no one is looking, the latter only when awkward doubts arise. Such, perhaps, would be a fair explanation of what George Eliot calls "those undeniable general proposi- tions which are usually intended to convey a particular meaning very far from undeniable," — examples of which are often given in her dialogues, as " He said it did as much harm as good, to give a too familiar aspect to re- ligious teaching ; " or " The coachman, if he had been asked, would have said, though he might have to fall down dead the next minute, that property didn't always get into the right hands ;" or "There's no knowing what may happen before Lady Day." But such cases do not, I think, account for the whole employment of these empty forms : and where the assertion is inirely devoid of all forward movement, our acceptance of it as bearing a meaning seems to be due to essentially the same slack- ness of mental tone that enables us to draw satisfaction out of circular proof Strictly speaking, the shifty assertions above noticed belong rather to Ignoratio Elenchi, — a subject to be discussed later: the fallacy being in such cases perhaps, not really that of accepting as capable of test or verification a proposition which con- tains no real subject-matter for Proof, but rather that of asserting one proposition, and believing, or trying to establish, another. The chief motive for Tautology proper seems to be the desire to say something (or to accept any ' explanation ' rather than none) on a subject of which our knowledge is not deep or exact. Such 122 FALLACIES. [Part II, desire is often coupled mth a dim feeling that caution in expressing ourselves is necessary : as in a passage which may be quoted from a certain Tourist's Guide — "The expense of travelling on the continent depends more or less on the habits and means of the traveller, and his mode of journeying ; and likewise on the rate of charges made in the various countries." So much as this might have been known without the help of any assertion at all, and the belief that it really tells us anything is obviously an illusion. It must further be noticed that there are occasions when a sentence which as it stands may seem to be the purest tautology, possesses a real value in spite of having, on its own account simply, no capacity for Proof. With these we have already made acquaintance, namely in the statement of Postulates, whether such Postulates are general or special, — ' Laws of Thought,' or definitions of given names. When we state the proposition 'A is A,' or when we say " A city is a large town possess- ing a cathedral," it is certainly true that in both cases the J is already contained, to say the least of it, in the meaning of the S. But these assertions, when so inter- preted, are not theses set up for Proof at all. They are merely our means of registering fundamental assumptions, whether general or special ; and they pretend to be no more than this. Or rather, if in any case they do pretend to capacity for Proof, then their real S or J becomes a very diff*erent one from that which appears on the surface. It is conceivable, for instance, that the expres- Chap. II.] THE KINDS OF UNREAL ASSERTIOX. 12:> sion ' A is A ' iniglit be used to convey some such meaning as " One fundamental postulate of thought is that the meaning of a term is capable of fixation/' — a proposition certainly not merely verbal : or again " A city is, etc." might be used to mean "the ordinary (or the best) meaning of ' city ' is, etc." — a proposition whose proof or disproof might indeed be difficult but is by no means necessarily out of question. These cases, therefore, do not affect the rule in any way, and are only worth mention in order to bring into greater prominence the difference between asserting anything as nvrthy of credence, and merely registering a Postulate in order to let the full extent of our ctssumption be openly known. As to the forms in which Tautology occurs, it follows from this interpretation of its nature that it is chiefly tO' be found in propositions that profess to be in some way explanatory, whether explanatory of names or of facts. Thus, a definition may be circular, as where each of two contradictories (as ' luxuries ' and ' necessaries ') is defined solely by the other, without reference to something known independently of both. Or again, we may pretend to explain the effect of opium by saying that it has a ' soporific virtue.' Or again, we may bravely put for- ward an abstract proposition (a 'law' or 'principle') which on inquiry turns out to need no bravery at all :. as, for example, when we lay down the law that " we ought not to do evil that good may come " — if, as is usual, ' evil ' be defined as equivalent to ' that which we ought not to do.' A proposition of this kind is, no doubt. 124 FALLACIES. [Pakt II. secure against disproof, but only in the same way as a dumb man may be called secure against speaking falsely, or as a suicide may be called secure against the less volimtary kinds of death. Passing by the grosser cases of Tautology, however, ^vhich have been sufficiently illustrated in the earlier chapter,* the chief problem for practical interest, in this danger as in all, is as to the borderland between what is fallacious and what is valid : the drawing of the line that separates tautology from real assertion. The great difficulty in deciding in practice whether a given assertion is tautologous or not, flows of course from the fact that, — outside names with a purely technical or artificial mean- ing, as ' triangle,' or ' city,' or ' fee simple,' — the meaning of a word is never completely fixed, but is subject to fluctuations, slow or rapid, gradual or irregular. If there were some competent authority to which appeal could be made in all cases, the fallacy of taking mere platitude for real assertion could no doubt be pointed out in any case with ease : we should simply turn to our dictionary and compare the meanings there given of the words employed. But as yet, unfortunately, no such universal authority exists. In the first place, when we speak at all of ' the ' meaning it becomes important to decide vjliicJi meaning is the object of our inquiry. For the same word may at the same time possess several different Idnds of meaning^ to say nothing of the different shades (or amount) of * Part I. Chap. II. Chap. II.] THE KINDS OF UNREAL ASSERTION. 125 meaning which it may bear to each individual who employs it. We may distinguish, for instance, as possible objects of inquii*}^ : — I. The meaning that the word does bear, (a) to ' most people ' — vaguely estimated : (/3) to some particular person or class of persons, (1) under the impression that it is the ' correct,' or the only, meaning : (2) As a postulate ; i.e. as a special meaning consciously put upon it as such by the speaker : II. The meaning that the word ought to hear, (a) for convenience in classification, etc. (/3) on historical, etymological, or other grounds. It seems, therefore, not quite satisfactory to say with Professor Bain * that " all newly discovered properties are real predications on their first announcement, although immediately on being communicated the}'- become verbal." In one sense, no doubt, this is perfectly true ; but the expression quoted needs to be interpreted with care. If, e.g. a chemist were to announce that some hitherto sup- posed element is really decomposable, we can hardly suppose that by the fact of such mere announcement all the rest of the world is at once prevented from investi- gating the matter : that the assertion has become a mere truism, that to doubt it is henceforth impossible and to test its material truth absurd. So much may no doubt be safely said as this, — that our ignorance or forgetfulness * Deductive Logic, p. 70. 126 FALLACIES. [Pabt IL of the truth of a proposition, and hence our power of viewing it as questionable, is what makes it real to us. But the point of first importance to notice and remember is, that as a rule when using a name we can only have before us quite a small part of its total meaning, and that we do not habitually remember even all we can : we only remember, or only keep prominently in mind, quite a few of the propositions, regarding the S in question, which we ' firmly believe ' to be true, and as a rule those last discovered are least regarded as forming part of the mean- ing of the name. Hence we may repeat, and with a real meaning, propositions expressing even facts discovered lonor ao-o, — as that the Earth is round, or that sunrise and sunset are due to its revolution. For purposes of Proof the important distinction lies solely between assertions capable of denial with a meaning, and those which to den}^ would contradict the postulated meaning of the name emplo^^ed as S. In our sense, then, the reality or verbality of a pro- position is not determined once for all by the fact asserted having been already discovered, or even being already generally known ; but varies with the purpose for which such proposition is novv' in the given case employed : I.e. it depends upon the jyvomiinence of the already-know^n fact in our minds at the time of using the name or names forming the S of the proposition. So far as the -fact, if known, is reniembered, so far is the proposition verbal, and any attempt to prove it involves of course a circle in •our thoughts : so far as the fact is hidden from memory, Chap. II.] THE KINDS OF UNREAL ASSERTION. 127 SO far there is real matter for Proof If rotundity enters into our notion of the Earth, then it is obviously futile to ask whether the Earth (so understood) is, or is not, round. But that many people find no difficulty in keep- ing the attribute of rotundity entirely absent from their notion of the Earth, habitually building up that notion piecemeal from remembered landscapes, if it may not be inferred a priori, at any rate may be surmised from the existence of the numerous pamphlets — long post- Copernican — catalogued in De Morgan's Budget of Para- doxes. And accordingly the assertion of the Earth's rotundity is capable of being ' real.' How then does Definition help in deciding whether a given proposition is or is not tautologous ? If no absolute and fixed meaning ever exists (except in the case of certain technical terms) how can we establish, in other cases, any general test of tautology ? The most we can reaUy do is to bind the assertor down to a special definition of his own ; to ask for the special meaning which he intends to keepj in view. The meaning of a word is much like the '■' market value " of an article, — a matter to be settled between the parties concerned. We can, it is true, satisfy our sense of justice, or of general responsibility to our neighbour, by accusing him of ignorance of the ordinary meaning (or, if we are very self-confident, of the best meaning) of the words he uses : but such an accusation is a totally difierent one from that with which we are here alone concerned. It afiects, no doubt, our opinion of the speaker's general level of 128 FALLACIES. [Part II. common-sense or of education, but not at all the question whether or no the assertion as made and intended admits of Proof and Disproof. It should be remarked, more- over, that there is often considerable difficulty, even in this way, in obtaining valuable results. People do not as a rule enjoy being cross-examined, — or only in the rare cases where both assertor and questioner are simply anxious to avoid mistakes ; where the claim to oracular dignity on the one side, and the spirit of mischief or obstruction on the other, are wholly wanting. For besides the real danger of platitude, there is an opposite danger to be avoided, namely that of undul}^ and vexatiously stopping an argument to have the terms explained. Without wishing exactly to defend those who made Socrates drink poison, one still cannot help recognising that there is a limit beyond which the laud- able desire for definiteness loses its value and becomes a hindrance and a snare. There is something so fatally- easy in the attitude of a sceptic or mere questioner. Any child can keep demanding explanations, any man sufficiently stubborn can delay the most important truth by pretending not to understand its import. An obstruc- tive policy of this kind requires no great intellectual power, and, when adopted solely for obstructive pur- poses it demands, as much as anything, a rule of urgency. Life is not long enough for exhaustive explanations. . Here at the outset, then, we find two opposite dangers, and no exact rules can be given for avoiding either. The most that practical Logic can do is to set up an ideal of Chap. II.] THE KINDS OF UNREAL ASSERTION. 129 clearness and precision, and to demand that where we fall short of it we shall show fair cause for doing so, — e.g. the need for saving time or for getting work accomplished. The assertion that explanation ought in a given case to be unnecessary can of course be proved like any other. II. Self-Contradiction. Whereas Tautology is chiefly a failing of feeble or timid folk, self-contradiction is a danger to which the rash and immature seem specially liable. As above remarked, it is more often a fault in expression than in thought. Half the Irish ' bulls ' (an Irishman once explained to me) are merely expressions that are too epigrammatic for the slow-moving Saxon mind. And of course, where this is the case, such assertions can always be translated into sober English at the cost of a little trouble or prolixity. If at least, in any case, they cannot be so translated, we have obviously no other means of getting their meaning clear in order to bring them to the test. It is often as painful to translate an epigram as to explain a joke, and a good example of such translation would be rather hard to find. May we say that when an orator once declared that his party had " a majority in everything except numbers," he himself was fully aware of the verbal con- tradiction, and only intended smartly to rap the knuckles of the god Majority ? The answer would depend upon our knowledge of the speaker's mental habits, rather than on any analysis of the words alone. K 130 FALLACIES. [Part II. But paradoxers (as "De Morgan called tliem), though sharing with some great discoverers the honour of being- despised at first by Common Sense, do not always re- semble pioneers in other and more essential points. There can be no doubt that a good deal of self-contradiction is in fact rather due to hastiness or crudity of thought than to any nobler origin. As Mr. Herbert Spencer notices, " the ability of men to compromise between con- flicting beliefs is very remarkable — remarkable, at least, if we suppose them to put their conflicting beliefs side by side ; not so remarkable if we recognise the fact that they do not put them side by side." Mere forgetfulness of our definitions may lead us into inconsistency just as well as into repetition: the main difierence being that whereas one element among the causes of tautology is often the sense of the need for caution, in self-contra- diction this sense seems to be wholly wanting, — often in fact to have its place suppHed by a reckless desire for some new thing at any price. Of contradiction between S and J (as distinguished from contradiction within a term, — which comes more properly under our next head) it may be said, first, that its danger depends to a great extent upon dilution. The simpler and shorter the proposition, the less easy is it to find really dangerous examples. " Twice two are five," for instance, runs no risk of beinsf mistakenlv accepted for a real assertion; and in treating the subject for our purposes we may in the first place cut oft' from consideration the cases which are so broad and €hap. II.] THE KINDS OF UNREAL ASSERTION. 131 ^evident as to amount to a mere jest. Self-contradictions •of this sort are endless, from the heaviest scholastic puzzle to the latest and lightest French or American comic item; and though these may be capable of pro- viding amusement, they are not likely ever to lead to serious error. It follows, however, from our extended view of what constitutes a proposition, that any two (or more) separable assertions, if intended to he taken together, may be viewed as one whole proposition ; and that therefore we may have a case of unreality even where there is considerable interval between the conflicting assertions. In this way a writer, for example, may contradict himself plentifully in the course of a book, the book as a whole attempting to pass off unreal -assertions upon the reader, though the separate items of information may be real enough, and only half of them false. But here again the self-contradiction is com- paratively easy to detect. A more difficult and subtle form of the fallacy arises in the case where no assertion is expressly made, but where a question is raised and debated as if an alternative answer (yes or no) were possible, when in fact one of these answers would be a tautology and the other consequently a contradiction. As an instance of this may be quoted the question ' Can one individual be at the same time a different in- dividual ? ' — a case which one would have thought too glaring even for use as an example, if it had not been discussed at some length and with more or less of genuine perplexity in actual writings. 132 FALLACIES. [Part IL Here, in fact, we begin to get a glimpse of the more serious difficulties in detecting and avoiding this kind of fallacy. Speaking broadly, we have seen that self- contradiction may be due to two, almost opposite, causes,. — mere carelessness, on the one hand ; and on the other hand all that may be included under the name 'epigTam,' a scale that may be made to reach all the way from simple impatient condensation of a sentence, up to the most praiseworthy attempts to rise above the artificial barriers of lano'uaofe. Inconsistencies of this latter kind cannot always be laid to the account of light-brained ' nihilism ' of thought, but are rather due to the spirit of deep in- quiry, casuistry, or over- carefulness. And the form in which the real danger offcenest ajDpears is, as just said, the raising debate upon unintelligible questions. We may, then, very briefly dismiss from consideration the simpler kind of self-contradiction, since here there is only one side to be considered. Every one will probably admit that mere carelessness, or confusion of mind, is a thing to be on the whole avoided, and only requires to be pointed out ; which may as a rule be very easily done. Thus when Bishop Butler, in his 'Analogy,' re- marks that where there is the sligJitest iweioonderance of probability, prudence requires us to act accordingly, and then goes on to say that in questions of gTeat consequence we have to be content with probabilities even loiver than this; it is not hard to see that the joint assertion is of much the same nature as the saying that " One man is as good as another, — and better." So too when a winter €hap. n.] THE KINDS OF UNREAL ASSERTION. 183 on Ethics laid down as an inducement to unselfish- ness the rule that '' the less we think about beinof re- warded, the better for us" it was probably a mere want of consistent thought which led him to overlook the fact that he was tellino- us in the same breath to reofard and not to regard consequences to oiu\selves.* Such slips are however of very frequent occurrence, especially when our case is weak. But the other source of inconsistent thought con- stitutes a standing difficulty. Nor does there seem to be any ultimate and quite satisfactory escape from it. It depends upon the real uncertainty of the line between a given term and its contradictory : the okl standing- difficulty, commonly known by the name Sorites (and more anciently called Soros), — the difficulty of getting a truly ' scientific frontier ' for the names we use. Where there is gradual change from one state to another, or where two opposites, however unchanging, may be viewed as difierent in kind only through being widely difierent in degree, how are we to fix the line between A and not-A? Where, for example, is the line between ' nation ' and ' tribe,' between ' solid ' and ' liquid,' between ' house ' and ' cottage ? ' Or how much money makes a man a ' capitalist ' ? The deeper we push inquiry into the exact meaning of any given name, the more certain it becomes that sooner or later we shall find ourselves approaching the main quicksand of language, — the fact that words neces- * Unless indeed it was merely intended as an argumentum ad hominem. 134? FALLACIES. [Part II. sarily postulate definiteness of outline, while as a fact complete definiteness of outline does not exist in Natui'e. The line dividing each class from its nearest neighbour is in some cases {e.g. between infancy and full age, at law) purely and confessedly a contrivance of our own; in other cases (as between ' good ' or ' tall ' or ' strong ' and their contradictories) purposely left vague because the phenomena either do not admit of, or do not for most purposes require, numerical precision ; in other cases (as between kinds, and even varieties, in Nature) is pro- visionally usefal until doubtful instances shall arise. But it is important to remember (1) that in all cases the line is so far an artificial one that it is we who have made and applied the names, and very often mistakenly, for purposes of our own; (2) that in all cases the line professes to be 'length without breadth,' while as a fact there always remains a doubtful margin.* The gap between the opposed classes is infinitely divisible, is subject to constant subdivision as time goes on, and, though it is being gradually narrowed away and its exact position altered by the acquisition of new knowledge, we can never know that the furthest subdivision is reached. A notable example is afibrded by the breaking down of ancient barriers that is even now taking place in all departments of Natural History as the development theory becomes more fully understood : one of the best- known problems, for example, that has lately risen into high importance, being — If ' man ' has directly descended * C/. Bain : Logic, bk. iv. chap. i. sect. 3. Chap. II.] THE KINDS OF UNREAL ASSERTION. 185 from ' beast/ at what point in the history of such descent does man, as such, emerge ? Various accounts have been given of man's differentia from other animals; among the most popularly known of which, perhaps, are that he is rational, has the power of laughing, the use of language, or of tools, or the practice of cooking his food. So far, then, as these points are themselves definite and clearly under- stood, so far but no further will the employment of any one of them as differentia bring clearness into our notion of ' man.' In other words, we may (and, for the purpose of attaining the highest possible degree of accuracy, must) push inquiry into definitions back and back until we reach quite firm and undisputed gTound. Thus it may be asked what constitutes rationality ? Does a dog reason, however hastily, when having once been scalded he ever afterwards dreads cold water ? Is a sense of the ludicrous absolutely wanting in the monkey, and always present in the man ? What is language but vocal sounds con- veying a meaning, and have not many brutes the use of these ? And so on. One definition rests upon another, and inherits the defects as well as the virtues of its ancestry : if the first link in the chain is faulty all the rest must sufier to that extent. Above aU, the difficulty shows itself, as just remarked, in that the further back we trace man's history the less we find of all these dis- tinctive qualities — the more imperfect reason, sense of humour, language, tools and cookery : and the inference becomes to many people irresistible, that at a still earlier period these attributes were wholly wanting, or if present 136 FALLACIES. [Part II. in the germ, at least as uncertainly recognisable as they now are in the case of 'beasts.' At what period, then, precisely, did man first deserve the name ? If it be ob- jected that owing to the scantiness of the data, man's remoter history is merely conjecture, we will dispense with this instance altogether, and instead of it take 'man' defined as a 'grown-up child :' at what exact period can the epithet ' grown-up ' be applied to him ? Most of us have in our own case a lively remembrance of the difii- culties in fixing this definition. It is, however, not our purpose here to attempt to do full justice to the difficulties of language, or to do more than point out vaguely where some of them lie. Words and their meaning are altogether full of unsuspected dangers, but to treat those dangers usefully demands a treatise to itself When we consider how languao^e has grown, throAvn up at first by savage ancestors living from hand to mouth, framed to meet their simple needs and to express the results of their desultory, unassisted obser- vation ; altered here and there to compromise with the growing knowledge, but often refusing stolidly to admit past errors, and merely adapting itself by some circuitous fiction to the new-fangled notions (as 'planet' now means no longer a wandering star as viewed from the Earth, but a body moving round a sun — thus including the Earth itself); the ignorance of one age taking root and hampering the efforts of the next to see things more nearly in their true relations ; always in fact lagging a little behind discovery, and delaying the birth of the €hap. II.] THE KINDS OF UNREAL ASSERTION. 137 best ideas that are taking shape ; when we consider all this, the wonder is, not that confusion frequently occurs, but that any consistent expression of our thoughts is possible. In fact it is probably not too much to say that we can never be quite secure from all taint of this error. There is consolation, however, in the fact that a good many of our needs too are rough and ready, and that a good deal of what we say is definite enough for the ordinary purposes of life. Where any practical harm can be traced to this difficulty, one business of the logician is certainly to point it out ; and to him it may even be to some extent satisfactory to recognise that there is plenty of work to do. In the case of self-contradiction, as in that of Tautology, much may no doubt be done by inquiring as to the special meaning put upon S hy the speaker. But the artificial character, and possible unsatisfactory results, of this safeguard rise here into greater prominence, since here attention is attracted rather more directly and openly to the defining line itself; and it must be admitted that, as things are, it is often unfair (or let us say, unpractical and obstructive) to press for exactness of line. There is some value even in vague assertion, — at least where, as often happens, nothing better can be obtained. While allowing that until the contradiction is removed by some means, Proof or Disproof in any strict sense is impossible, it is well at least to recoomise that self-contradiction is not necessarily so flat and unprofitable as Tautology. Often, of course, it flows from mere love of paradox, often 138 FALLACIES. [Part IL also from haste or inattention : but sometimes it will be found that existing language, and not the speaker, is most to blame. And on such occasions the paradox may usually, with sufficient patience, be translated into a real assertion ; or else may be accepted easily, and tasted, in an after-dinner frame of mind. III. Meaxixgless Term. The third class of verbal assertions is far less simple in character than the two just discussed. To treat it fully, in fact, we should have to exhaust the question as^ to the limits of our power of defining efiectively : and this can, of course, not be attempted. There may, however, be some use in showing where that difficulty lies. But in the first place any term may be meaningless either (1) simjdy, — i.e. through want of definition; or (2) by self-contradiction, — as where, in a complex term^ opposed meanings are verbally combined. This second case is so closely allied to the kind of verbal assertions discussed in the preceding section, that not much remains to be said. The diff'erence in fact is chiefly a grammatical one ; instead of saying ' A belongs to the class not- A, with the differentia B' {e.g. 'man' belongs to the class 'not-man' with the differentia ' evolved ' or ' Life is a gradual death ') we here say ' A which is not-A is B ' (e.g. ' Unconscious hypocrites are always the worst ') or ^ B is A which is not-A ' {e.g. ' A Chap. II.] THE KINDS OF UXEEAL ASSERTION. 139 continent is an island which, through mere difFerence of degree in size, is not an island ; ' which assertions might be resolved into double, or joint, propositions, one member of which contradicts the other. But there is some use in treating these self-contradictory terms separately, since the junction of incompatible members into one term has, on occasion, certain excuses which seem to apply more specially to this case than to that of contradiction between S and ^. In the first place, when a term has from any cause lost its original meaning, there is of course no contradiction in combining with it another which contradicts the original meaning but leaves the acquired one free. We may, for example, use the expression ' bad goods/ or again ' dry humour,' with complete reality of meaning : nor, in a sentence such as " They overlooked the boundless field that was before them within the legitimate limits of the Science," does the solecism in- validate the assertion made. Conversely, too, a legitimate excuse for such propositions may be simply the desire to call attention to the wrong use of a name, as in 'The present Government is no Government at all/ or, ' If your facts are false, your inference is useless.' And in the second place, though such an expression as a 'round square ' would be generally ruled out of court as meaning- less, it seems to be quite allowable to speak of an ' irre- gular square,' or of ' a globe which is not quite globular. In two distinct cases under this head there is a recog- nised license to combine terms really contradictory; — (a) where the qualification is only slight, and the ex- 140 FALLACIES. [Part II. pression is intended to be merely rough and ready, — as in the instances just given; and (b) where the intention is to indicate a mean between opposed notions, as in ^Liberal-Conservative' or 'blue-green colour,' or 'dead- alive.' Considerable caution, therefore, should be exercised before accusing a complex term of being really suicidal : so much must be allowed. But when all possible ex- ■cuses have been made, there remains a residuum of cases which are purely fallacious, and which are by no means so rare as might be supposed. No doubt it is chiefly through our power of fluctuating unconsciously between two difi*erent beliefs that these ' beliefs ' justify themselves to the believer: each separately is seen to convey a real meaning, and it seems to be dimly supposed that since each is a positive belief (how many errors that word ' positive ' has to answer for :) the total result cannot in the nature of things be a non-entity. Indeed, this defence has been sometimes almost openly put for- ward. No doubt where the sole object is to find some form of words ' true ' which is at the same time admitted to be ' incomprehensible ' we have a contradiction already as a starting-point, and it is perhaps only natural that others should be needed to support it : but natural or not, such a process is apt to confuse people's minds as to what is meant by belief at all, and to blunt the edge of their conscience towards themselves. Possibly this is one reason why the habit of delighting in mysteries retains its hold so lono-. CiiAP. II.] THE KINDS OF UXEEAL ASSERTIOX. 141 Turning now to the case where a term lacks mean- ing for want of being defined, we may distinguish in the first place the two varieties : — (a) where the term simply has not yet been defined by the speaker ; and (h) where a definition has been given, indeed, but one which does not really explain. The remedy in the first of these cases is of course simple enough ; in fact, it only needs mention by way of introduction to the second case. It is clear that when we say ' X is good,' or ' every man is x,' there is no subject- matter for proof until the meaning of the x is declared : and that if it can be declared this had better be done as soon as possible. What then are the limits to our power of giving names a ' meaning ' ? And how can we avoid false security in the matter ? Since for definition it is necessary to refer to some higher class (Genus), it is clear in the first place that the most general notion of all — whatever that may be — cannot in strictness be defined. A sumimwi genus, indeed, is usually taken to mean something much less extended than the one highest genus of all, namely to mean the highest in any given series, — which series may of course be a quite arbitrary selection of our own. Thus in the series 'Mineral, rock, stratified rock, limestone,' 'mineral' would be the summum genus, although a higher class, namely ' material substance,' might easily be added to the series, and beyond that again the class ' nameable thing.' It is therefore incorrect to say that no sumniwii 142 FALLACIES. [Part II. genus is definable, — unless we are speaking only of the one highest of all ; or unless we consider the inexplicable nature of this ultimate notion to vitiate all other general names, since all may be traced up to it. In absolute strictness there seems, in fact, to be no escape from this difficulty. It is, no doubt, always theoretically lawful, though not always practically expedient, to push inquiry into the meaning of a name back into Metaphysics, — just as it is possible to demand any other kind of ultimate explanation. Any objection to such inquiry can only rest on the plea of practical needs ; and it is not easy to say how far such plea itself will bear stretching, — for who is to decide that our view of practical needs is sufficiently long-sighted ? It certainly seems as if — to quote Prof Bain * — " the highest universe of all must contain at least two things, mutually explaining," and that our highest definitions must accordingly be merely circular. Short of this ultimate circle, or assumption, however, we can of course take care to avoid all narrower circles in defining. The only other kind of delusive definition that need be noticed in this connexion is that sometimes called ' defining ignotum per ignotius/ as where a writer explains the meaning of ' miracle ' to be " an abnormal exercise of constitutional sovereignty on the part of the very divine Ego, in respect of the subsistere of the cos- mical selfhood of the metamorphosed Non-Ego." Here we can of course either take the requisite pains to make * Deductive Logic, p. 59. €iiAP. II.] THE KINDS OF UNREAL ASSERTION. 143 out the real meaning intended, or we can wait for some more easily intelligible information. But until such additional process has been performed, any proposition containing ' miracle ' as S or ^ remains obscure. As regards the whole question of the need of definition, it should be remarked that the mere fact that the terms have not yet been defined, or have been imperfectly defined, does not of itself necessarily deprive an assertion of all ' real ' meaning. If this were so, indeed, the con- veying of information would be even a more lengthy and troublesome process than at present. It is only when the need is felt, as such, by the person addressed, that the assertion can fail, in this way, on the ground of unreality : for where the audience put a ivrong meaning (i.e. one not intended by the speaker) on the terms employed, there is misunderstanding, perhaps, and there may be fallacy on one side or the other ; but inasmuch as the audience do put some meaning on the assertion, it is real to them. lY. Unreal Assertion: Concluded. We have seen, then, that against the fallacy of taking an unreal proposition for a real one, the remedy in all cases is to be found in definition of the terms employed ; and that everything depends upon the special meaning given to them by the assertor ; since any apparent tautology or contradiction may have its fallacious character removed, any unknown meaning may be made 144 FALLACIES. [Paet II. known (within the limits indicated above) by such special explanation. We have seen, too, that Tautology is intimately connected with the fallacy of Petitio Prin- cipii, or circular proof, while self-contradiction, except when merely used to condense a real proposition, is really a case of inconsistency, — sometimes due to mere careless- ness, sometimes to the fact that lines of distinction in nature, on the preservation of wdiich all consistency depends, are artificial contrivances of our own, which do not exactly fit the facts, but can only be roughly justified. And as regards explanation of the meaning of a term, we must admit, I think, that there is a point beyond which any attempted explanation becomes unreal ; and, hence, that the distinction between reality of meaning and mere verbahty has a value only so long as we keep away from the deepest difficulties. Before leaving the subject, there are one or two points to be noticed as regards unreal assertion in general rather than any special form of it. First of all it may be well to distinguish clearty between verbal assertion (i.e. tautology) and verbal questions, — as where a disputed point is said to be "merely a question of names." Whately has expressed as concisely as any one the distinction between verbal and real questions, — "If it . . . appear . . . that the opposite sides of a certain question may be held by persons not differing in .their opinion of the matter in hand, then that question may be pronounced verbal, as depending on the different senses in which they respectively employ the terms. If, Chap. II.] THE KINDS OF UNREAL ASSERTION. 145 on the contrary, it appears that they employ the terms in the same sense, but still differ as to the application of one of them to the other, then it may be pronounced that the question is real, — that they differ as to the opinions they hold of the things in question." " If, for instance," he continues, " two persons contend whether Augustus deserved to be called a 'great man,' then if it appeared that the one included under the term 'great' disinterested imtriotism, and on that ground excluded Augustus from the class, as wanting in that quality, and that the other also gave him no credit for that quality, but understood no more by the term 'great' than high intellectual qualities, energy of character, and brilliant actions, it would follow that the parties did not differ in opinion, except as to the use of a term, and that the question was verbal. If, again, it appeared that the one did give Augustus credit for such patriotism as the other denied him, both of them including that idea in the term great, then the Question would be Real." In short, there may be a real assertion made about a name just as well as about any other S ; and often this is made in so con- fused a fashion that there is difficulty in seeing what is intended. Of course, where two persons really agree about the actual qualities possessed by Augustus, and one says, 'these qualities, good and bad together, on the whole entitle him to a place in the class of great men,' while the other says ' precisely the same qualities do not entitle him to the name,' the former really asserts, while the latter denies, that (in their respective opinion) the L 14G FALLACIES. [Part II. best meaning of ' great ' includes that particular mixture of qualities which both allow to belong to Augustus. But the difficulty in the matter usually flows from the fact that neither party to the discussion knows very clearly either what qualities he does actually suppose Augustus to possess, or what qualities he does actually include within his meaning of the name. All that we are concerned to notice, however, is that the confusion — if confusion there be — is not that of mistaking an empty form of words for a real assertion, but of mistaking one real assertion for another. The question whether or no a given definition is a good one may indeed be properly called a ' verbal question,' but it is clearly not a question without meaning or without important consequences. An assertion about the meaning of a name, when under- stood as such, is not a verbal assertion in the sense of being incapable of Proof. Another question, of side interest, may be just mentioned for dismissal. Since the reality of an asser- tion is coincident with its capacity for Proof and Dis- proof, are we to distinguish degrees of ' reality ' according to the completeness and definiteness of the possible test to which difierent real assertions are liable ? It is obvious that assertions vary very much in this respect. Is, for example, the assertion, ' You will find him in the next room,' more real (because more capable of being brought to a conclusive test) than an assertion regarding the details of the distribution of ice over Europe during the last Glacial Epoch ? Certainly not. As I have intended Chap. II.] THE KINDS OF UNREAL ASSERTION. 147 to use the term ' real ' throughout, there are no degrees in it, — no standing-room between real and unreal. If it be desired to express the distinction just spoken of, there are other words, — such as 'verifiable' — which would -answer the purpose better. By ' capacity for Proof and Disproof was not meant the degree of ease or certainty with which the assertion might be established or over- thrown, but the mere fact that there is at least no absolute impossibility, in the assertion itself, that relevant evidence, weak or strong, should ever be produced. The unreality ■of a proposition is not in any way connected with the mere inaccessibility of Proof and Disproof, but with their total inapplicability. To establish or demolish some ' real ' hypotheses may be as difficult as to establish a dynasty, or to remove a mountain ; but to support or disprove an unreal proposition is as impossible as to support a dead Pretender, or to remove a hat from a head already bare.. CHAPTER III. THE BUEDEX OF PROOF. Supposing a Thesis sufficiently free from the taint of unreality, two other main objections or opportunities for attack remain. And the first of these, as already said, is the objection that no proof has been attempted, — that the thesis is a mere assertion, standing entirely without support or evidence. Evidence, it should be at once noticed, is not here used in the more restricted sense that would contrast it (e.g.) with ' authority ' or with ' hearsay ; ' but as broadl}' as possible, so as to include the weakest kinds of evidence as well as the strongest. It is just as truly an argument, for example, however fragile, to claim that a given assertion is true because it occurs in a certain book, or was made by a certain person, as any other ' reason given for belief would be. The contrast between supported and unsupported assertions does not depend on. the strength or weakness of the reasons, but on whether or not reasons of any kind are given. The full question as to the burden of Proof is sufficientlv confusino- in Chap, ni] THE BURDEN OF PROOF. 149 itself, without our introducing further entanglements jDrematurely. Two cases are to be distinguished : — (1) Where an assertion is put forward simply as ' self-evident/ or free from all need of Proof; and (2) where the assertor supposes (or tries to lead his audience to suppose) that his sole concern as assertor is to frustrate, one by one, attempts at Disproof made by some one else. The first case need not detain us long. For while fully admitting that without some ' self-evident ' truths, no Proof of any assertion would be possible, it can hardly be denied that what seems self-evident to one person may seem to another to stand much in need of external support. And since the whole meaning of the Need of Proof is need as felt by the audience, and not as the assertor happens to think the audience ought to feel it, they, and not he, must be the arbiters. If the assertion is not to them self-evident, they are under actual dis- ability to believe it until external evidence is produced. I am speaking, of course, of genuine belief, intelligent and rational, and not of mere voluntary acceptance of a formula, as an act of obedience or otherwise. It may, indeed, often happen that the grounds are so numerous, or have been so long forgotten through disuse, that their production would be difficult or impossible. Deep-lying and complicated beliefs, especially when illumined by emotion, or when the more physical element in them is prominent, are very liable to this difficulty, — the beliefs {e.rj) on which our likes and dislikes of persons 150 FALLACIES. [Part 1L or of systems, or of courses of action, are founded. But none the less unsatisfactory must such beliefs remain to an audience not already convinced, until the grounds can be openly brought forward and examined : and our concern is, of course, entirely with the point of view from which the assertion is still a tlicsis, and not with that from which it is a firmly established conclusion. Until the grounds can be examined no test is possible : the assertion may or may not be true, for all the audience can say. Against the honest objection, ' This is not self- evident io me' there is clearly no appeal ; and no remedy except through the production of real external evidence. The second case, however, is far more complicated ; sufficiently so, in fact, to have notoriously confused the mind of no less a logician than Archbishop Whately. This- is another of the numerous cases where statement is easy but application difficult, and where the whole practical value depends on the application. Stated shortly, the fundamental rule is that "He who asserts must prove ; " * and so long as an assertion is undisputed^ difficulty cannot arise. But the chief source of real per- plexity lies in attempting to keep a clear line between denying a thesis, and merely reserving judgment,*!- or * Even in Law tliis maxim seems to be fundamentaL Cf. Sir Jas. Stephen's Digest of the Law of Evidence, 3rd ed. pp. 100 ff. "The burden of proof as to any particular fact lies on that person who wishes the Court to believe in its existence" (art. 96). See also Articles 93 and 95. t Hence De ]Morgan and others have preferred to treat displacement of the burden of proof as a case of Ignomtio Elenchi. See also the examples at p. 188 of this book. Chap. Ill] THE BURDEN OF PROOF. 151 between disputing an argument and merel}^ asking to have it expanded and made satisfactory. This, at least, is one of the points at which confusion is in the first place most apt to creep in. It is obvious that an unsupported assertion may or may not be true, and it should be carefully noted that the absence of produced evidence, — or even the absence of the possibility of pro- ducing evidence, — is a very different thing from Disproof. Where nothing is said either for or against a thesis, its truth simply remains an open question ; and where nothing ca n be said, the doubt is only more permanent in character, not otherwise more triumphant. The objection, ' This is bare assertion,' does not attack directly the truth of the assertion in question, but attacks the sup- position that such truth is as yet established. Hence assertions which are confessedly mere suggestions escape unscathed, since all the harm which the doctrine of the burden of proof can do to them is done already, and willingly, by their assertor himself It is only where an assertion is definitely made that the grounds of belief can be demanded with any meaning. The simple statement of the rule, that "he who asserts must prove," needs, however, certain explanations before it can be accepted in its entirety : and the best way to bring these forward seems to be by pushing the simple rule into its extreme cases. In the first place, then, if the burden of proving lies always on him who asserts, it is clear that whoever asserts that a thesis is false must accept a burden too: and also that he who 152 FALLACIES. [Part II. asserts a reason as sufficient, or claims that it is certainly insufficient, is in exactly the same position. These three cases do not present much difficulty, and will, I think, be readily admitted by all. Suppose, for example, I assert some article of popular faith, — such as that women ought not to enter the learned professions ; my audience may either accept the assertion offhand, or deny it offhand, or be content to ask for reasons. In the first case the burden passes simply unnoticed. In the second case, the audience, as assert or s accept a burden of their own. In the third case the burden rests on me, just as it would if I pro- claimed the most startling novelty. For the doubt may be suggested that though widely believed, the assertion is possibly without secure foundation. That is to say, two courses are now open to me — unless my audience are unusually feeble disputers — either to take my stand on the bare unsupported assertion, and so leave my questioner certainly unconvinced ; or else to attempt to remove the burden by producing the best available reason. If I adopt the latter course, it is clear that any permanent removal of the burden depends on the strength of the evidence brouofht forward. But the difficulty is, that at every stage of an argument the line between interrogation and flat denial is often hard to preserve, and a sophist, when pushed by awkward ques- tions, will always try to shift the burden upon his questioner. Thus, I may perhaps argue, in favour of women's restrictions, that "one needs to know that a Chap, III.] THE BURDEN OF PKOOF. 153 given innovation is not dangerous, before proceeding to say confidently that the time has come when it may be made." Very true, but I am now shifting my own ground, and trying to fasten on my questioner a positive assertion which he has never made. I have quite ignored the third alternative that lies between 'saying confidently that the time has come ' and my own equally confident original assertion that such time has not yet arrived; namely, the alternative of holding my tongue, or at least of softening assertion into mere suggestion and asking modestly to hear the possible objections. If my opponent understands the doctrine of the burden of proof, he naturally proceeds to point out my mistake. We need not develop this particular argument any further, since enough has been shown to illustrate the point imme- diately before us. Whatever reasons I may produce, so long as difficulties in seeing their cogency are genuinely felt, it is clearly my concern to remove them if I can. Secondly, it seems undeniable that even the most cautious sceptic cannot escape a certain responsibility. The burden of proof must rest on him who asserts that an assertion is doubtful, just as much as on him who asserts it true or imtrue. But two very different mean- ings may be distinguished, in calling an assertion doubtful, — the one, that I (the objector) feel a doubt ; the other, that you (the assertor) ougld to feel one. If I merely intend the former of these two meanings, my responsibility (which may still be fully admitted) applies not at aU to the point at issue, but to a matter of side- 154? FALLACIES, [Part II. interest, — the question whether I am, or am not, honest in making the demand. It is conceivable that I shall not take any pains at all to avoid the imputation of quibbling. The sceptic may in general be more easily content to leave the other side alone. "VVe are seldom as anxious to prove our ignorance or obtuseness as to prove our knowledge or insight, and hence the sceptic may cheerfully neglect such burden as falls on him. And, in any case, the course he chooses to take in this matter does not affect the point at issue between the parties. Lastly, it follows that even he who asserts the most widely accepted doctrine cannot escape the ' burden ' of supporting it by reasons. The burden of proof rests, for example, on those who maintain the theory of gravitation or of the rotundity of the earth, just as truly as on any- one who should set up for his thesis the denial of either : the difference is that in asserting such truths as these the burden is apt to pass unnoticed, from the fact that the evidence is strong enough to shift it easily, while in denying them the burden might really be felt as a serious weight. And this leads us to speak of the chief practical difficulty in the matter, — the point where Practice demands that inquiry shall be stifled. Whately's doctrine of the burden of proof* was brought forward, as his readers will remember, partly for the purpose of annihilating Infidelity by a short and easy method : but it is none the less worth considering in itself, since the confusion into which he feU is a verj- * Rhetoric: Part i. chap. iii. § 2. Chap. III.] THE BUEDEX OF PEOOF. 155 excusable one, though probably not often effective against the more modern kind of Infidel. " There is a Presump- tion" he writes ''in favour of every existing institution" . . . "Christianity exists; and those who deny the divine origin attributed to it are bound to show some reason for assig^ninor to it a human orio-in." Of course, there is " a presumption in favour of any existing institu- tion." Since it already exists, any one wishing to abolish or alter it must, of course, in the first place make an assertion to that efifect, and also produce his reasons, — or else nothing will probably be done. But a pre- sumption of this kind is a very different thing from a presumption that an assertion made by an existing institution is true. Various forms of Paganism exist ; are we therefore to believe without inquiry whatever their followers may choose to assert about them ? No doubt this verbal ambiguity was complicated also with another confusion, — that between denying and question- ing the divine origin of the institution : the Archbishop very naturally failed to put himself exactly in the position of a real unbeliever, and was considering only the case of one who should set out to prove to a believer that his belief was misplaced. In such a case certainly the burden would in the first place lie on the infidel, as being the person making the assertion. But it is surely not often that infidels are so generous. Or rather, to put it more fairly, they have not the same reason to be anxious to convert believers as the latter have (ad- mittedly) to convert them, — since no infidel pretends to 15G FALLACIES. [Part II. believe that a Christian will miss incalculable benefits on account of his Christianity. Hence it is the unbelievers who really take the unassertive position, not professing to have any valuable information on the points directly in question, which information they are eager to impress on the other side ; but quietly willing to examine (with minds, at least professedly, open and candid) any asser- tions brought forward and supported. It is the believer whose mind — even on his own showing — is no longer open : he it is who claims to have already weighed all the arguments and arrived at a firm decision ; who claims the possession of valuable information which he is burning to impart, — information so valuable that, except on the plea of extreme difficulty in producing unexploded reasons, it seems almost cruelty on his part to be content with bare assertion. Certainly, any one who should set up, to a believer, the thesis 'Christianity is of purely human origin' must bring forward his reasons for that thesis, or else expect the believer to remain unshaken : but on the other hand any one who Bets up, to an unbeliever, the thesis ' Christianity is of divine origin ' is in exactly the same position. Professed ignorance, however often a mere pretence, and however often (when real) a sign of culpable indifference or of pitiable want of power, is also the natural and normal position of the anxious mind, until anxiety is removed by the production of evidence that at least seems sufficient. And here it seems in place to notice that the real difficulty as to the burden of proof is somewhat deeper Chap. III.] THE BURDEN OF PEOOF. 157 and more serious than might be supposed either from a bare statement of the fundamental rule, or from a rough description of the cautious attitude in one or two rather artificial controversies. In Loo^ic altoo-ether there is often a danger of treating words as more than counters, and so of giving an air of wordiness and trickery to the results attained ; and in all this matter of the burden of proof the danger in question is perhaps especially active. It is not only in disputes and verbal arguments that the correct placing of the burden m important, but wherever we are called upon to judge whether all objections to an assertion have been properly taken into account ; as where, for instance, we have to- decide between accepted theory and awkward fact. The difficulty at last resolves itself into that of saying what shall constitute ' practically conclusive ' prejudice. How far, for example, are we 'bound to explain away ' a so-called fact ? If we already have an ap- parently well-established theory regarding, say, the impossibility of corpses reviving, or of * spirits ' holding communication with the living, or even if our theory goes no further than to deem some given behaviour of mind or matter a physical impossibility, what is the rational attitude towards a claimed miracle, or ghost- story, or mere narration of marvellous fact for which no explanation is ofiered ? We need not now, of course, hesitate at any purely verbal obstacle. We may say, if we like, that the bare notion of a ' miracle ' involves a contradiction 158 FALLACIES. [Part IL in terms ; tliis merely means that if we were sufficiently wise there would be no room for wonder. But that the blind should receive their sight in an unexpected manner, or that a conjuror's performances should lie beyond our powers of explanation, involves no contradiction or im- possibility, except on the assumption that we have already exhausted all there is to learn. When Mr. Venn * says that " few men of any really scientific turn would readily accept a miracle, even if it appeared to happen under their very eyes," what is meant is that, though surprised at first, they would either " soon come to discard it afterwards, or so explain it avray (i.e. bring it under known laws) as to evacuate it of all that is meant by miraculous." The rough and ready doctrine may be called that of the existence of ' fair presumptions,' whether left indefinite, as in common parlance,! or — as in law — * Logic of Chance, p. 450. t And perhaps in Science. Thus Professor Tjndall, in speaking {Floating Matter of the Air, p. 305) of the experiments to disprove Spontaneous Generation, claims that whereas life in the sealed test- tube may always be due to errors of manipulation, the absence of life " involves the presumption of correct experiment." The difference between scientific 'presumption' and unscientific is, however, worth noting. By this claim it is not meant that a single failure to find life in certain conditions is sufficient at once to remove all doubt : the jDatience with which Professor Tyndall's own full investigation was ■conducted bears witness to the contrary. But it is merely claimed that where the instances for and against are equal in number, the evidence is " not equally balanced," and that " as regards the fruitful flasks [a careful inquirer] would . . . repeat the experiment with redoubled ■care and scrutiny, and not by one repetition only, but by many, assure himself that he had not fallen into error." Chap. III.] THE BUEDEX OF PEOOF. 159 defined to some extent by set rules. It amounts, in brief, to this, that where there exists a ' fair presumption ' in favour of a belief, or where a belief is in harmony with prevailing opinion, the assertor is not ' bound ' to produce evidence, but that whoever doubts the assertion is bound to show cause why it should not be believed. The value of this procedure, as a short cut or as a weapon against mere obstruction, must be apparent at once. A Law Court, for example, one of whose unavoidable limi- tations seems to be the occasional necessity of sacrificing the individual to the average — i.e. of resting content with caring not at all about the rainima of justice — may derive on the whole great advantage from such special rules, at any rate as regards speed in getting through its work. Thus, a person found in possession of stolen goods soon after the theft, is presumed to be the thief, and has to prove innocence although he is the accused party. If a married woman in this awkward situation proves that she stole the goods in the presence of her husband, but asserts that he compelled her to steal them, she escapes the burden of proving this latter assertion, since the Law considers it self-evident.* And every rule that dictates in general how given facts or admissions shall be con- strued, is an example of this procedure. Convenient, how- ever, as such a plan may be where there is an authority competent to frame the rules, it is obvious that out- side certain artificial institutions, existing for some * Cf. Stephen. Digest of the Law of Evidence. Articles 95 and 96. C'f. also De Morgan : Formal Logic, p. 261. 160 FALLACIES. [Part II. special puri^oses, no such authority exists. Argument in general cannot undertake to be bound by what this man or the other, or any body of men, may happen to- consider a ' fair presumption.' Logic shrinks into mere cleverness under the bondage of Rules for Debate, and dogma cramps the reasoning powers. If, as Whately claimed, those who put forward assertions in harmony with ' prevailing opinion ' were to be altogether exempt from givino' a reason for the faith that is in them, or if those who bring forward facts in opposition to pre- vailing opinion were to be thereby ruled out of court at once, with whom would rest the right of deciding what assertions and facts really come within such privilege ? Even an Archbishop, it must be acknowledged, might fail to catch the precise moment when a struggling truth reall}' begins to ' prevail : ' and ordinary folk, who only desire to follow the safest leader, have often the greatest possible difficulty in deciding which party shall claim their allegiance and support. At least it might very well happen that any two people should fail to agree as to what is the prevailing opinion, — much more, as to what it ought to be. Perhaps then we must rely upon the submissiveness of our audience ? Such a view comes, near being an ' Idol of the Cave.' Rather, it should perhaps be called an Idol of the Hothouse, — a tender plant, that can never thrive long in the open air. Common-sense has, of course, a very justifiable liking for short cuts wherever practicable. Rough and ready rules for interpreting facts have a value certainly^ Chap. III.] THE BURDEN OF PROOF. 161 even outside a Court of Justice. But there is all the difference between using these as our servants, and allowing them to become our masters. So long as they are employed confessedly as a mere apparatus for saving- time at the cost of some exactness, no harm is done : for where the thesis is more than usually important we can take more than the usual care. But if we suppose that whenever a bold assertor takes refuge behind his two- thirds majority, the spirit of free inquiry ought at once to apologise tamely for having dared to put awkward questions or to bring forward awkward facts, we have only ourselves to blame for the loss Ave suffer. The assertor who shirks inquiry can always be shown to be shirking, by the simple process of putting the question clearly and letting others see that it remains unanswered. Both the practice of relying on prevailing opinion then, and also readiness in accepting subversive facts as undeniable, have a double edge, and need a little care in using. If Science la^'s dowm a theory, or Guess- work a doctrine, conflicting facts or probing questions may both be awkward. But a question differs, after all, from an asserted ' fact ' in one very important particular, — it carries no burden itself A ' fact ' stands in need of evidence, whether or no it conflicts with theory : and clearly, the firmer the theory the greater the caution required in accepting evidence for the conflicting fact. We find, no doubt, very often, that the ease (or difiiculty) with which a ' fact ' is accepted depends more on pre- judice against (or for) a given theory than on the presence M 1G2 FALLACIES. [Paet IL (or absence) of undeniable support for the fact itself: but even where the fact does rest on evidence of its own, we should not forget that in judging that evidence also there is involved a very large amount of rough and ready presumption ; that in all observation there is involved a certain amount of inference. To say that the supporter of a theory is in any way ' bound to explain away' a given supposed fact, may be just as high-handed a proceeding as for the theorist to condemn the fact unheard. It must be proved to be a fact before it has any bearing on the theory; otherwise, it is clearly a case of "so much the worse for the facts." There can thus be no law laid down which shall settle all disputed cases « p7'iori : we can only come back, after all, to the one fundamental principle that wherever proof is demanded, we must either be prepared with sufficient evidence, or prepared to see the hopeful proselyte un- convinced. Shortly, we may sum up the worst of the difficulties surrounding the question as to the burden of proof as due partly to the unfortunate ambiguity of the expres- sion itself, and partly to an endless source of trouble, — the practical need of striking some balance between faith and hesitation. The mere ambiguity of the expression may be met by remembering that the ' must ' of the rule is only sanctioned by the assertor's eagerness to convince his audience ; and that to ' assert ' must therefore be defined to exclude that milder type of assertion where we^either state an opinion as a fact in our mental history. Chap. III.] THE BURDEN OF PROOF. 163 or tentatively and with a view to learning what the objections to it really are. In Logic, then, when we speak of the burden of proof, we are not speaking of some artificial law, — some merely legal, or perhaps Parliamentary rule, — with artificial penalties attached to it. No doubt much that has been "svritten, even in logical works, has been written with some such view. For centuries after Aristotle's time, argument appears to have been regarded as a kind of intellectual game, in which each player might try to obtain what advantage he could, so long only as he obeyed the rules laid down. The microscopic ingenuity with which the Schoolmen carried on the elaboration of these rules was well worthy of a better object. But here, at any rate, we are free from any such limitations. No penalty follows the misplacement of the burden of proof, in the strict sense in which we here use the expression, except the natural consequence that the assertion remains untested, and the audience therefore (if inquiring) un- ■convinced. To lay the burden on another, therefore, is not to demand Proof at the point of the sword, but rather to request it as a favour. There is no ' obligation ' on any one to prove an assertion, — other than any wish he may feel to set an inquiring mind at rest, or to avoid the imputation of empty boasting. It is a natural law alone with which we are here concerned, — the law that an unsupported assertion may, for all that appears, be either true or false. And a corollary is that the more intelligent the audience the less easy wiU it be to pass 164 FALLACIES. [Part II, off upon tliem a bare assertion under the pretence that they are in any way ' bound ' to disprove it or explain it away. And, as regards the practical need of recognising fair presumptions, the best key seems to be to keep quite clear the fine distinction between two really different doctrines ; one, the firm foundation of all the cogency that Proof can ever attain, and the other the tottering- shelter for boastfulness that fears to be found out. The former may be described as the doctrine that before we can safely accept a given theory we are bound to discard all possible rival ones : the latter the doctrine that before we can presume to decline to accept a given theory, we are bound to provide an efficient substitute. Nakedly stated like this, perhaps, their difference is easy enough to see, but there are aspects (or uses to which they may be put) under which they become rather more difficult to keep distinct. Thus, for example, a theory occurs to us as satisfactory, and instead of actively trying to find out all that can be said against it, or what rival theories are possible, we entitle it a ' provisional theory,' or a ' work- ing hypothesis,' and then proceed at once to dismiss all doubts from our mind. I am not, of course, saying that this provisional contentment is always to be avoided, — only that there is more of it in circulation than would, perhaps, be the case if our notions of the burden of proof were kept quite clear. The inclination to believe without inquiry has long ago become a confirmed habit of the human race; dating, no doubt, from the times when Chap. III.] THE BURDEN OF PROOF. 165 sheer necessity — poverty of knowledge — led us to invent our facts : while the use of provisional theories as such, ■ie. with full recognition of their imperfections, seems to be an art which, with all our good intentions, we are only slowly learning. Further, since where no Reason is given the Thesis may be either true or false, a second corollary is, as already noted, that the absence of a reason given is no conclusive condemnation of the assertion made. Whether it should even raise a presumption of weakness depends, of course, •on circumstances. It would not do so, for example, where the assertor, without any motive for untruth, is merely relating unmistakable facts within his own ex- perience, — as that he came down by the Midland Rail- way, or that he usually buys his books at a certain shop. As a broad rule, in fact, we might say that the need for •proof depends on three classes of circumstances, — the likelihood of mistake, the likelihood of falsification, and the importance of the assertion made. Where all three of these are at a minimum, the need for proof is at a minimum too : where any one of these rises into pro- minence, the demand for proof begins. Thus the asser- tions (1) that I saw a ghost, or, (2) that defendant was elsewhere at the time the deed was committed, or, (3) that the earth will be baked to a cinder in 1897, would be generally felt to stand in need of evidence. Closely bound up with the need of Proof is, of course, the pre- sumption of weakness which its continued absence is apt to raise. That is to say, where the need is strong the 166 FALLACIES. [Part IL call is usually audible ; and deafness is known to be often largely voluntary. But so far as appears, no general rule can be framed for judging of the strength of such presumption in a given case. Even distinct unwilling- ness to produce the grounds of belief is an ambiguous sign, — much more so is the mere absence of evidence,, however strong the call for Proof Unquestioning faith, for example, — the failure to see any necessity for ex- amining the grounds — is often a cause of unsupported assertion. So is the simple desire to avoid trouble. So is distrust of our audience. So again, as already noticed, are the mere number and extent of the reasons, and our fear of failing to do them justice. Insecure faith — the fear of losing the belief if strict inquiry should be made — is only one cause among many : nor, even if it were the sole explanation of such unwillingness, would the sign be beyond dispute. For misplaced timidit}' in our beliefs is not altogether unknown. Much the same applies to the case where the assertor does produce evidence, time after time — either old argu- ments or new ones — and yet every time such evidence is found, by the best tests obtainable, to be insufficient. The practical difficulty is that of saying where our rooted distrust shall beoin. The failure of argument, however long continued, never indeed amounts to conclusive dis- proof; since either the real difficulty in producing' the sufficient grounds, or the assertor's want of skill, may be to b'ame. But it can hardly be denied that the pre- sumption does in certain cases become very strong Chap. III.] THE BURDEN OF PROOF. 167 indeed, — quite sufficiently so for many rough practical purposes. Since, however, there does not yet appear to be any means of generalising the cases satisfactorily, it seems best only to notice this as a standing difficulty in the complete practical theory of Proof, at present beyond the reach of anything more definite than what may be called a kind of logical tact. It is, however, a side issue, and does not affect the 'burden of proof itself It is quite possible, therefore, to be over-pedantic or vexatiously unpractical, in demanding Proof, just as in demanding explanation of the meaning of a term. And in this case as in the former the question whether a given demand is on the whole conducive to the interests of practice may indeed itself be raised and answered, but otherwise lies quite outside the scope of our inquirj^ In strictness any assertion may have its grounds called for; and until they are produced and examined, the assertion remains untested. Whether practical con- venience decides that in certain cases the assertion may safely be left in this state, is another matter. We are only concerned with those assertions which are already erected into theses; i.e. which have, in the opinion (mistaken or not) of the audience, sufficient importance and doubtfulness to make proof desirable and demanded. SECTION II.— NON SEQUITDE. CHAPTER IV. INTRODUCTORY. When a real assertion is made, and reasons of some sort given for believing it, such reasons may perhaps be inadequate as a guarantee. In a former chapter (p. 102) it was noticed that all the dangers in accepting any Eeason as evidence for any Thesis, may be reduced to the two main heads, (1) Failure in formal adequacy, and (2) Failure in material truth, of such Reason ; and further, that the first of these departments is the only one that needs analysis in Logic. Non sequituv is thus co-extensive with failure in the formal adequacy of the Reason. We here reach what may be considered the central and most important part of the whole subject, and the part which certainly presents by far the greatest difficulties. The chief source from which these difficulties flow is one whose influence is not confined to Logic, but is felt more or less in all departments of knowledge, — the need for compromise between the completest possible Chap. IV.] INTRODUCTORY. 169 investigation and a sufficient degree of speed in practice. It seems to be inevitable that in applying Logic some compromise between these conflicting desiderata should be made : all that can be done is to recognise the com- promise as such, keeping a jealous guard against un- justified encroachments, yielding, of course, where it can be seen that the gain is worth the price, but in such cases remembering always that a certain risk is being run. To speak less generally, the main difficulty against which any methods for the accurate detection of Fallacy have to contend is the convenient practice of employing guesswork. In many cases it is possible to see at a glance, with quite sufficient accuracy, what the cause of the fallacy has been ; and it is then, perhaps rightly, felt as a waste of time to set about the search in any lengthy painstaking fashion. When, for instance, such an argu- ment is met with as that " we ought to be guided by the decisions of our ancestors, for old age is wiser than youth," even the most cautious person can hardly help feeling a high degree of security in guessing that the operative cause has been some misinterpretation of the meaning of Reason or Thesis or both, whereby the full difference between ' ancestors ' and ' persons old in age ' has been overlooked. So again where we find it argued that ' every effect must have had a cause, since otherwise it would not be an effect,' we are, no doubt, justified in suspecting some attempt to argue in a circle. So in a considerable number of cases Common Sense can lay a 170 FALLACIES. [Pakt II. finger at once on the cause of the fallacy, and thus go to the root of the matter without elaborate inquiry. A very little inspection of actual instances, however, will show that this is far from being always so eas}^. The causes of Non sequ'diiv are manifold, and in the large majority of cases the same false argument may be due to one of several ; and these, morever, not necessarily acting in isolation, but as a rule two or three combining to establish a false belief A given fallacy may be partly due to misinterpretation of language, partty to forgetful- ness of logical principles, partly to incomplete analysis of facts observed, and so on : the union of causes often makes their strength. Whether or no it is these difficulties, however indistinctly felt, that have led several writers to declare the systematic treatment of fallacies to be altogether hopeless, at any rate the facts have been dis- tinctly recognised and deplored by others. Whately, for instance, writes, " It must often be a matter of doubt, or rather of arbitrary choice, not only to which genus each kind of fallacy should be referred, but even to which kind to refer any one individual fallacy." And he further speaks of the "utter impossibility" of framing any classification which shall be completely secure from this objection. Mill endorses Whately's opinion, but intro- duces into his own list of fallacies one class — those of Confusion — under which he says, "almost all fallacies might in strictness be brought. ... A fallacy can seldom be absolutely referred to an}' of the other classes." The outcome of all which is, that it is very easy to give an Chap. IV.] INTEODUCTORY. 171 actual case of fallacy a wrong name, very difficult (hope- less except by means of special knowledge of the circum- stances) to be sure that we have named it rightly ; and quite impossible to guarantee that even the honest fallacious reasoner can be made, in this way, to see his error. We are led then to recognise 'Plurality' (and combination) of causes of JS'on sequitur as a fact, and to admit that any attempt to determine what has misled another person is open to exactly the same risks and difficulties as any other attempt to read our neighbours' thoughts or motives. What is meant b}^ classifying Fallacies or classifying anything ? All classes whatever are formed not by ' Nature ' only, but by ourselves reviewing the facts pre- sented there, and wishing to sum them up conveniently for purposes of our own. Finding some point of resem- blance between A, and B, and C, . . . we give them a common name, and thereby erect them into members of the class which the name denotes. This is never done without a purpose, however dimly conceived ; and such purpose is, ultimately, always the comparison of new cases with those already known. Just where the possibility of identifying instances ceases, the value of any classi- fication ceases too. The whole purj^ose of framing classes of fallacy is to enable us to compare any new instance of faulty argument with others already known to be fallacious, — if possible with the most simple and naked example of the class. And if our classes be such that the identification of actual instances is " a matter of 172 FALLACIES. [Part II. doubt or rather of arbitrary choice," or, as Mill puts it, if men's actual errors will not always or even commonly fall into our classes, the preservation of the names (unremedied and without full explanation of the limits of their use) is likely to lead to a very false sense of security. To some readers it may seem unnecessary to raise difficulties over the confusion of causes of fallacies with ' fallacies ' themselves ; but the fact is, that there are few kinds of confusion that are really more difficult to avoid. The name ' Fallacy ' is commonly used in at least four different senses, and before proceeding further there may be some use in setting these out, and choosing one of them. A ' fallacy ' is used to mean : — (1) A piece of false reasoning, in the narrower sense ; either an invalid ' immediate inference,' or an invalid syllogism ; a supposed equivalent form which is not equivalent, or a syllogism that breaks one of the rules. (2) A piece of false reasoning, in the wider sense ; whereby, from true facts, a false conclusion is inferred. (3) A false belief, whether due to correct reasoning from untrue premisses (reasons or sources), or to incorrect reasoning from true ones. (4) Any mental confusion whatever. Now, clearly there is no guesswork required for saying what is wrong with a given immediate inference, or syllogism, expressed in full. It either is or is not Chap. IV.] INTEODUCTORY. 173 a case of ' undistributed middle/ ' illicit process/ and sa on. But since, in practice, arguments are very rarely so expressed, we really run a considerable risk in accusing a reasoner of falling into one of these paralogisms. If, for example, a person appears to be using an undis- tributed middle term (as when he argues that some one who ' rushes in where angels fear to tread/ is therefore a fool), the error — if error there be — may really be due either to his ignorance of syllogistic needs, or to his mistakenly confusing the major premiss with its re- ciprocal (' all those who rush in, etc., are fools '), or to his mistakenly believing the reciprocal true; or, again, to some confusion as to the exact meaning of some of the separate words employed. And to accuse him of undis- tributed middle is, in practice, interpreted as judging that it was the first of these four causes to which the error may be definitely traced. That which is a fallacy in the second, third, or fourth senses above noticed may be no fallacy in the first sense ; and similarly that which, is a fallacy in the third and fourth senses may escape being so in the first and second ; and ' mental confusion ^ is obviously wider than any of the other meanings, covering cases which they would allow to pass untouched. Hence, the narrower the meaning we give to the word, the more liable we become to the dano^er of undertakino- to guess at the cause ; and on this account it seems better to interpret ' Fallacy ' in the fourth of the above senses. There is indeed one way in which the old names. 174< FALLACIES. [Part IL or many of tliem, may be preserved witli real advantage : and that is, not by simply deploring the difficult}^ of identification and then thinking no more about the matter, but by trying to understand clearly the causes of it. So far as we can obtain the laiu of the difficulty, we are in a fair way towards being able to judge in the given case whether and how far identification is possible. It is therefore on this account that I would draw attention to the risk of failure that is always run, for the sake of speed, in attempting to find at once the source of a given fallacy. However valuable such a practice may be for saving time, and however justified in certain cases, we must admit with Mill and Whately that there are many other cases where it necessarily fails. The remedy seems to lie, first in recognising clearly and consistently this possibility of failure, secondly in trying to improve our process of guesswork, and lastly in providing some surer if more lengthy method to fall back upon in doubtful or disputed cases, — wherever the matter is more important than the time. Such a method Logic really furnishes, — that of the Reduction to absurdity, * or, as it is more popularly called, ' pushing the argument home,' a method not by any means infallible, but free at least from the danger just referred to. Although Language remains faulty and treacherous, * This is, however, to be distinguished from the process so-called by Euclid, which corresponds to the ancient " ductio per contradirtoriam propositioyieni sive per inipossihile," by which the moods BaroTco and Bolcardo were to be justified. See Aristotle : Top. viii. 14. See also p. 353 of this book. Chap. IV.] INTRODUCTORY. l75 and our knowledge of Nature incomplete, yet if this method be fairly and cautiously applied we thus avoid at least the too common error of dogmatically misreading the mental processes of other people. This, then, ^vill be the plan adopted; and having already recognised the fact that to guess at the source of fallacy necessarily exposes us to a certain risk of failure, the next point is to inquire what can be done to improve the methods of guesswork. CHAPTER V. THE EMPLOYMENT OF GUESSWORK. I. Gexekal axd Special Soueces of Fallacy. For tlie purpose of attempting to detect Fallacy ofF-liand, it is clear that some classification of fallacies is ia the first place required : we must be able to give the detected fallacy a name. And the most obvious and useful principle of classification appears to be the attempt to distinguish (1) the main sources of danger to argument in general, and (2) the special dangers to which special forms of argument are chiefly liable. Some such principle, not perhaps ahvays intentionally followed however, seems in fact to lie at the root of most of the distinctions which have been made by logicians, and ccjually of those v\'hich have won a permanent place in popular usage. Thus the great distinction made by Aristotle, between fallacies in dictione and extra dictionem, calls attention to one large general source of Fallacy, — the snares of language ; while inside the second main class the varieties are partly common to all kinds of argument, — as the FaUacia accidentis Chap. V.] THE EMPLOYMENT OF GUESSWORK. 177 (interpreted widely), the Ignoratio elenchi, and the Petitio principii, — partly special to special arguments, as the Fallacia consequentis, the Xon causa i^vo causa, and the Fallacia pluriuni interrogationum. So agam Mill's division into a priori fallacies and those of 'in- ference/ aims apparently at marking off in the first place a large source of error common to all forms of argument, while under the second head the same function is performed again by the class called 'fallacies of con- fusion,' the remainder of the second class being divided according to the special forms of Inference, namely Induction and Deduction. And when we look at the names of fallacies which are widely recognised in popular usage, this principle of classification is equally noticeable, * verbal ambiguity,' ' missing the point,' and ' begging the question,' having come respectively from ' in dictione/ 'Ignoratio elenchi' and 'Petitio principii;' and such names as ' false analogy,' ' over-generalisation,' ' over- looking alternatives,' etc., referring more directly to failures in special kinds of argument. I propose then to make some use of this principle of classification. In face of the difficulties to be en- countered, a certain aid towards satisfactory guesswork may perhaps be given by examining broadly both the chief snares common to argument in general, and also those characteristic of the special forms or types of argu- ment. And the discussion of both wiU, I hope, be of service towards appreciating the value and meaning of the method for reducing to absurdity. 178 FALLACIES. [Part IL II. A List of General Objectioxs to any Argument. Probably if any one akeady accustomed to the practice of detecting Fallacies, but yet possessing a mind un- burdened with the more abstruse logical technicalities, were asked to classify all possible objections to arguments in ofeneral, the division made would be somewhat as f oUows : — 1. That the Keason given (or the objection) is beside the point. 2. That the Reason given begs the question. 3. That some important factor has been overlooked or forgotten. 4. That if the argument be cogent, some absurdity (or at least untruth) must also be believed. At any rate such a classification does not err on the side of too great depth or intricacy. Can it be made useful for our present purpose ? A note must be carefully registered, in the first place, that this division, however obvious at first sight, is purely one of convenience, not otherwise defensible. In strictness these four, if not quite alternative attacks, each equally capable of being made against any unsound argument, are at least to a very great extent overlapping. It will be seen that the first of these objections corre- sponds roughly to the charge technically known as Igno- ratio elenchi ; the second to Petitio principii ; the third and fourth having received no technical names. But so Chap. Y.] THE EMPLOYMENT OF GUESS^YORK. 179 long ago as Aristotle's time it has been pointed out * that every case of Non sequitur may in one sense be viewed as Ignoratio elenchi; while it is quite clear that the first and second of the above heads are, strictly speaking- cases of 'Untruth implied.' If the Reason is beside the point, or if the sufficiency of the Reason itself depends on the Thesis being true, it is clear that the Thesis cannot really depend upon the Reason in the manner implied in every argument. As regards Petitio principii it would, no doubt, be considered rather a straininor of lanojuaoje, were we to claim that the other heads might be brought under it : and yet, in this rather far-fetched sense the name Petitio iDvincipii is some- times employed, — at least in cases where the point is missed and in those in which some palpable absurdity is implied. For when we give as valid a reason which is beside the actual point at issue, we beg (not indeed the expressed original question, but) a question then perhaps for the first time seen to be remotely involved in it and essential to its establishment ; namely, that of the con- nexion between the Thesis which is, and that which ought to be guaranteed. This may be seen, for example, in the case where metaphor or analogy is employed in argument : to the assertion that the o-rowino^ size of London bodes evil to England because London is the heart of England, and a swollen heart is a sign of disease, it is clearly optional whether we object that " R is beside the point, hecause the analogy does not in fact apply',' or that " R * Soph. El. vi. 180 FALLAC;iES. [Part II. begs the question lioiv far the analogy holds good, which is the real turning-point of the argument;" or, again, that R and T together imply the absurdit}^ (or untruth) of supposing vjhat is in fad a mere nietaplior to hear literal interpretation. In all three cases the objection is funda- mentally the same, and our adoption of one form or another depends solely on rhetorical considerations. Again, where a Reason is given which, taken together with the Thesis, leads to absurdity or untruth, we some- times hear the objection brought that such Reason begs the question by assuming the fact on which the question is plainly seen to turn. As De Morgan says {Formal Logic, 255), though he strongly objects to the nomencla- ture — ''It is the habit of many to treat an advanced proposition as a begging of the question the moment they see that if established it would establish the question." R is accused of covertly assuming the truth of some highly doubtful proposition which is plainly required to establish T. So again it is open to us to view any case of palpable question-begging as 'beside the point,' inasmuch as it provides no real evidence in support of the point actually in question. If for the Thesis ' War is unjustifiable ' the Reason be given ' We ought not to do evil that good may come,' it is quite optional to object, either that ' this begs the question whether war is, on the whole, an evil,' or that ' the maxim is an excellent one in itself, but beside the point in the present case, since war is not necessarily a doing of evil' * And lastly it does not need any lengthy * Readers who have been interested ic the formerly disputed question Chap. V.] THE EMPLOYMENT OF GUESSWORK. 181 exposition to show that in all cases where Fallacy has crept into an argument, some relevant fact, whether as to things or as to the meaning of names, has been over- looked. " We might, perhaps," says Mr. Sully,* " charac- terize all illusion as partial view^," and elsewhere he identifies illusion, at bottom, with fallacious inference. In spite of such difficulties, however, this fourfold division may be put to considerable use in guessino- at the seat of Fallacy. But it wiU need some special Avhether or no the Syllogism itself is a Petitio principii, will easily see the connexion of what has just been said, with that ancient difficulty. Every Syllogism runs a risk of being in fact a Petitio principii ; it is so unless the argument employing it either appeals to admissions already onade (thus becoming a legitimate argumentum ad hominem), or else only aims at forcing into explicitness a principle, or an application of a principle, on which the point at issue turns, — in order that the material truth, as yet supposed capable of disbelief, of such principle or appli- cation may be now inquired into. If I argue that A is B because A is C (or because C is B), the Syllogism employed is, of course — C is B: A is C : .'.A is B. In using this Syllogism I may be either appealing to a former admission that C is B (or that A is C), or I may wish now to obtain that admission, and then the further consequence that my thesis is true; and lastly I may either try, consciously or unconsciously, to hide, or may openly confess, this wish. Supposing the Reason itself true, the whole question of the truth of the Thesis turns upon the truth of such further assertion implied by Reason and Thesis together, and to ' assume ' the truth of such further assertion is, no doubt, to ' assume ' that upon which the question really turns. But there are two kinds of assumption — underhand (or unconscious), and open, — and it is only the former which can do harm. A Syllogism rightly employed is just as much, and no more, an assumption of the point in question as every express assertion is. If I assert that A is B, I ' calmly assume ' that such assertion is true ; but I do so in a manner which, if my assumption is not sup- ported by an appeal to valid reasons, exposes me at once to the necessary hostile criticism. If the view here taken of the burden of proof be a correct one, it is only covert assumptions which are illegitimate. * Illusions, 2nd ed. p. 336. 182 FALLACIES. [rART 11. care in keeping the classes distinct. We shall have to limit the meaning o£ some of the names, in a way which their etymology at least would hardly warrant. III. The Objection Ignobatio Elenchi. First, it should be noticed that the common application of the terms Ignoratio elenchi and Petitio lyrincipii is rather uncertain. As regards the former, we have already seen that in one sense it may be stretched to cover nearly every possible fallacy, while in another sense it is often narrowed to misinterpretation of the meaning of the Thesis. A third sense, rather wider than this last, is simply the objection that oiving to some con- fusion or other as to meaning, the Reason is accepted as a guarantee for the Thesis, when in fact either this actual Keason at most guarantees some other proposition merely resembling the Thesis and mistaken for it, or when some other proposition merely resembling R guarantees this actual Thesis. When the charge ' E, beside the point ^ is brought, in the sense here referred to, what is meant is that owing to some misunderstanding, whether of R or of T, the former is unduly accepted as a guarantee for the latter. To use an expression of Mr. Milnes' — " The journey has been safely performed, only we have got into the wrong train." If we accept this meaning, the next thing is to dis- tinguish carefully two cases of misunderstanding; first where, without any opponent as yet in existence, an Chap. Y.] THE EMPLOYMENT OF GUESSWORK. 183 assertor brings forward, in support of his Thesis, some Reason which, though really valid for some other (similar) Thesis, is strictly irrelevant to the present purpose ; and, secondly, where the misunderstanding takes the form of an objection by an opponent, to an assertion made, or an argument employed, by ourselves. It is in the former of these two cases that the chief practical difficulty is to be found, but in both cases the difficulty is considerable. In no department of logical practice, perhaps, is the danger of undue dogmatism so great as in that of deciding whether mismterpretation has really taken place. This is, in fact, the chief point at which the functions of Logic are apt to be confused with those of Grammar. Since in any advanced language there is much substantial agree- ment both as to the meaning of names and of forms of speech, and since in such languages Grammar is always at hand to confirm and to o'eneralise this ao-reement as far as possible, there springs up easily the supposition that meaning resides solely in the words and their arrangement, that a printed sentence bears its fuU inter- pretation on its face, which has only to be deciphered and the thing is done. Bat, as a fact, interpretation is far from being so simple a matter : the same meaning- may be expressed in many difierent forms, and the same word or set of words may carry many different shades of meaning. If any doubt be felt on this head, let the reader take any collection of ordinary examples of pro- position, e.g. those in chaps, iii. and iv. of Jevons' Studies in Deductive Logic (and these, be it remem- 184« FALLACIES. [Part II. bered, are always artificially straightforward), and ask himself iii how many of the four traditional forms (A, E, I, and 0), each will bear interpreting. Still more uncertain is the meaning of the separate names em- ployed. A few there are, as already noted, the sense of which is, practically, fixed; but these are com- paratively few. Not only does the meaning of most words in common use undergo a constant gradual change as time goes on, but at the same period it varies greatly according to the varying knowledge, or even the passing emotions, and physical states, of the speaker ; and much of what every one ' knows ' he is liable to forget. All names which have gathered round them a cluster of inveterate associations (and what names have not ?), depend for a large part of their essential meaning on the past experience, and present mental states and habits, of the person using or hearing them. Many words bore a different sense to ourselves as children from that which they bring to us later in life : though the old names and phrases may remain, their meanings grow and alter widely. So again, a shght difference in the context, or even in less obviously connected circumstances, will often make a difference of meanino- amountino- to the actual reverse of that conveyed by the same words at another time : witness the possibility of " damning with faint praise," or the wrath of authors whose sentences have been criticised apart from their surrounding explanations. We need not search further for illustrations of so trite a fact. The purpose of these remarks is merely to bring Chap. Y.] THE EMPLOYMENT OF GUESSWORK. 185 to mind the many-sided difficulties attending all attempts at finding the exact meaning of an assertion. To all this it may, however, be answered that, just as in deciding whether a proposition is real or not, so m deciding the total question of its meaning, the only feasible plan, where doubt exists, is to put questions until such doubt is removed. It is here, in fact, that the practical value of the third ' Law of Thought ' — that of Excluded Middle — comes into operation. That Law, regarded as a statement of fact, is of course the barest truism, — A is either B or not-B : everything is either something, or something else. But its value, in this connexion, springs from the fact that, having postulated this undeniable truth, w^e gain the right * to require from a speaker the answer Yes or No to any intelligible question j put about the meaning of a name or other form of speech. " When you say that Solomon was wise, do you mean wise according to our present standard, or some other ? " " When you say that familiarity breeds contempt, do you mean that in every case the maxim * It is very difficult to avoid using expressions wliich, strictly inter- preted, may seem to refer to some set of artificial rules for debate. It is, however, possible, I hope, to keep these convenient expressions, and yet strain all such meaning out of them ; using them only for brevity. Strictly, of course, we have no ' right to require ' any answer at all : what is meant is only that if no answer is forthcoming, the argument falls through, since either the Thesis or the Season remains ' unreal ' to us who ask the question. t It should be noticed that if A sometimes means B, and sometimes not, the question, "Do you mean A or not ?" becomes no longer in- telligible. 186 FALLACIES. [Pakt IL holds true ? " " When you say that some Irish are indus- trious, do you mean that the majority are idle ? " When an hon. member said that the House o£ Commons is ' largely composed o£ English gentlemen,' did he mean to imply that it is not entirely so composed ? There is no limit to the possible varieties of question that might be put, and wherever the question itself is intelligible, only the two answers — Yes or IN'o — are possible, and one or the other must be true. Where doubt arises as to meaning, therefore, we have this method at hand for removing it. But the chief source of misinterpretation is the fact that such doubt does not arise as freely as could be desired. We do not halntually weigh either our own assertions or those of other people — life being short, and occupations various, — but are content to throw our words out somewhere near the mark, and to seize the gist of what is said ; glad if we escape the grosser kinds of in- accuracy. Very likely there are excellent reasons for this practice, but it has its dangers also ; and it is about the dangers only that we are here inquiring. Apart from the plan of systematic questioning, can anythiag be done to avoid misinterpretation ? Much may be done, no doubt, but not in the shape of a few plaui rules. To deal with the pitfalls of language at all fully, at least a separate volume would be required. In one sense, indeed, the subject is inexhaustible. No one can pretend to be perfectly safe from all danger of misiuterpreting language until he can claim a complete CnAr. Y.] THE EMPLOYMENT OF GUESSWORK. 1S7 knowledge of all nameable things, and also entire freedom from all effects of our ancestors' mistakes in namino- • and, so far as this goal remains at present unattained, so far there exists a source of misinterpretation against which nothing can securely guard. It is true, no doubt, that there are many errors in interpretation which spring, at least directly, not from imperfect acquaint- ance with the thino's that hear the names, but from ignorance of the principles of naming, classifying, and defining, from too careless employment of language, or from too ready subservience to its tyranny. But the task of completely remedying even these defects is a somewhat more extensive one than can be here at- tempted, except by means of occasional and indirect suggestions. It is obvious, further, that if there is to be an abso- lutely clear mutual understanding between speaker and audience as to the meaning of every separate w^ord em- ployed, and also of the assertion as a whole, a larger part of every speaker's life w^ould be occupied in the process of defining, or explaining his statements, than could well be spared from his other occupations ; and that, long- before the meaning of most assertions could be settled, their value as practical information w^ould have passed away. Accordingly, the point of first importance for practice is to know on what principles the compromise had better be conducted ; when once there is seen to bo need of inquiry into the special meaning given to some word or phrase, the process of inquiry is simple enough. 188 FALLACIES. [Part IL and has been already sufficiently indicated. To a de- finite question a definite answer may be, with reason, demanded. Wliere there are alread}^ two opponents, though Igno- ratio elendd is unfortunately common enough, it is far less dano-erous than in the other case. As a rule, when we are met by opposition we are ready enough to discover anv misunderstandinoj of our views. The grosser cases, at least, therefore, would present no difficulty : it will be sufficient to call to mind a few of the leading- varieties. Thus, mildly denying that a certain thing is absolutely all-important, we are met by arguments to show that it has some use : boldly pointing out that something else is altogether valueless, we are met by the answer that we ' can't expect perfection : ' asserting that some doctrine lacks arguments to prove its truth, we are referred to excellent reasons for believing in its utility : endeavouring to trace the manner in which some highly developed growth {e.g. conscience) originated, we are supposed to be refuted by a mere description of its present nature : disputing an argument, or an instance, we are supposed flatly to deny the theory in support of which these were brouo-ht forward : makincr some o o merely tentative suggestion we are asked for definite proofs. The varieties are endless, and the reader's ex- perience w411 easily supply him with a longer list of instances than we need here set out. But the real importance attaching to this kind of Ignoratio elendd begins when we reach the finer shades CuAP. Y.] THE EMPLOYMENT OF GUESSWORK. 189 of it. There is no doubt that the most frequent cause both of real misunderstanding and also of interpretation which is only too penetrating, is the attempt to read between the lines of what is said. Time being short, it seems to be generally recognised that some ellipsis in expression may as a rule be expected. It saves time and trouble in many cases to go behind the actual words, answering not what they strictly say, but what the objector supposes they really intend to insinuate. There are familiar euphemisms, for instance, whose ironical meaning is hallowed by custom ; and there are wa}' s of saying much by saying little, — and vice versa. But probabl}^ the most dangerous of all the sources of misunderstanding, is the gradual change that unavoidabl}^ takes place in the accepted meaning of words, so that both old and new meanings are, for a time at least, left existing side by side. The most marked examples of this are perhaps those due to the influence wrought on lan- guage by Science, or the deepening of knowledge, on the one hand, and by the allegorical or superficial spirit on the other ; very many words possess in this way no less than three broadly marked meanings, — the scientific (or technical), the popular, and the poetical. The various meanings in which the familiar word ' Law ' is used, will perhaps sufficientl}' illustrate what is here intended. Or again, through what is loosely called mere lapse of time, the meaning of a word may wholl}" alter; as the word ' Sophist,' originally from a6(pog, has now come to mean a quibbler. A public instance of Ignoratio elenchi due 100 FALLACIES. [Part IL to this latter cause, was presented in a recent trial.* '' It Avas complained," said counsel, " he had written ' I never expected to hear a coxcomb ask two hundred guineas for flinging a pot of paint in the public's face,' but .... what is a ' coxcomb ' ? I have looked out for tite vjorcl and find that it comes from the old idea of the licensed jester, who wore a cap and bells with a cock's comb in it. If that is the true definition, Mr. Whistler should not complain." So in, perhaps, the majority of cases where Etymology is relied upon by an afterthought as giving the ' true ' meaning of a word at the present day, there is involved some attempt to use the word in one meaning and to defend it in the other. f We have already had occasion to notice George Eliot's reference to '•' those undeniable general propositions which are usually intended to convey a meaning very far from undeniable," and it is not only general propositions but general names also that are used largely in this manner. The meaning of any name consisting, as it does, of very many particular facts regarding the objects named, it becomes easy on occasion to forget conveniently some of these facts while defending our use of the word, although we were far from forgetting them in the meaning really * Wliistler V. Ruskin. t Cf. Geo. Bentham, Outline of a Xew Systeyn of Logic. '' Where correct information, and consequently perspicuity in language is the object, the greatest attention should be paid to employ, in preference to others, such figures as have by long use lost, as it were, their original sense." Cf. also H. Spencer, Psychology, vol. i. p. 97. " The best -svords are those from Avhich long use has worn away all, or nearly all, traces of their origin." Chap. Y.J THE EMPLOYMEXT OF GUESSWOEK. 191 intended to be conveyed. The gathered associations, for instance, which words take on, and which they are sure to convey when used, can be very easily left out of sight while defending our use of them. This is especially insidious in the case where the meaning of the word used is relative to some standard, and where truth or false- hood depends upon the standard taken. As marked instances may be mentioned 'good' and 'bad/ 'great' and 'small/ ' hot ' and ' cold/ and all names which con- fessedly indicate points variably selected on a scale. In its finer shades the danger is almost ineradicable, since the standard employed by different people in judging is apt to vary with tlieir personal peculiarities, tem- porary or habitual, and past experience ; so that where no thermometer can be appealed to it becomes exceed- ingly difficult to fix any objective standard at all. Even if we understand our intimate friends, it is notoriously difficult to make full allowance for difference of standard in the case of all our casual acquaintances. It is easy, however, in this manner to enumerate a few of the leading ways in which assertions may be mis- imderstood, and even to write a loose and general homily upon human liability to error in this respect. But there seems to me very little practical value in so doing. The IDractical question would be, — What is it incumbent on us to do, for the purpose of detecting, and so avoiding, misintei-pretation ? And to answer this with any real completeness would lead us further afield than we can here afford to o-o. 192 FALLACIES. [Part IL But as reomxls the first of the two kinds of misunder- standing, it may perhaps be suggested as a broad general rule that inquiry into meaning, for the purpose of raising the objection that K is beside the point, is only advisable where the person inquiring has himself a definite view, if not of all the possible ambiguities involved, at least of the fact that some given ambiguity is probable. It is true that in this way much false argument would pasH unnoticed, but the only alternative seems to be a loss of more time than the results would probably justify. If in every case where an assertion is made and grounded, it were to become at once incumbent on us simply to- assume, until the contrary was shown, that some irrele- vance was present between R and T, it is clear that the waste of time would be on the whole enormous. Although Ignoratio elenchi may be the commonest of all fallacies, and although, perhaps, some slight shade of uncertainty as to our meaning is present in nearly all assertions actually made, nothing would, I think, be practically gained by treating intelligent assertion as the exception, verbal confusion as the rule. There should be somethino' to set us on the track of an Ignoratio elenchi; w^e should not be left imder the necessity of inquiring for it at large. If this be admitted, — and I see no resource but to make the admission, — it follows that the power of guard- ino- ao-ainst this kind of mental confusion is not one which can be given in a few hours or days, by the careful study of any dissertation on the subject, however Chap. V.] THE EMPLOYMENT OF GUESSWORK. 193 searching and complete. It must be rather a growth, dependent on the growing power and habit of distinguish- ing betw^een the different senses which any given word or phrase may bear. It is the power of seeing difference that is of prime importance, — difference, in this case, between one possible meaning and another. And the power of seeing differences cannot be obtained by merely recognising its value, though that is no doubt one im- portant step towards the attainment of the power. As regards the second kind — that which more truly corresponds to the literal meaning of Ignoratio eleiichi, — it may also, I think, be laid down that the assertor is, in every case, the arbiter of what he means to say. Where, under cross-examination, he contradicts himself, or shifts his ground, this can be pointed out, and the request can be made that he will abide by one alterna- tive or the other. He either means a given thing or he does not. There is no middle ground between ' Yes ' and ' No.' IV. The Objectiox Petitio Pbincipil A similar difficulty exists in fixing the meaning of Petitio 'principii, to that noticed already in the case of Ignoratio elenchi. De Morgan observes * that "Aristotle hardly ever uses the phrase apxvi^ alraidOai, 'principiuTii petere : it is To t? apxnQ> and To Iv apx{h that which is (ought to come) out of, or is in, the prin- * Formal Logic : p. 256. 1945 FALLACIES. [Part II. ciple. By the word irnnciimim he distinctly means that which can be hnoicn of itself !' . . . " Among the earlier modern writers, as far as I have seen them, there is some diversity in their description of the j^etitio ^jr^^cipi^'. That the j:>rr/?c?priC7/i was meant to be the thing known of itself, the apxv of Aristotle, as far as the introduction of the word is concerned, seems clear enough. Was it not then by a mere corruption that it was frequently confounded with the conclusion, the ' quod in princijno quoesitum fuit ? ' Did not the same inaccuracy, which confounds the To ev apx\i of Aristotle with the apxv itself, govern the change of the word ? Most writers take the fallacy of the petitio irnncipii as meaning that in which the conclusion is deduced either from itself, or from something which requires proof more, or at least as much, ignotius, aut mque ignotum." And De Morgan's own opinion seems to be (ibid. p. 254), that " strictly speaking, there is no formal fetitio irrincipii except when the very proposition to be proved, and not a mere synonym of it, is assumed." Nothing, however, appears to be really gained by restricting the name to so small a compass as this ; and there is no doubt that such a restriction would be very much at variance with the popular acceptation of the term. Still, some restric- tion seems needed, or else, if we define it as ' covert assumption ' in general, it is difficult to say where the application would really stop. Although, even on so wide a view, deductive proof would not be a begging of the question, since there the turning-points of the argu- Chap. Y.] THE EMPLOYMENT OF GUESSWOKK. 195 inent are openly appealed to ; yet, on the other hand, we should have to say that question-begging in its finer shades begins where there is even an unconscious fear of allowing Principle and Application to stand their trial. Question-begging, then, as we shall understand the term, never arises except in two cases ; namely, (1) where the relevancy, and (2) where the truth of R is already called in question, and where in answer to such objection, some proposition equivalent to (or including) the original T is given in support. Of the first of these cases, an example given above (p. 169) may be taken as fairly typical, — "Every effect must have a cause (T), since otherwise it would not be an effect (R)." We have seen that to call in question the relevancy of the Reason is, in other words, to ask for the missing premiss required for full Demonstration, and here it is plain that this can only be the original Thesis itself — " Every effect must have a cause." For if it be possible that an ' effect ' should hap- pen Avithout a cause, then the special signification which the name ' effect ' is employed to bear would be lost, and its value as a label would accordingly be spoilt. Hence in order to complete the formal cogency of the argument, we need the material truth of the Thesis, — which is just the point at issue. For the second case we may take as a conspicuous example the dialogue given by Whately in illustration, — but somewhat altered and shortened : — " ' Every particle of matter gravitates equally.' [T]. ' Why ? ' 196 FALLACIES. [Part IL ' Because those bodies which are heavier always contain more par- ticles, even if more closely condensed.' [R]. ' How do you know that ? ' [i.e. ' I doubt whether E is true.''] ' Because, all particles of matter gravitating equally, [original TJ that mass which is specifically the heavier must needs have the more of them in the same space.' " It is seldom, of course, in practice that we find Petitio 2)rincipii thus openly relied upon. Actual arguments are usually longer, more complex, and less explicit, than those which are required for illustration. As Whately puts it, " A very long discussion is one of the most effectual veils of Fallacy. Sophistry, like poison, is at once detected and nauseated when presented to us in a concentrated form; but a Fallacy which when stated barely, in a few sentences, would not deceive a child, may deceive half the world if diluted in a quarto volume.'" But it is by seeing any fallacy in its nakedness that we can best learn its central nature, and hence the need of sometimes appealing to examples which are so obvious as to be free from serious harm. The real difficulty, for practice, always lies in the stripping off disguises, and reducing what is said, and urged, to T and R. And here, too, when we raise the all-important ques- tion as to the means of deciding in practice whether question-begging has in fact taken place, we become extremely liable to the danger of accusing an opponent unjustly ; for the means of escape are numerous. Take for instance, the following argument of Mr. Jerm^m to Felix Holt : "You must permit me to check your use of the word 'bribery.' The essence of bribery is that it should be legally proved. Unproved bribery does not Chap. V.] THE EMPLOYMEXT OF GUESSWORK. 197 exist." Here we may, perhaps, have a very strong- suspicion that the Thesis is needed to support the Reason. The Thesis evidently is " This case ^^ (i.e. differs from) bribery ; " and the Reason " Bribery — > judicial conviction thereof," (the further assertion being "This case -\ — > judicial conviction of bribery.") It seems almost quixotic to hesitate to accuse the speaker of begging the question, for it is clear that if this case is bribery (which is the point at issue") the Reason must be untrue, — provided, at least, as Felix Holt would certainly have admitted, that no judicial decision had yet been given against the case in question. And yet, if we accuse Mr. Jermyn of begging the question, he has an easy escape. '' I mean," he would say, " to assert in the plainest language, that it is little short of libellous to accuse another person of bribery with- out bringing legal proof to support such accusation." This may, it is quite evident, have been his real intention in the speech. That is, his speech may have been an Ignoratio elenchi so far as the question bribery or no bribery is concerned. But by treating the argument in a less hasty manner, the covert assumption may be prevented quite as effectually and without run- ning the risk of mistaking the speaker's intention. " Do I understand you to assert," we might ask, " that if A pays B for his vote, no bribery has been committed, unless and until the fact is proved in a court of law ? If such a transaction does not in itself deserve the name of bribery, what name does it deserve exactly? It is of 198 FALLACIES. [Part IL sucli transactions that I wish to speak, whatever their name may be." So far as question-begging may be due to misinter- pretation of the language used, the difficulties are of course the same as those briefly noticed in the preceding- section. But more commonly it is the result of much the same state of mind as that which leads to Platitude. We have already had occasion to notice the nature of the harm done by tautologous propositions and circular ex- planations, and since Proof is the counterpart of Explana- tion, and every argument merely a complex proposition, it is easy to see the fault of circular Proof If we start with the implied supposition that the Thesis is true, it i& obvious that the more correct the subsequent logical process, the more certain shall we be of reaching the required result. Such Thesis has therefore had no fair trial : its supposed ' proof ' has been a pretence. Essen- tially the same, too, is that commonest and most insidious of all practices, the employment of what Bentham called " question-begging names." If a name properly belongs to S, the whole meaning of that name is applicable : but, at the same time, if ])art of the meaning is plainly ap- plicable, we are apt to suppose that the name may be ' properly ' applied. In this way the leap from part to whole is easily made, and the assumption hidden.* * This form of Fetitio principii is of near kindred to False Analogy (see p. 265), and also to material untruth of the minor premiss in an ordinary deductive argument. The difference is, in fact, like that be- tween analogy and metaphor, a gradual difference, depending on the degree of espUcitness merely. In the deductive argument we rest our < Chap. V.] THE EMPLOYMENT OF GUESSWORK. 199 It is not, however, only when we wish to deceive, nor even only when we use words carelessly, that this dano-er arises : for the number of words that have gathered no associations — especially associations of praise or blame — is comparatively small, and with the best intentions and the greatest care it is difficult to avoid all taint of question-begging. It is through the power of these associations to prejudge a question that so much import- ance is attached to the exact name given, even by a person who is himself fully capable of using words as counters merely : in the absence of a colourless word, and in the presence of two words highly tinged with opposite colours, he is forced to choose that which wiU mislead the least. " It is said that we have failed in Ireland. I do not admit the failure. I admit the success to be in- complete." In the same way, the choice between ' reign- ing' and * governing,' between 'sovereign' and 'suzerain,' between ' mob-rule ' and ' popular government,' between * liberty ' and ' license,' between ' famous ' and ' notorious,' and between endless other pairs of alternatives, may often lead to unavoidable unfairness, or at best to a rough balance between opposite wrongs. The remedy is essentially the same in this case as m all other cases of Petitio princijni; and, in a wider sense, in all cases of fallacy, — the forcing into daylight that which would prefer obscurity. Names in themselves case quite openly on the disputable premiss that ' S is M ; ' in the argu- ment from analogy we suggest ' S is, as it ivere, M,' or * practically the same as ' M ; while, if we desire to beg the question by means of a name, we assume as quietly as possible that the name applies. f^OO FALLACIES. [Paet IL are harmless so long as their misleading associations can be kept away from them, and by putting the point-blank question whether or no this or that meaning is intended, the assumption, if any, may be compelled to produce its credentials, or to confess that these are wanting. More than this Logic can never do. A fallacy stopped at one moment may always bide its time, and come into opera- tion again when the incident has been forgotten and the pressure removed: and, as just seen, this is a danger which all names that are rich in gathered associations especially tend to foster. On this account it is that in cases where, as so often in Politics, the determination is strong on both sides to take every possible advantage, however unfair, there is often practically no better re- source, even in the interests of truth and fairness, than to meet question-begging with its ovra weapons, just as one false analogy may often be met and destroyed by another equal and opposite. In this way, out of two wrongs a rough and ready right may be made to emerge. But here we certainly step over the line which divides Logic from Khetoric, or the task of detecting and recog- nizing Fallacy (or, as an alternative, preventing it for the moment) from the ^ider problem of counteracting its operation. CHAPTER VI. THE EMPLOYMEXT OF GUESSWORK: CONTINUED. I. The Objection 'A Factor overlooked.' It is difficult to find any one short name which shall fairly describe the third of our four general objections to an argument. We have already noticed that in the ordinary sense of the words, some important factor has been overlooked or forgotten wherever any fallacy — even Ignovatio elenchi or Petitio princiioii — has been com- mitted ; so that the name here taken is too vague to be reaUy descriptive. And the same difficulty seems to attach to any other short name that can b^ suggested ; thus if, for example, we attempt to sum up this third objection as the charge of ' supei-ficiality of view,' it will be necessary to add that the ' view ' spoken of may be either a view of objects, qualities, and events, directly, or a view of the meaning of names and propositions. For sometimes, in proving, we make use of knowledge already formulated, and sometimes we go direct to the facts for ourselves : while, according to the special mode of argument employed, will be, to some extent, the special liability to error. 202 FALLACIES. [Part II. Without, then, spending time in trying to get a per- fectly accurate name for the purpose, it becomes necessary now to examine, briefly at least, the leading types or forms of argument, noticing the points at which they are specially vulnerable, and the special form which the objection may take. And in spite of all difficulties and complications, it will be found that the possibilities of fallacy are, fundamentally, fewer and simpler than might at first be supposed. Although the kind of argument employed may to a great extent be used as the key in guessing at the seat of possible error, yet the value of the key will be much increased by recognising the essential similarity of dangers which thus take on some- what difierent forms. II. The Types of Aegument. § 1. Introductory. In reducing the almost endless variety of possible arguments to a few generalised types, it must be remem- bered that these can only stand, towards the arguments actually found in use, in somewhat the same relation as the ' roots ' of language are (by some) supposed to stand towards modern forms of speech. That is to say, the forms of argument now commonly in use are, for the most part, much more complicated than these types ; and yet, in spite of all their complications, they are capable of analysis ; the roots, however modified and combined, can stiU be discovered in them. Chap. YL] THE EMPLOYMENT OF GUESSWORK. 203 Without some such artificial simplification of the in- quiry, it would be practically impossible to find a path at all securely through the maze of details presented ; and with due precautions there need be no more danger in this expedient than in any other employment of the generalising or simplifying process. If, as is frequent in real life, a given argument employs in combination several of these typical forms, it is only by guarding against the dangers to which each part of the complex whole is separately liable, that we can take the w^hole in hand. Failing some method of the kind, we should require so large a number of special rules of evidence that to frame, to grasp, or to handle them effectually would be far beyond our power. It is probably already beyond the conceit of all but the most contented io-norance. The purpose of thus reviewing the fundamental types of argument is, then, that we may be able to catalogue their special dangers, so that, meeting with any argu- ment, we may obtain some guide to the points at which to look for weakness : and, at the same time, it is in- tended to bring these special dangers under a more general view. § 2. Demonstration and Real Proof. For such a purpose, however, many of the distinctions made, both in the traditional logic and in common usage, may be left out of consideration : for example, the dis- tinction between ' Demonstration ' and other kinds of Proof. 2()4r FALLACIES. [Part IL ' E/ it will be remembered, means 'Reason (or reasons) actually given ; ' and R may therefore either contain in itself both Principle and Application, or may express (or even suggest) only one of these, leaving the other im- plied. In other words, the proposition R — > T, implied in every argument, may mean one of two things : — either (1) that R includes T in its meaning, so that R being given, T may be known by a mere process of in- terpretation : or (2) that the truth of R may be accepted as a sicm. that T is able to stand ao-ainst adverse criticism. In the former case, the argument is technically called a ' Demonstration,' or complete Syllogistic proof ; in the latter case there is, I believe, at present no strict technical name, but for our present purposes I propose to call such arguments (by far the commonest in practice) Real argu- ments, whether empirical (including analogical and in- ductive) or deductive. The distinction between Demon- stration and Real Proof bears a certain likeness to that between Tautologous and Real propositions, already dis- cussed (p. 42). Just as in the one case the proposition as a whole gives us no more information than is con- veyed by the S alone, so in the other case the argument as a whole makes no real advance upon the Reason ofiven. The name Demonstration is perhaps not quite free from ambiguity. The popular notion of its meaning seems to be much the same as ' unanswerable,' or ' con- clusive,' or ' complete.' When the illogical person finds some theory no longer defensible, he not unfrequently Chap. IV.] THE EMPLOYMENT OF GUESSWORK. 205 takes refuge in the disclaimer, '' Of course I cannot demonstrate it, with mathematical certainty : the case does not admit of demonstration" — thereby implying, amongst other things, that if it were 'demonstrable/ there could no longer be any question raised about its truth, and that all that the disputer has done is to demolish this impossibly perfect kind of certainty, leaving the practical certainty intact. In this sense, probably, the following passage was written, — "However much one may be unable logically to demonstrate that there is such a thing as luck, there can be no question as to the fact of its existence." If the word ' demonstration ' means anything, it is thought, surely it must mean com- plete and conclusive proof. And hence, by a curious piece of inconsistency, the name often works round again, in popular usage, to mean proof which is ' suf- ciently ' or ' practically ' conclusive ; — as, for instance, in the case of a criminal caught redhanded in the act, whose guilt would be commonly said to be 'demon- strated.' Complete and conclusive, in a manner, Demonstration (in its technical meaning) certainly is. It is formally complete, and it is conclusive as against all who admit the material truth of the premisses. It is, in fact, an unanswerable ccrgumentuni acl honiinem, and, so far as mankind agree about the truths which may be un- questionably accepted, so far but no further reaches its universal binding force. Hence its especial connexion, in the popular view, with mathematics, — the simplest 20(3 FALLACIES. [Part II. example of its operation. The axioms of mathematics do not need to be reconsidered (even if we have the power really to do so), and so far as Demonstration appeals to them, so far it is conclusive as against all of us. But wherever any premiss, whether in a Demon- stration or in other kinds of Proof, meets with any doubt as to its material truth, the conclusiveness of the argu- ment depends entirely on such doubt being cleared away : a preliminary question is raised, which, unless answered satisfactorily, will destroy the material cogency of the Demonstration. Hence the real force of Demonstration rests ultimately on the same basis as that of all other kinds of argument, and reaches exactly the same level of objective cogency. Demonstration says, in fact, ' You admit the truth of the thesis indirectly, since you have already admitted the truth of this and this, which to- gether include or imply it.' For, unless the premisses are supposed to be admitted true, to assert them as un- assailable reasons for believing the conclusion would clearly constitute an insidious kind of ' begging the question at issue.' On this account, therefore, Demon- strative Proof is, as a rule, less easy to obtain than Real Proof ; for to obtain it, means, in fact, to obtain a person's consent to the conclusion without his knowledge. If there were any firm and sharp line to be drawn between absolutely binding proof, and proof tainted with human fallibility, each kind standing on opposite sides of a clear-cut chasm, then the name Demonstration mio-ht indeed be applied in its dictionary meaning. But as it Chap. VI.j THE EMPLOYMENT OF GUESSWORK. 207 is, the limits of ' axiom ' and theory ' are too ill-defined and imdefinable, one man's meat in this respect being too often another man's poison. Even our senses — that is, our 'direct perceptions/ which always include an element of inference, — are, it need hardly be said, liable to illusion : much more so is the complicated mental process by which we recognise a ' fact ' as con- clusively certain. Many an innocent person has before now been " caught redhanded in the act." Accordingly, the nearest approach which we can make towards apply- ing the name Demonstration in its etymological meaning, and at the same time preserving its definiteness of out- line, is to employ it for the kind of certainty which, though materially fictitious, is formally complete ; which, though not guarded absolutely against all possibility of error, is guarded against it on condition of the premisses being materially true. And it is probably on this account that the name has been in Logic technically restricted to complete Syllogism. Technically then only those arguments are demonstra- tive in which the thesis is included in the 'meaning of the reason or reasons given. Logical necessity is merely the necessity of avoiding self-contradiction, for the purpose of preserving a consistent meaning : ' necessary truth' is merely truth which is already admitted in another (usually a more circuitous) form. Thus the truth that two and two make four is already admitted in the full definition of the terms employed. If at least there be anything more in 'necessity' than is here 208 FALLACIES. [Part IL claimed for it, it is something of no importance to oui present purpose. Strictly speaking, Demonstration is of two kinds, — Immediate and Mediate (without or with a 'middle term ' *). Hence I have said in the last paragraph ' reason or reasons.' But in practice, w^hen challenged to prove an assertion, one has seldom the chance of appeal- ing to a simple equivalent form which is already admitted true ; for the obvious reason that ' immediate inference ' is so extremely easy that the person admitting the equiva- lent form is not likely to challenge the thesis itself. Mere rarity of occurrence would indeed be no ground for neglecting all exposition of this mode of proof, if it were not for the fact that indirectly we have already had plentiful occasion to exhaust the subject so far as our purposes demand. The sole equivalent form of any pro- position, apart from such equivalence as is merely due to synonymous words or to variations in grammatical structure, is that already spoken of under the ' Law of Counter-indication,' and it seems unnecessary to add that any assertion includes a denial of all other assertions that conflict with it : so that the Aristotelian proposition I is included in A, and in E ; for this is implied in the full interpretation of the Maxims of Consistency. Now w^hen the Reason contains expressly both a principle and an application of that principle to the^ case in hand, it is clear that nothing more remains to be done than to confront these two elements of R at once with * See pp. 234, 239. Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 209 observed or admitted fact. That is to say, tlie operation of Looic as reofards the oric^inal Thesis is at an end, and all that remains to be done is to erect, if necessary, these two elements (the Principle and the Application) into theses themselves. But occasionally it happens that such complete Demonstration is erroneously supposed to be present : and then we have either what is sometimes called a ' Syllogistic fallacy ', or some misinterpretation of the language used, or, thirdly, the vague intention of raising merely a ' presumption ' in favour of the Thesis. It is by no means always that we can tell with even approximate certainty which of these three causes has been in opera- tion, — often all three have had a share. Aristotle indeed declares that in his day even a mathematician * might be deceived by the argument, " Every figure has its three angles equal to two right angles : for every triangle has its three angles, etc., and every triangle is a figure : " and in Plato's Bepuhlic we frequently find such arguments admitted as valid : but this after all amounts to no more than saying that inconclusive demonstration was then in fact often accepted for conclusive, — a proposition true of modern times also: as to the exact cause of such acceptance, that is another matter. Completely demonstrative arguments, or those even pretending to be such, are, however, the exception, not the rule. They are, in fact, seldom employed in serious reasoning (outside certain departments of mathematics) but are nowadays chiefly confined to cases where some * Soph. El. vi. — Kol 01 Te-)(v7Tai kol oAcos ol iin(rTr]fj.oves. P 210 FALLACIES. [Part IL more or less ingenious quibble is plainly intended, — as in " Dry bread is better than wisdom : for dry bread is better than nothing, and nothing is better than wisdom." The almost universal practice in these times is to save circumlocution by giving as Reason either the Principle or the Application (more commonly the latter), but not both too'ether. In the case of 'chain aro^uments' — perhaps the commonest arguments of all — the Reason becomes as a rule still more elliptical ; for we there give expressly neither the Principle itself, nor its application, but merely the Reason which appears to be chiefly needed in support of one of these. Take for instance the not very complicated argument in favour of Home Rule in Ireland, that " Federalism is the finished product of civilisation and political ingenuity," and consider the further suppressed links required to complete its cogency. Three at least may be at once very easily distinguished, — the Principle that "to be the finished product of, etc., — > desirability," and two other propositions to complete the complex Application o£ such principle to the present case, — " Home Rule — > separation of Imperial from National and Local questions," and " separation of, etc., etc., — > Federalism," — none of which appear in the express statement. In many actual arguments, of course, the suppressed links are far more complicated, as in — " Tithes really fall on the landlord ; for the rent of tithe- free land is higher than that of land of the same quality and the same advantages of position subject to tithe," — where a considerable amount of special knowledge of Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 211 the subject is required in order to properly disentangle all the propositions implied. These chain arguments need not, however, become in any way a stumbling-block ; since where we do not at once see all the hidden implications, there is a very simple means ready at hand for arriving at them. How- ever many links there may be, they are all capable of being summed up in the concise expression — ( " If R, then T, and ) 1 If not T, then not R," I and we have only to call for the grounds on which this proposition is believed, in order to have the links set out as fully as we need. '' How does R prove T ? " we ask. Thus in the example just given a person entirely ignorant of all the ordinary conditions of the tenure of land, and of all the deeper facts brought to light by Political Economy, would be as capable as any one else of erecting into a new T the connexion hetiueen the R given and the original T : it would take him longer, of course, to arrive at the rights of the matter than it would take another person who had already considered some of the questions involved, since he would have to push inquiry further back towards first principles ; but his present ignorance of the subject is only a temporary and removable bar. Such then being the difference between Demonstra- tion and the other kinds of Proof, it is clear that in treating the opportunities for error that occur in the latter we really treat those that occur in both. If, when •either Principle or Application alone is given we can 212 . FALLACIES. [Part IL recognize the needs of formal adequacy sufficiently to avoid accepting as further assertion a supposed Applica- tion or Principle which does not really apply, a fortiori we are guarded against accepting two insufficient pre- misses when both are expressed. We shall accordingly dismiss all consideration of Demonstration as such, and confine attention to the forms and the dangers of what is here called ' Real Proof.' § 3. Induction and Deduction. In the chapter on the Process of Proof in general,* it was seen that the real foundation of Proof is always the recoo-nition of resemblance and difference between thinojS' or events known, or observed, and those which are on their trial, whether such recognition is based on know- ledge abeady reached, and formulated in names or pro- positions, or on direct observation and experiment. In proportion as we openly and distinctly refer to known principles — already generalised knowledge — is Proof de- ductive : in proportion as we rapidly and somewhat dimly frame new principles for ourselves from the cases observed, is Proof inductive, empirical, or (in its loosest form) analogical. The whole history of the rise and growth of know- ledge, it has been also already remarked, is a record of fruitful rivalry and interaction between two opposite processes. Observation of facts has demanded theory — * Part i. chap. v. Chap. YL] THE EMPLOYMENT OF GUESSWORK. 213 statement of ' laws ' or uniformities — to explain, and €ven to name, the things and events observed : theory in its turn has alw^ays been more or less liable to the purging criticism of 'fact.' In the strictest sense, of course, Deduction and Induction are modes of Inference, not of Proof at all. Strictly speaking, all Proof, so far as really Proof, is deductive. That is to say, unless and until a supposed truth can be brought under the shadow of some more certain truth it is merely self-supporting, or circular. Unless we have some more comprehensive and better tested generalisation within the sweep of which to bring our thesis, we reach no foundation broader than itself ; no assurance beyond what may be derived from the fact that nothing has yet been found to contradict the theory. But yet there is a meaning in the distinction, and, with certain limitations and apologies, I propose to make some use of it. Although the dependence of any Thesis on its Reason must be rationalised — i.e. must have the under- lying principle made clear — before the testing operation can be called complete, yet in regard to special dangers it makes considerable difference whether the principle is at first definitely apprehended or not, — whether (as it is commonly expressed) the Proof 'pr of esses to rely upon Laws known or supposed to be true, or upon facts ob- served or supposed to be observed. We must distinguish then, as far as possible, between that kind of Proof which rests openly and distinctly upon already generalised knowledge — Deductive Proof, — and that which rests upon what may be loosely described as ' isolated facts,' 214 FALLACIES. [Part IL or 'perception of resemblance and difference,' or 'ob- servation and experiment/ or ' circumstantial evidence/ or however the phrase may run, — that which is com- monly known in its highest form as Inductive Proof, and in its lowest form as the Argument from Analogy. The required limitations in preserving the distinction appear to be, in the first place, a clear recognition that although in Induction the Principle, or Law, connecting the cases observed with those inferred is in the case of Inference commonly dropped out of sight, or at least left highly indistinct, yet the whole cogency of Inductive Proo/ depends upon the extent to which such Principle is first rendered definite and then confronted with ob- servable or admitted fact. So long as the Principle is left indistinct, we may be fighting under false colours — misled, that is, by false analogies, or hampered by dis- tinctions without a difference — in extending our know- ledge to the supposed ' parallel cases,' or in drawing our line exactly where we do. There is, in fact, probabl}^ no more fertile source of real (as opposed to merely verbal) fallacy than just this neglect, or dread, of ' ra- tionalising' our beliefs, — of bringing their underlying principles out into the daylight. The name Inductive, then (as also ' empirical ' and ' analogical '), is properly a name of a mode of Inference. It describes the fact that in arriving at our Thesis the Principle ivas left more indefi- nite than if we had reached the Thesis deductively. The provinces of Analogy, Induction, and Deduction are thus merely rough divisions on a scale : the more definite the Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 215 Principle the more the inference possesses the deductive character, the less definite the nearer it approaches to loose Analogy. But equally in deductive and in analo- gical arguments, in order to rationalise the belief the underlying Principle must be made definite. The chief value of the distinction, for purposes of Proof, is that it serves to call attention directly to that part of an argu- ment which stands in pressing need of careful examina- tion : meeting with an empirical argument we may often shorten the process of testing it by inquiring in the first place what the underlying Principle really is, — how far it will bear reduction to definiteness and comparison with fact. Empirical arguments are, too, so far as em- pirical, free from mere snares of language, — which play so large a part in all deductive proof : their chief danger may be summed up as the adoption of some theory with- out examining, or perhaps even seeing, the alternatives. But this will be more fully discussed presently. The second difficulty in preserving the distinction lies in the fact that as a rule the Empirical and Deductive processes are found in combination, both being employed on the same subject-matter. Not only does Inductive Proof — in its higher forms — make large use of Deduc- tion, for verifying the hypotheses put forward, but all Proof, however professedly deductive, is in the habit (at least where the generalised knowledge is not very firmly established in the individual mind) of drawing- much confidence from successful prediction, and even from merely congruent facts. Some Free-traders, for 216 FALLACIES. [Paet II. instance, lacking robust faith in the abstract propositions from which that theory may be deduced, or failing to hold them clearly in memory, are apt to feel an accession of security when statistics ' prove them right ; ' and weak or vague generalisations, such as that ' Roman Catholi- cism and national poverty go hand in hand,' commonly draw what strength they possess jointly from the two sources, prejudice (i.e. 'kno^vn law') and observation. It would certainly be hard to find a single instance of in- ference, within historic times, in which we could say beyond all doubt that Deduction was wholly wanting or had contributed nothing to the belief; and since any of the causes of a belief are liable to be relied upon as reasons on reflection, it is rare to find professed empirical proof entirely free from the deductive element.* Sometimes, no doubt, from one cause or another, either method may dwindle into insis^nificance beside the other. A p'reat many people, for instance, are inclined to settle the claims of ghost stories deductively ; — partly perhaps because they find as a rule that their hands are more or less hampered and their eyes rendered more or less use- less, before they are allowed to begin experimentation. On the other hand, in Meteorology, from a deficiency of known laws we are thrown very much upon bare facts * Even in attempted Proof we commonly find the two processes mingled, as where Parson Lingon argues in favour of cock-fighting, not only that under it " England had been prosperous and glorious," but that " the practice sharpened the faculties of men, gratified the instincts of the fowl, and carried out the designs of heaven in its admirable device of spurs." Chap. VL] THE EMPLOYMENT OF GUESSWORK. 217 as recorded in statistics ; what certainty we have regard- ing the weather is mainly empirical. In all cases of real proof, however, it is probable that nowadays both pro- cesses play some part. These two considerations make it, of course, extremely difficult in practice to label every argument at once with one or the other name. Sometimes, as where the Reason is a direct statement of the Principle itself, or again where it consists of a record of some experiment, no hesitation need practically be felt as to where the danger lies ; but in a large number of cases we have no means of decidino^ whether the argument may best be classed as empirical, or deductive, or both. In those logical treatises in which Inference and Proof are not clearly distinguished, and where consequently the distinction between Induction and Deduction occupies a very prominent place, there seems to be a desire to restrict the name of Inductive Proof as far as possible to the establishment of lavjs by means of isolated facts. Analogical Proof to the establishment of facts by means of resembling facts, and Deductive Proof to all other cases. But we have seen that both Principle and Appli- cation are required for all completed proof whatever : that is, until both are brought to daylight and examined, the testing of the Thesis remains unfinished. Sometimes — i.e. in Demonstration — both Principle and Application are expressly given by the Reason ; at other times one or the other only. But yet it will not do to say that wher- ever the Principle is merely implied we have a clear case 218 FALLACIES. [Pakt IL of Empirical Proof, since it is sometimes through extreme famiharity, rather than through insufficient definiteness, that its statement is suppressed; as where we argue " The Pope is faUible, since he is human." In many such cases the Principle relied upon might well be definitely enough apprehended to warrant our calling them cases of deductive proof. What then, it may be asked, is left of the distinction at all? Have not these imiocent limitations and apologies in fact proved too much ? If we cannot tell for certain in the given case whether the argument is properly an empirical one or properly deductive, why keep the names and make a pretence of using them ? In the first place, we are here intentionally seeking to make the best use of the guesswork system of detecting- Fallacy, and with that view may be thankful for even rough distinctions suitable to the purpose. Nor, because the distinction breaks down when pressure is put upon it, need we consider it wholly worthless. It possesses a solid core of applicability, and if we can be content to use it as a rough guide in finding the Aveak point of an argument, much value may still be extracted from it in economy of time. Again, if the names Induction and Deduction make us think of Inference rather than of Proof, we are not obliged to use them. However we choose to name the two difierent kinds of armiments, the distinction between them has a certain real importance, as already shown ; and all that is intended to be done with it is to recoo-nise Chap. YI.] THE EMPLOrMEXT OF GUESSWORK. 21 D that so far as the given argument may be seen to belong to one or the other class, so far we are already some way on the track of ' special dangers.' A thesis, then, whether abstract or concrete, is some- times supported by bringing forward a congmoent fact^ or a number of cono-ruent facts : in this case the thesis, when abstract (as e.g. the law of Gravitation, or of Natural Selection) is usually called a theory. An abstract theory is offered both as an explanation of the facts on which it rests and as a means of prediction in the future^ thus basing a general law upon individual facts observed. When the thesis is concrete it is rarely called a theory, but professes to argue direct from case to case, by what is called Analogy, or Resemblance, or Extension to parallel eases. Or, secondly, a Thesis, also either abstract or concrete, is sometimes suppoi*ted by appealing, expressly or other- wise, to an already recognised law. Here the Thesis (except when explanatory) is not as a rule called a theory, — probably because that name carries Avith it by custom a shade of uncertainty, which seems to throw unnecessary doubts upon the ' already-recognised law:' it is occasionally called a 'deduction,' but more often has no distinctive title. As to the nature of the Reason, sometimes the law itself is expressly mentioned, but more commonly the S of the thesis is labelled with some name, or said to have acted or suffered in some particular way which is ' known ' to carry certain consequences. In other words, whenever the Thesis professes to be deduced from some already- '220 FALLACIES. [Part II. framed law, the Reason either expressly mentions this law, leaving its application implied, or it appeals to some xign, expressly asserted to be present in the given case, leaving the universal trustworthiness of such sign implied. Accordingly, the two main kinds of argument may be called respectively the Argument by Example and the Argument by Sign. In the former we rely primarily on ^ facts ' observed, no law to cover the case being as yet ilistinctly admitted ; in the latter we make use of the recognised results of past observation, whether registered in express propositions or merely taken for granted in the meaning of the names employed. s:} 4. Certa'ni Minor Di-'itinct'ious.* Before further subdividing these two main forms of argument, it will be well to notice briefly certain other distinctions which are sometimes made, but which mark differences that are quite unimportant for our purpose. Thus we have seen that the distinction between conclu- sive and jJi'csiunj^f ice proof, though useful perhaps before inquiry begins, is altogether too loose for adoption into Logic. In one sense no proof is conclusive, in another sense unless proof professes to conclude the inquiry it is not proof at all. Really, the distinction seems to be * This section contains several technicalities which could not be explained, or omitted, -without considerably lengthening the exposition, and it seemed desirable to save space as much as possible, since the section is not essential to the main thread of our subject. The techni- calities can be easily found in any logical text-book. Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 221 intended to mark roughly the difference between a Thesis asserted and one that is merely suggested ; and such hesitating theses lie quite outside our present interests. Further, certain names, such as circumstantial evidence, are almost synonymous with others that will here be employed; empirical evidence including circumstantial evidence as the whole includes the part. Again, 'testi- mony,' ' hearsay evidence,' etc., though marking distinc- tions valuable perhaps for some purposes, are varieties which do not readily admit of any special treatment, except where there exists, as in Law, some authority competent to lay down strict rules w4th a merely average balance of good result. Logic is less pressed for time than Law, and can afford to decline to generalise where generalisation is only so roughly justified. Again, there is the distinction between hypothetical arguments and those which are commonly called cate- gorical. A hypothetical argument, of whatever kind, is simply one in which the major premiss (the Principle) takes the form of a hypothetical proposition. The dif- ference between a categorical and a hypothetical propo- sition is, we have seen, merely a grammatical one, conveying at least no difierence of meaning that is of importance to our view of Logic. Any categorical argu- ment may therefore be expressed in hypothetical form, and vice versa. While, however, the danger in hypo- thetical and in categorical arguments is essentially and fundamentally the same, the language in which it has to be described is, under the predication view, somewhat 222 FALLACIES. [Part II. different. The hypothetical proposition divides into Ante- cedent and Consequent more naturally and readily than into S and P, and accordingly the ' middle term ' of a hypothetical argument is hard to find, — or rather it seems almost a straining of language to call it a middle term at all.* In a categorical argument the middle term of the Syllogism involved is often difiicult enough to disentangle clearly, t but since in hypothetical arguments the middle 'term' is itself a proposition, namely, the Antecedent (or, for a negative conclusion, the denial of the Consequent) of the Principle, any search for the middle term, as such, is more often a source of confusion than of help. In fact, in all cases of difficulty, translation from the categorical into the hypothetical form will, I think, be found the easier plan, for then we have merely to see whether or no the minor premiss properly affirms the Antecedent (or denies the Consequent), or improperly denies the Antecedent (or affirms the Consequent). The fallacy of 'affirming the Consequent' in hypothetical argument is essentially the same as that of employing an ' midistributed middle ' in a categorical one ; and in like manner it may be shown that ' denying the Ante- * See also Bain's Logic, bk. i. chap. iii. sect. 30. t As, e.g. in the argument from difference — Cesare or Camestres — where, in order to bring M to the position required, we have to contra- posit the major premiss. Let the T be ' Whales are not fishes,' and the R * they cannot remain always under water,' the principle involved is clearly, 'Fishes proper can remain, etc. ;' but it is only in the contra- positive form — viz. ' That which cannot remain, etc., is not a fish,' that we can bring the middle term into the position required. Chap. VI.] THE EMPLOYMEXT (3F GUESSWORK. 223 cedent ' is essentially the same as ' illicit process of the major.' But in order to describe the danger in these cases in the words that are most simply and naturally applicable to them, it seems better to preserve the dis- tinction, merely noting that it is of grammatical rather than logical interest. Of further varieties of argument the complete list Avould be a very long one. Numerous small distinctions, unnecessary for our purposes, have been made from time to time. Thus we have the nineteen valid moods of the Syllogism (several of which never really occur in prac- tice), or again the argumenta ad personam, ad verecun- diani, ad popidiim, etc. — names which imply a large amount of insight into other people's motives. As regards the Syllogistic moods, while preserving to some extent the differences on wdiich they are founded, we may reduce their number considerably. In fact, under the liberal treatment here adopted towards the exact words in which any assertion may happen to be clothed, some simplification in this respect follows of necessity. Thus, while we shall be obliged * to take some account of the difference between an affirmative and a negative Thesis, we do not need to distinguish in every case a negative proposition, as understood in the Aristotelian scheme, from a positive one ; and again, every ' particular ' pro- position, so far as it makes a tangible assertion at all, is negative in our sense. A negative proposition, as we have elected to understand it, is only a proposition which * See p. 2-i3. 224i FALLACIES. [Part IL intends to deny some positive assertion already made or believed, not every proposition which happens to contain the negative particle, in however close connexion Avith its verb. The traditional mood Celarent, for ex- ample, is probably hardly ever used for Disproof, Camenes probably never used at all. And, as "will be seen later,* all the fourteen syllogistic moods with the conclusion in I or O may be conveniently reduced to two. The remaining distinctions we shall have to make will be entirely within the two main ty[3es, the Argument by Example, and the Argument by Sign ; and they are set out in a table (IV.) in the Appendix (E), which may be usefully kept in view during our discussion of the special types of argument. § 5. The Argument hy ExaTaple. What is here called the Argument by Example, or by ' Congruent Fact,' is not quite the same as that which is commonly known as Proof by Circumstantial Evidence, though closely similar : on the surface at least, the latter mode of argument relies upon facts {i.e. circumstances) which together confirm the Thesis. It is difficult, indeed, to say precisely what is ' commonly known ' under the name Circumstantial Evidence, since popular usage aeems to vary. The common acceptation of the term is, how- ever, almost certainly, somewhat narrower than that to * Cf. iiifra, p. 241, and Appendix (C). Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 22-5 which its literal (i.e. derivational) meaning would point. Literall}^, circumstantial evidence should include, one supposes, every case of proof from the circumstances (or aggregate of isolated facts) observable or known : so that (1) a geological explanation, founded on Nature's foot- prints, or (2) our opinion of a neighbour's character, founded on his general conduct, or (3) a political pre- diction, founded on the signs of the times, or (4) any law of nature, founded on wide observation and experiment, would all equally come under the title. But no doubt such an employment of the term would be considered a straining of language. The name circumstantial evidence shows a decided tendency to restrict itself, in common usage, if not solely to the case where a crime is traced home to the criminal by means of the marks that he (or his act) has left behind him, at any rate to proof of the cause of a concrete fact where the evidence of eye- witnesses cannot be obtained, and where the circum- stances are singly Aveak. In Law, of course, the reason for the importance given to this distinction is mainly the recognition that ' facts may bear more than one interpretation,' while direct testimony is, in the large majority of cases, free from all danger excejDt that of deliberate perjury. Under Proof by Example, however, will be here in- cluded all cases where a proposition, whether abstract or concrete, is supported by the production of a fact, or of facts, which are simply given as agreeing with the theory, or as forming cases under it, when at the same time it is Q 226 FALLACIES. [Part IL recognised that there is as yet no definitely known Law in the matter, to which appeal can be directly made. The primary danger in all such cases is the same, — namely, that the fact or facts produced will admit of some other interpretation than that put upon them by the theory. But this danger takes certain special shapes, Avhich it will be worth while to consider more in detail. The subdivision to be made under the Argument by Example is that into : — (a) The Argument by Analogy. (h) Proof of a Generalisation, by the facts which it is intended to explain. The first of these is what we have already had occasion to notice (p. 104) as ' extension to parallel cases ; ' the second embraces what are commonly knoAvn as the pro- blems of Induction, — so far as Proof is concerned. (a) The Argument by Analogy. Analogicar reasoning, or the argument from indistinct resemblance, is one of the most difiicult subjects to treat with satisfactory completeness, since arguments of ap- parently the most diverse forms are apt to contain more or less of it, and on the other hand we rarely meet with a case of open reliance on Analogy pure and simple. That is to say, where we do find Analogy unmistakably employed, there is also commonly a strong inclination either to soften the force of the assertion made in the Thesis, so that the process should be viewed less as an €hap. YI.] the employment OF GUESSWORK. 22/ attempt at proof than as a mild suggestion ; or else to put forward the analogy rather by way of illustration than as evidence. It was not without a reason that we avoided choosing a symbol for the assertion of indistinct resemblance between S and ^. For essential resemblance, it will be remembered, we found * a symbol (the now familiar — >) ; but for the too common assertion ' S is strikingly like §b/ oui" scheme provides no place. The reason is that this vague assertion can only be conceived as ac- ipiiring a practical value for Proof (valuable though it may ahvays be for Discovery) by emerging from its safe obscurity through the claimed resemblance ceasing to be any longer indistinct. Resemblance, it is on all hands admitted, varies in degree. A given individual, w^e say, for instance, is more like his father than his mother ; distantly re- sembles a cousin; and still more faintly, a stranger, a savage, or some particular animal. A cloud in the sky may bear a fancied resemblance to some familiar object, but not so close a resemblance as one pea bears to another. Now the only manner in which gradual variation can be represented seems to be by means of numbers, — or at least of pictures with measurable pro- portions, — and measure implies the conception of relative number. Hence, it seems, we are driven to say that resemblance varies in some manner expressible (if at all) by means of numbers. * See p. G4. 228 FALLACIES. [Part II. To meet tlie needs of accurate comparison, we have accordingly established the familiar phrase 'points of resemblance.' John resembles his father in the eyes^ or hands, or hair : he has his mother's accent, and a touch of his grandfather's gout : holds the same opinion as his friend on a certain important question ; has a less hasty temper than his enemy ; and it is in ' expression ' only that he resembles a mastiff or a bidl. But Avhat are these so-called ' points ' ? Are they simple units, which have only to be counted, for and against, in order to work the sum by straightforward addition and subtraction ? I fear it is not always easy to avoid all taint of this plausible error. Accurate measure- ment seems at first sight to demand equality of units. The fact appears to be, however, that no so-called ' point ' of resemblance or difference is known to exist which is not in theory further analysable, and few that are ultimate even to the naked eye. The colour of the eyes, for example (to choose out of the list just given the point which seems on the whole least likely to yield further component parts), may be broadly classed as blue or bro^vn or black and so on; but it can hardly be disputed that between these rough distinctions, end- less shades of difference are possible. As for accent, liability to gout, similarity of opinion, or of temper, or of expression, each of these is plainly seen to be built up. of innumerable components; the numerical difficulty is only verbally solved and really shelved, by determining to treat any given ' point ' as ultimate. €uAP. VI.] THE EMPLOYMENT OF GUESSWORK. 229 If we cannot then arrive at valuable results by simply counting the points of resemblance and difference, as we count black and white balls in a ballot-box, what other resource is open ? Only one ; namely to estimate as well a,s we can their relative lnvpoi'tance as regards the matter in hand. For this purpose the phrase ' essential points ' has been invented. ' Essential resemblance ' means ' re- semblance in the point (or group of points) M,* which is essential ; ' and by essential is here simply meant ^ sufficient to prove a certain other assertion ' to which reference is thus indirectly made. Without this indirect reference to some further proposition, the phrase ' essen- tial resemblance' becomes, not perhaps quite meaning- Jess, but deprived of any meaning that exists in definite shape : for to reduce it to definiteness would be just to .state wherein the essentiality consists. It has been ■sometimes said, for instance, that the State essentially resembles a family ; and vaguely every schoolboy can see the likeness at once. But beyond a mere oriental delight in simile for its own sake ; and beyond the hazy satisfaction which is still apt to follow even the cheapest attempt to classify ; when we push the question home, and ask what exactly is intended to be conveyed by the assertion, we find ourselves really hoping, by means of the asserted resemblance, to register our right of arguing (within certain indefinite limits) froon family to State ; * The symbol M (Middle term) is here chosen in reference to the manner in which the fundamental structure of the analogical ai'gument corresponds to that of the deductive one. See also pp. 232, 234. 230 FALLACIES. [Part II.. that is, of saying that since some given assertion may be made about the former it may also he made about the- latter. It is this further assertion, whether clearly apprehended as the purpose or (more commonly) not, to which the ' essential ' refers : and an ' essential point ' is a resemblance or difference, wide or narrow, complex or apparently simple, that may be used as a sign of the- truth of such j)roposition. As yet, however, the difficulties in fully understand- ing the analogical argument are hardly more than begun. And first, as to the symbolic expression ; here some care is needed in order to avoid ambiguities. It clearly will not do to use S and ^ as the terms of both propositions, the Thesis and the Reason; but with the aid of the symbol Z in addition, we can sufficiently express all that is necessary. If we also use the symbol for Re- lation in general, the universal form for the analogical argument would run as follows : — (Thesis) S Z ; for (Reason) ^ Z.* This, it must be confessed, just as Mill's formula on which it is based, f is a statement simplified artificially to the utmost. An actual analogical argument may be * It should be noticed, ho-wever, that this formula is only valid on the condition that the symbol means approximately the saraB in Thesis and Eeason. f Mill's formula is stated, however, as if discovery, not proof, Avero chiefly contemplated. It runs, " Two things resemble each other in one or more respects ; a certain proposition is true of the one, therefore it is true of the other." Chap. YI.] THE EMPLOYMENT OF GUESSWORK. 231 complicated by failure of complete identity between Z in Thesis and in Reason, or even perhaps between the respective copulas.* Or again, Analogy is very commonly employed as part of a full deductive process, as in " Colonies ought not to rebel against the mother-country, since they are (so to speah) its children, and {it is an accepted law that) children ought not to rebel against their parents." Every kind of argument, in fact, may have an analogical element in it, and wherever the analogical element is present the danger is to that extent the same. But this special danger will be spoken of later ; at present we have only to set out and describe the various kinds of argument. A more serious difficulty may be stated as follows : If, as appears, what is really relied upon in the argument by Analogy is a supposed ' essential resemblance ' between S and ^, and if by essential resemblance is meant resemblance in the point M, such point being claimed as a sign for the purpose required ; wherein does the attempt to prove by analogy differ from the purely deductive argument ? Clearly, it may be said, unless the resem- blance is declared essential for the purpose in hand (i.e'. for proving the Thesis), there is nothing to show the relevancy of the argument ; until the points of resem_ blance are recognised as such, how can we even begin to inquire whether they are important or wholl}' trivial; and if their possible triviality is still an open question, whence our confidence in their binding force ? * The ' copula ' is the sign of relation. See p. 54. 232 FALT.ACIES. [Part II. The answer must be that this is exactly the question which Logic has to put to the person whom an analogy convinces. The difference between the analogical and the deductive arguments is a difference in the degree of distinctness with which the existence of the link M. and the fact of its being a truly important link, are recognised and appealed to. We need a name by which to describe the cases where these two opportunities for error have been left to take care of themselves, — where ready and generous faith, rather than the cold and grudging spirit of strict inquiry, has been in operation, — and for this purpose the name Analogical Reasoning has won a firm place in our terminology. By analogical reasoning we denote what may be called embryonic deductive argu- ments, — arguments which are as yet in happy uncon- sciousness of the troubles in store for them later. The solution of the seeming paradox is therefore not difficult to find. The argument from analogy is, properly speaking, not so much a mode of attempting proof, as a mode of attempting to dispense with the serious labour of proving. It lies at that end of the scale of cogency which is furthest from Demonstration. Instead of win- ning its results openly, in the face of hostile criticism, it prefers the easier course of simply claiming already to hold them safe. It is only this claim which causes the puzzle just noticed; we are apt to forget that a claim may be made without any valid foundation. In this connexion, there remains one further difficulty, though not of any great importance. It will perhaps be €hap. YL] the EMPLOYMEXT OF GUESSWORK. 233 ■doubted at first sight whether the analogical argument should properly be considered to come under Proof by Example as here understood ; since, the Thesis being itself the ' theory/ the Reason is not a ' fact agreeing with the theory/ except on condition that the analogy holds good ; which condition cannot be simply taken for granted with- out begging the question. ' ^ — > Z ' (e.g.) is only a fact agreeing with the tlieory that S — > Z, on condition that there is essential resemblance between S and ^ ; and the question whether or no this essential resemblance exists is just the turning-point of the argument. But the reason for treating Analogy as Congruent Fact is that inasmuch as the employment of an analogical argu- ment implies in itself that the analogy is supposed (by its employer) to be a valid one, wherever analogy is appealed to as proof it is clear that R is given as heinrj a fact agreeing with the theory ; inasmuch as the case given is supposed by the arguer to be a case in point, the argument is brought forward as resting on a fact agreeing with the theory. The central type of Analogical reasoning is, then, that which we have already briefly noticed above as ' Extension to parallel cases.' Case S and case ^ being- seen to be ' similar,' a certain assertion true of the one is supposed to be true of the other. If the sugar trade is to be protected, w^hy not the iron trade or the cotton trade ? Since the Irish Church has been disestabhshed, why not the English Church also ? Such examples as these, how^ever, lie on the borderland between the 234 FALLACIES. [Part II. arguments from analogy and from sign. The technical distinction between the argument from analogy and the deductive argument from sign or mark (or middle^ term) being that in the former the exact points of re- semblance and difierence between the things compared are admittedly not yet distinct, it follows that so soon a^ the details of resemblance become clearly recognised as a warrant for considering the cases parallel, these points of community become at once a sign relied upon, and the- argument rises to the deductive rank. Thus in the instances just given, if the sole (or sufficient) point of resemblance claimed be the fact that both are trades or that both are national Churches, then the assertions that the sugar trade ought not to be protected or that the English Church ought to be disestablished, are based no longer on mere analogy but on imjAied 2^TmcipIes under which they are brought by means of the respective signs or middle terms. The case of the suo-ar trade is in this way referred to the recognised principle that protected trade is on the whole uneconomical ; the case of the English Church is referred to a precedent supposed to have been created (i.e. a principle supposed to have already received tacit recognition) by what has gone- before. (6) Proof of Lavj from Fact. The second mode of Proof by example is where the example or examples given are not supposed parallel cases to the theory, but instances, and if possible ' cru- Chap. YI.] THE EMPLOYMENT OF GUESSWORK. 235" cial ' * instances, of the operation of the supposed law.. And, first, there is a further simplification to be made, after the pattern of that used by Mill in framing a uni- versal formula for Analogy. The generalisation which appeals to facts as evidence may, as we have seen above, either be expressed directly as an abstract proposition, or lie hid under cover of a concrete or abstract-concrete one. The attempt to prove, for example, that S (a known concrete event) vxcs causally connected with ^ (whether the latter be also kno\vn to have existed or not) by means of some fact merely agreeing with such theory, — such as that S immediately preceded or followed ^, either in this case or on past occasions — belongs properh' to this mode of argument just as truly as the attempt to prove by the same means the simple direct generalisation that S is (in general) thus causally connected with ^. In other words, the evidence produced for any assertion may conceivably be (is sometimes) of an empirical kind. In supporting any variety of thesis, the exact law, or outcome of conflicting forces, relied upon, may be so> dimly conceived that to call the process in its present stage deductive would be to confuse a very important distinction, while any attempt to search firut for the faults to which deductive proof, as such, is mainly liable, would be a waste of time. This being the basis of the distinction, we shall find * A crucial instance, in its modern sense, maj be defined as any single instance deemed sufficient to prove a law: as in many cases of Proof under the method of Difference. See Appendix (B), p. 346. '2oCj FALLACIES. [Part IL that, in attempting to frame a typical formula for the inductive argument, it is best to take for the Thesis an abstract proposition. Not only are such arguments the kind in which the evidence is as a fact most frequently empirical, but that in which it is most rightfully so : since a concrete proposition that rests on merely empirical grounds has, and is widely recognised as having, a merely jjrovisional suj^port ; while it is equally clear and also sufficiently widely recognised that our deepest basis for abstract law is concrete fact. To deal with concrete subject-matter successfully, in the complexity in which it actually occurs, — which complexity is ever becoming- more manifest as our view ojDens out and hidden dif- ferences come to light, — Ave need at least some glimpse of the uniformities concerned, some knowledge of what may be expected a priori ; and this whether the concrete Thesis is explanatory, classifying, or predictive. In practice it is safe to say that wherever a concrete Thesis is supported by appeal to congruent facts alone, the first step towards testing the value of the evidence must be to get the supposed underlying laws clearly stated ; and that where an abstract-concrete proposition is thus sup- ported, it is the abstract element in it which stands first in need of proof After what has been already said on the subject of Analogy, this more direct kind of generalisation needs little further preliminary notice. Whereas in analogical reasoning the leap from one supposed parallel case to the ■other is made with only a dim recognition of the law Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 237 (M — > Z) which should bind the cases together, here w^e have the law itself directly set up as Thesis. ^ has been observed in a certain connexion wdth Z, in certain cir- cumstances which seem to Avarrant our saying not only that when (if ever) we meet Avith ^ again we may look for Z, but that M Avas that particular element of ^ Avhich was essential, and that the Avider laAA^ M — > Z can hold its OAvn against all but unpractical doubts. Any ' thing ' we like to name, — let us here name it ^ — is analysable into component circumstances. Let ^, for example, be that CA'ent called the arrival of a ship at St. Kilda. Some time ago " it AA^as a general belief at St. Kilda that the arriA^al of a ship gave all the inhabi- tants colds." * Let ' unusually numerous colds among the inhabitants ' be represented by Z. The inhabitants, then, Ave are told, commonly believed the truth either of the simple laAv ^ — > Z, or possibly (if the material frameAvork of the ship itself be denoted by M) the law M — > Z. But this easy explanation did not satisfy Dr. John Campbell, and he began to analyse ^ a little more deeply, and to ask AAdiat distinguishable circum- stances there were, forming part of that Avhich was broadly described as ' the arriA^al of a ship ; ' and after taking " a great deal of pains " he ended by explaining it " as the effect of effluvia arising from human bodies." We are not told more definitely Avhat he meant by this, or AAdiy the arrival of a single ship at the harbour should * Dr. Pai'is, Pharviacologia, p. 89, quoted by Prof. Fowler, Inductive Logic, p. 310. :238 FALLACIES. [Part II. mean so great a difference in the amount of effluvium in the island, but at any rate such was his explanation ; and if we denote ' effluvia arising from human bodies ' by N, the law at which he arrived Avas either ' N — > Z/ or ' ^, when N, — > Z.' Dr. Paris, however, either himself discovered, or at least quotes and endorses the discovery of, another element insei3arable from ^, and in his view more im- portant as regards Z. This was the fact that '' the situa- tion of St. Kilda renders a north-east wind indispensably necessary before a stranger can land." Let N.E. wind be represented by 0. " The wind," he adds, " not the stranger, occasioned the epidemic ; " or, in other vv^ords, he views the real law as O — > Z. This law, it may be usefully noticed in passing, was not then discovered for the first time. was already known as a vera causa of Z, while M and X were not. If we had no known laws -already, discovery of explanations would be a slower process than at present. But Dr. John Campbell had left the supposed law in an unsatisfactory condition : the assertion ^ N — > Z was in possession, and it had to be made to face a hitherto unsuspected alternative, — that which Dr. Paris suggested. It seems hardly necessary to remark that the symbols M and Z were only chosen in order to show more clearly the connexion between Induction and Analogy. Bat in framing a formula for the inductive argument, we may now return to S and ^, without any danger of misinter- pretation. I do not see how to put the whole inductive Chap. YL] THE EMPLOYMENT OF GUESSWORK. 239 argument into symbols ; but we may state it in a con- veniently short form as : — S (universally) — > ^ : for here are (one or more) cases of which this la.w is the best explanation : proper precautions having been taken against all rival theories. The discussion of these proper precautions will be more in place when we speak more directly of the dangers of Empirical proof. At present there remain the deductive arguments to set out. § G. The Argument by Sign. In speaking of Analogy, we have akeady sufficiently noticed the indistinctness of the line between this and Deductive Proof, and the manner in which the analogical argument becomes deductive as soon as the points of supposed resemblance between S and ^ are definitely apprehended as a warrant for the inference. And just as the analogical argument may apply to any kind of subject-matter, so may the strictly deductive argument. We may attempt to prove or to disprove either an abstract or a concrete proposition, and either an explanatory, a classifying, or a predictive one, by means of a definite middle term. And, further, the nature of this middle term, or link, must also already be sufficiently obvious. If it is to be really a link, it must be a sign ; or, in other words, it must be known to us (or expressible) as the S •of an assertive proposition. 240 FALLACIES. [Part IL It remains to be added, liOAvever, that although in every deductive argument M may certainly be viewed as a sign, this is not always the most direct description of it that can be given. Various types of deductive argu- ment are distinguishable, and it is only where the Thesis is affirmative that we really gain much by resting our case on plain, straightforward indication. Thus, where the Thesis is 'S (or This S) — > ^,' if we know already the law that M — > ^, M is well described as a mark or sign which it should be our aim to show that S pos- sesses. And, on the other hand, if ' S — > M ' be given as a reason, the relevancy of such reason plainl}^ depends on the trustworthiness of M as indicating ^. This for- mula, it will be seen at once (namely ' S — > ^ : for S — ^ M, and M — > ^ '), corresponds to the ancient syllogistic mood Bavhara (or to Celarent, where the E conclusion is affirmative in the sense here used *), or, in the language of the hypothetical syllogism, to the modus ponens.^ Our known law is that ' if or wherever M can be indicated, ^ is indicated also,' and our application is that here, in the case before us (namely S), M can be indicated. But take next the case where the thesis is an ' Asser- tion of Difference,' as S- ^*^ ^ : here the word ' sign ' (in its ordinary restricted meaning, at least) is far less directly applicable. To the deductive argument to prove * See pp. G5, 60, 73. f WTiere M is negathe (i.e. iu tlie disjanctive argument), this is called the modus toUendo ponens. Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 241 such a thesis, the name 'Distinction by point of differ- ence ' seems better applied : two ' things ' are seen to be distinct, since one has, while the other lacks, a certain quality. For example : — " The release of the Kihnainham prisoners was not a case of ' pay- ing black mail : ' for now, sir . . . what is paying black mail ? To pay black mail is to give something that you would not otherwise give. Are we going to do so ? " And accoi-ding as S or ^ is the possessor of the quality, w^e get two slightly different formulae : — {Cesar e) S ^' ^ : for S — > M, and ^ — > non-M : (Gamestres) S ^ ^ : for S — > non-M, and ^ — > M : or, expressed in hypothetical form : — (modus 'ponendo tollens) S /-w ^ : for if ^ were in- dicated the absence of M would follow : but here (namely, in the case of S) the presence of M is indicated : {modus tollens) S ^^ ^ : for if ^ were indicated, the presence of M would follow : but here, the absence, etc. And, lastly, take the case where the thesis is symbo- lized as S H — > §,* — the case where (by means of a middle term) an exception is brought against some generalisa- tion. It is somewhat difficult to frame any single for- mula for this mode of argument, while introducing any mention of a middle term. But the varieties may be reduced to tivo that appear fundamental, all minor kinds being capable of being shown to belong to one or the other.! These two are : — * The symbol -f^ was explained on p. 68. ' - t For the reduction of these in detail, see Appendix (C) . f^42 FALLxVCIES. [Part II. (1) S -i^ g^ : for S -j-^ M, and g^ — > M (Baroko) : (2) S -i-> §: : for M -f-^ ^, and M — > S (Bokardo). The distinction made is briefly as follows : the first formula includes every case where, in support of a bare denial, some point of difference is shown to exist in one or onore instances between S and ^ of the positive assertion denied, or where S is shown to possess, in one or more instances, a sign (M, or non-M) of the absence of ^. The second includes every case where an instance, or a part of the class spoken of, is brought forward as contradicting the generalisation. We may, for conve- nience call the former 'Exceptive disproof by Sign or Difference,' and the latter 'Exceptive disproof by Example.' As instances, we may take for the former : — " Quibbling is not necessarily a case of sophistry : for quibbling may be unintentional, while sophistr}- always implies the intention to deceive." Or— " Honesty is not always the best policy : for honesty sometimes means starvation (and what ends in starvation is certainly not, etc.)."' And for the latter — " The radical is not always ca man of lofty motives : your mere malcontent, for exami^le, is often rather a selfish being, and every mal- content is of course a radical." Or-~ " It does not follow that a stickler for truth-telling need be narrow and severe : quakers, for example, make a great point of telling the exact and literal truth, and they are often charitable enough." . Three main kinds, then, of deductive argument are distinguishable : — 1. Proof by Sign : €hap. Vr.] THE EMPLOYMENT OF GUESSAVORK. 243 2. Distinction b}^ Point of Difference : 3. Exceptive Disproof : And it has been noticed tliat these three apply respec- tively to the support of the three different kinds of thesis, — S — > ^^ S ^w ^, and S H — > ^. It seems necessary, however, to remove a possible misconstruction here. It must not be supposed that Barbara and Celarent are themselves never used in Disproof, or Cesare and Camestres never used in Proof On the contrary, both Disproof by sign, and Proof by essential difference are possible. Thus we might appeal to the sign that 'his hat is hanging on its peg,' in disproof of the assertion ' he has gone into the city ; ' or, on the other hand, we might prove, by means of a point of essential difference, the positive assertion that between whales and fishes a useful distinction may be made. But since on the whole the formula Barbara (or Celarent) is more often used to support a positive assei^ion, while the argument from Difference is more often used to support a bare denial of analogy or of superficial classification, it seems better, in treating the special arguments broadly and typically, to connect the former with Proof, the latter with Disproof. And as regards the assertion S -\ — > ^, although from our point of view this may be treated as purely negative, yet it is undeniable that the vague and flimsy positive assertion which such propositions are on occasion used to express, may also be supported by the same evidence as that employed to support their meaning of bare but downright denial. This verbal difficulty need not, I 24i FALLACIES. [Part II, hope, after what has been ah^ead}' said about the inter- pretation of grammatical forms, occasion a real stum- bling-block. And we may now, before speaking of the dangers of deduction as a whole, briefly discuss the occasions and purposes for which each of its three typical forms is most commonly employed. ((0 Proof hij Sign. In one sense, of course, all attempted Proof is art attempt to show signs. The Reason itself is always- given as a supposed sign that the Thesis is true. But as contrasted with Empirical Proof, there need be no danger in restricting the name of ' Proof by Sign ' to the cases where the sign given is plainly recognised as being such in general ; where, that is, a middle term is in some way referred to, and where accordingly the attempted Proof approaches the deductive type. The distinction between empirical and deductive proof lies, as already said, in the fact that in the latter the proposition stating the universal trustworthiness of the sign asserted has already taken more definite shape in the mind of the person using the argument. Where, as in empirical proof, we argue that a theory is true because it is the 'best explanation' of certain facts, the proposition summing up the grounds on which this is taken to be the best explanation is nearly always too complicated to admit of statement Avithout much preliminary labour, if at all. But so far as we refer to a sign, with definite consciousness that it Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 245 is (in general) a sign (jf the ^, so far the argument is deductive. The employment of Proof by Sign is one of the chief purposes, and clearly the directest purpose, for which <3very abstract proposition exists. In every abstract pro- position, something is said universally to indicate (to be a sign of) ^. And that 'something' becomes thereby capable of being made the middle term in Proof by Sign. If, therefore, any S can be identified w^ith (or shown to indicate) such M, it indicates also, of necessity, that which the sign signifies ; for nota notae est notarei ipsius. In a former chapter * we saw that general names might be viewed as labels attached to the ' things ' that bear them, and in Proof by Sign we have the clearest instance of the operation of the naming process. What- ever facts, positive and negative, are included in the meaning of a name, are true, of course, of anything which rigJdfidhj deserves the name. Hence, in order to prove one of such facts about a given S, we need only show its rightful possession of that particular label. While, then, this mode of Proof sometimes proceeds by stating both Principle and Application (full Demonstra- tion), and sometimes by stating the Principle only, the commonest form is where the Reason states that S de- serves (or, for the disjunctive argument, does not deserve) the name of M. Proof by Sign is, in fact, so familiar and so funda- mental a process that it seems hardly worth while to * See p. 109, above. 246 FALLACIES. [Pakt II. spend more time in merely describing it. The dangers to which it is liable are our real concern, and these will be spoken of presently. But the other two modes of deductive argument call for a few words of further description. (6) Distinction by Point of Difference. The exact point of difference between S and ^ i« sometimes just as dimly conceived as is the resemblance relied upon in the Argument by Analogy. As the reader . may have often noticed, the same class of minds that are satisfied with viewing S as ' exactly like ' ^, will also be satisfied on occasion (and equall}^ through ab- sence of discriminative power) to view them as ' totall}' distinct.' To discriminate is to see i^oints of difference^ not merely to deny at large all resemblance whatever. For some reason, however, the argument from ' indis- criminate difference ' has obtained for itself no express recognition, though it certainly exists. Possibly this is. to be explained by the greater pleasure which the view of resemblance gives, and thence the greater frequency of loose analogy. But since the danger here is essen- tially the same as the danger of Analogy, — namely the^ absence of exact discrimination, — there seems to be nothing further to say about it as a special kind of argument. The remedy is, to call for the supposed point of essential difference, and thus to raise the argument to the deductive rank. Chap. VI.] THE EMPLOYMEXT OF GUESSWOKK. 247 Next, the expression ' essential difference ' is one of those which have passed so freely into popular use as to be often employed without a clear apprehension of their meaning. Essential means again here, essential for some purpose understood. And the purpose of essential differ- ence always is, to break down some supposed analogy, or to deny that S rightly deserves some name. Hence it is chiefly for Disproof that Distinction by point of difference is used. It is clear, however, that any point of difterence, essen- tial or not, so long as it is thoroughgoing, — so long, that is, as S and ^ entirely differ in regard to its possession, one (universally) having it and the other (luiiversally) liaving it not, — is sufficient to support the thesis S f^ ^. But S may differ from ^ in many points, and yet a given analogy between them hold good. The whole force of this argument, when used in Disproof o£ analogy or sign, depends upon the question whether the point of differ- ence (M) is essential for the purpose in hand. Those who have not fully grasped the meaning and importance of the doctrine as to the burden of proof, may find at first sight a difficulty here. Is it incumbent on the disputerof an analogy to prove that the difference (M) is essential, or must the believer prove the essen- tiality of the resemblance relied upon ? The simple answer is, that whichever asserts essentiality, whether of resemblance or of difference, must prove it or else be content to make an apparently unfounded assertion. It is, of course, possible that the disputer of an analogy 248 FALLACIES. [Part IL may commit himself so far as to say boldly that the analogy fails essentially; but this would be a highly gratuitous — often a rash — proceeding on his jiart. He ma}^ usefully make a milder assertion about it, namely that he sees a point of difference and is anxious to inquire whether the believer, having duly taken it into account, has reason to suppose it unessential. In that case, of course, he avoids all burden of proving anything but simple difference, leaving it to the other side to show wherein essentiality consists. If, however, — as it is sometimes safe to do, — he risks the full assertion that the given analogy does fail essentially, let us see what it becomes incumbent on him to prove. The analogical argument attacked is, say : — S— >Z: for^— >Z: But, says the objector, " ^ — > M, while S — > non-M, and M is essential^' He asserts then that it is only because ^ — > M that ^ — > Z ; that where M is absent the supposed indication of Z is worthless. This assertion, therefore, is implied in calling the difference essential, and must be proved, like any other assertion, before the case is made out. From these considerations it follows that Distinction by Essential Difference can never be used except in Disproof, since the ' essential ' always refers to some- thing gone before. And it is also clear that Distinction by Simple Difference can rarely be used except with reference to some supposed mistake, since the positive assertion contained in saying merely that two things •CiiAP. VI.] THE employ:mext of guesswork. 249 -differ is so safe as to be practically trivial. Everything •differs from everything else in some points, — even a coin from its neighbour struck the next moment from the Mint, — just as everything also resembles in some point (even if it be only in being 'nameable') every other thing. The real value of a given assertion of difference is to contradict some supposed exaggeration of the im- portance due to a superficial or ' striking ' likeness. (c) Exceptive Disproof. That the exception proves the rule, has passed into a popular saying. It is by seeing exceptions, and thus guarding our statements, that we establish any law on a firm basis, making it henceforward unexceptionable. By searching for exceptions we test, or try, the law set iip for Proof I am aw^are that this much-abused pro- verb is also sometimes interpreted to mean that since the given fact deserves to be called an exception it must be comparatively rare ; but such an employment of the phrase (apart from its etymological shortcomings) borders so nearly on the Petitio lyrhicipii — having no practical value except as a somewhat epigrammatic avgumeniuT)% ad Iw'ininein, and being often in fact employed for a very different purpose — that it seems best to keep in view the other and more fruitful meaning. A supposed law which is found false in one instance becomes thereby fallible in all, until the exceptions are incorporated into its statement and thus its application narrowed. Hence 250 FALLACIES. [Part II. Disproof by exception is one of the most important processes of verifying, and so establishing or discarding^ our theories. The ' best explanation/ or ' proved theory/ is that which remains over as a residue when all possible holes have been picked in the crude or sweeping assertion first put forward as a guess. Exceptive Disproof is therefore the most frequent mode of attacking a generalisation directly: attacking, that is, the law itself asserted, not its grounds. To attack its grounds, as will be shown presently, the best way is either to point out" essential difference be- tween the cases observed and those inferred, or else to point out simple difference and inquire whether or no it is known, or why it is judged, to be unessential. But exceptive disproof finds at once the contradictory instance. Amonofst the misleading; statements that float about so freely in common parlance is one to the effect that " Nothing is so hard as to prove a negative." The re- verse is the actual case. Disproof, qiid Disproof, is safer and easier than Proof, just as destruction is less trouble- some than construction. In Disproof, since the Thesis is a bare denial, we commit ourselves to the least possible amount of dogmatic statement. We mereh' assert that some other given proposition is false, with- out venturing to say exactly what is true in place of it. The fact that underlies, and (with proper explana- tion) may be held to justify, the popular expression above quoted, is mainly the difficulty that attaches to- such far-reaching words as ' never,' ' nowhere,' ' no CHAr. yi.] THE EMPLOYMENT OF GUESSWORK. 251 one/ and the like. ^ Positive ' assertions, whose cor- responding negatives are obliged to employ these words, are, through their vagueness, so securely guarded against being brought to an actual test, that Dis- proof often becomes practically impossible. To prove, e.g. that my neighbour has never been in New York, or that no one has ever held a certain opinion, is of course to disprove the very vague assertion that these events may (at some time or other) have happened, — an asser- tion with which it is commonly safer, and perfectly harmless, to agree. Again, Disproof is sometimes as difficult as Proof — not more so. To disprove the exist- ence of Buddha, or of table-rapping spirits, is manifestly impossible so long as there is no admitted test to which the question can be brought. But, as De Morgan has remarked, whenever we set out to 'prove (in the narrower sense) any Thesis, we must be prepared to dis]prove any one or more of an indefinite number of other assertions that conflict with it; while in order to disprove any Thesis we need only reduce it to absurdity ; which is often possible without our being prepared to prove a single positive assertion about the matter. A definite theor}', whether abstract or concrete, can be disproved by ' experience ' more easily than it can be proved : foi- in disproof we have only to find some single instance which conflicts with the assertion if abstract, some single point in which it fails if concrete. It is in fact mainl}' by means of this simpler disproving operation that the securest experimental Proof takes place. All testing of 2dZ fallacies. [Part II. a Theory set up is, at "bottom, nothing else than a search for contradicting facts existing or inferrible. On the thoroughness of the search the value of the test depends. After a long life of honourable security any theory may be in a moment upset, or at least may be found to need qualification, by the discovery of a single hidden circum- stance : and experimental inquiry in its highest form is in reality an attempt to dispose beforehand of all rele- A'ant facts that can by any means be brought to light. As regards the two varieties of this form of argument, (given on p. 242) not much requires to be said. The use of the one or the other clearly depends on the nature of -our previous knowledge bearing on the question raised. Neither mode can, I think, be called altogether safer or better than the other, since even direct identification of M with S may well be mistaken. If, however, any pre- ference is to be given, perhaps the latter (Bokardd) should have it. The dangers in the way of these, as of all forms of deductive argument, will be treated in a later section. III. The Dangers of the Argument by Example.* {a) The Dangers of Analorjy. In both kinds of Argument by Example, — Analogical reasoning and Inductive Proof — the primary danger is that of overlooking some hidden element in the facts, .and thereby generalising too freely, rather than that * The clangers peculiar to the special types of argument are shown , :all together, in a table (Y.) in the Ai^pendix (E) . Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 253 of accepting a definite principle wliicli, true or not^ does not apply. We are not here concerned with an}^ dangers to argument when the principle relied upon is simple and clear, but solely with those incident to rapid unconscious employment of some highly complicated principle, or to our hurried summary of the total outcome of a conflict between unnumbered dimly formulated laws. It was said above that in adopting Mill's formula for Analogy as typical, Ave must bear in mind that an actual argument, though truly analogical, may easily appear on the surface not Cjuite to fit the formula. But this formula is nevertheless a perfectly legitimate simplification, since it serves to o-eneralise the one dano-er to wdiich all analo- gical arguments, in so far as analogical, are primarily liable : the danger, namely, that the resemblance between the cases supposed to be analogous is only a superficial one, — or, more widely still, that the resemblance, even if on the whole real and deep, is not essential for the purpose intended. So far as an argument professes to rest on analogy, the matter of first importance is to ascer- tain, if possible, the exact points of resemblance and difference between the cases compared, and to inquire further whether the resemblance as thus defined and limited has any right to be considered essential in regard to the purpose for which it is in the given case employed. We saw^ also that the real difiiculty in clearly placing- the argument from Analogy among special kinds of Proof, arises from the fact that as soon as the exact points of resemblance relied upon come into clear view" 254 FALLACIES. [Part II. the argument ceases to be analogical, and becomes deduc- tive. That is to say, if we rest our belief that S — > Z on the observed fact that § (which resembles S in the jjoint 21) — > Z, we are really beginning to employ, instead of mere analogy, the full syllogism ' S — > Z, for S — > M, and M * — > Z.' Our clear recognition, that is, of the exact extent of resemblance relied upon, is itself a recognition of the underlying Principle by virtue of which S and ^ are considered ' parallel cases ; ' in other words, is an assumption of a Law from which our thesis may be deduced. Take, for instance, the argument sometimes employed against Sunda}^ closing, that since the upper classes have their clubs open on that day it would be unfair to deprive the poor of their only places of resort and refreshment. It is clear at once that we have here a case of complicated or double analogy, clubs being considered to ' essentially resemble ' public-houses, and the upper classes to essentially resemble the lower. But what is meant by ' essential resemblance ? ' Not, surely, that the things compared are precisely alike in all respects, — else detection of false analogy would be a far simpler matter than at ]n'esent : but that for the purposes immediately in view, the points of difference may be neglected. Now, as soon as we begin to neglect points of difference, no matter where, we begin to generalise : that is to say, we extend the possible range of our assertion. That which constitutes individuality is always the difference {i.e. peculiarity) that an individual possesses * If not universally, at any rate equally when limited by S and ,S. Chap. VI.] THE EMPLOYMEXT OF GUESSWORK. 255 over and above any class to which he may belong, just as we have seen* that it is differentia that the sub-class or species possesses over and above the genus. So far, then, as we neglect the points of difference between clubs and public-houses, or betAveen one class of men and another, we speak of them no longer as distinct individual things, but as members of some wider class which includes them and may possibly include other things as well. In the instance quoted, the key to the class intended is expressly given in the case of the analogy between clubs and public-houses : it is the being- places of 'resort and refreshment' that is considered essential : this is the point of resemblance in virtue of which {i.e. to the extent of which) what is true of the •one is supposed to be true of the other. As regards the analogy between upper and lower classes, it seems to have been thought unnecessary, or unsafe, to give the key expressly; such maxims as that "no class in the State should be specially favoured without reason shown " being widely accepted as a basis of legislation. And if this account of the analogy intended be a correct one, — if it is only as being places of resort and refreshment that public-houses are to be kept open for the benefit of the poor in their sole capacity of citizens of the State (or whatever may be the wide class to which upper and lower classes equally belong) — then we thereby imply the Generalisation, or Law, or Principle, "All citizens of the State are {a pvioTi) equally entitled to their * Cf. p. 108, above. 2dG fallacies. [Paut il places of resort and refreshment ; " by means of which, if true, the Thesis may be deductively proved. However important, therefore, Analogy may be as setting us on the track of a fruitful Inference, as a mode of Proof it is in itself almost Avholty worthless, — only sufficient, that is, to raise a vague and slight presumption where no better evidence can be obtained. It is perhaps, more widely airplied, in common discourse, even for Proof as well as for Inference, than any other form of argument. But this seems to be chiefly due to the slack- ness with which our examination of evidence is commonly carried on. It is so much less trouble to see that two things bear a ' striking resemblance ' than to discriminate accurately how far the resemblance really goes, and the points wherein they differ. There is nothing, pro- bably, that is more characteristic of the higher* in- tellect as contrasted with the lower than its greater power of discriminating, — i.e. of seeing points of differ- ence. It is differentiation that is always the law of progress. Knowledge begins as a vague blur, Avhich gradually becomes distinct. Everywhere the specialist's eye sees finer shades of difference than are visible to the public, — as the shepherd knows his sheep. It is incapa- city for seeing difference that lies at the root of all crude^ ill-considered generalisation, and therefore at the root of the mental ' narrowness ' (as it is usually called) which is * Cf. H. Spencer, Pgiicliology, p. 220. " Incident forces that seem alike to a lowly endowed creature, seem conspicuously unlike to a crea- ture endowed with the sense-organs required for appreciating them." Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 257 ever ready to accept a principle unduly simple and wide in its asserted sweep, and therefore unduly rigid in its actual application. It is neglect of difference that always marks the ruder nature, easily content with the roughest weights and measures. It is the besetting danger not only of ignorance as opposed to experience, of clumsiness as opposed to delicacy of touch, but also of the habit of dreamy theorising as opposed to patient reverence for fact. In thus noticing the harm of neglecting difference, I must not be understood, of course, to advocate the neg- lect of real resemblance ; only to say that this is a fault to wdiich the majority are in practice far less liable. The inducements to over-generalise are on the whole stronger than those to indulge in excessive hair-splitting. And apart from mere ignorance or incapacity, it is always less trouble to avoid distinguishing, even when we have attained the power : the recognition of resemblance, whether justified or not, is always a more pleasant operation, simplifying Nature and thereby giving freedom, and also much self-satisfaction, to the mind that sees the supposed analogy. Hence, no doubt, much of the charm of metaphor and of the cruder kinds of poetry, and hence the efficacy, in spite of its unfairness, of caricature. Whatever appeals to our idleness, while at the same time gently flattering our sense of ' breadth of view,' always bids fair to win a wide reception. In its effects, hair- splitting is perhaps a more deadly fault than coarseness of vision, though less the property of the uninstructed, the 258 FALLACIES. [Part IL thoughtless, the impatient, and the clumsy. The power of seeing differences, exclusively cultivated, leads no doubt to a casuistry and a hesitation which are far from being either pleasant or practical. So, too, the mere neglect of resemblance, without at the same time a distinct and conscious vision of differences, cripples our power of ex- tended sight and of useful generalisation. This forms indeed no fallacy, as the term is generally understood ; but it is a serious limitation, as the existence and spread of o-eneral names, and of science itself, bears standino^ witness. Often, no doubt, it is merely the recoil from hasty generalisation that leads to the adoption of ' rule of thumb : ' in any case, however, this is of course a falling short from the ideal. It is the undue neglect of difference, then, in the midst of recognised resemblance, that constitutes the fallacy of False Analogy, just as the due neglect of difference con- stitutes sound generalisation. While the ideal is, to give to both Resemblance and Difference their due weight, the actual course of the history of knowledge, so far back as it can be traced, is a record mainly of unsuspected dif- ferences brought to light. Where any sound generalisa- tion has been reached, it has in most cases either been preceded by deep analysis, or is itself the residue of an unsound generalisation after it has gone through a pro- cess of limitation and restriction in order to make it fit the facts. Further back than any records go. Philology helps us to see that the earliest traceable formation of language has proceeded also by analysis o£ what first CiiAP. VI.] THE EMPLOYMENT OF GUESSWORK. 259 seemed simple. First we find one word employed for what we now know to be many diflferent things : gradu- ally, as insight deepens, new words grow up, in order to mark off groups and portions as distinct. While there may be a synthesis based upon analysis, the first step is to analyse what before seemed simple. The shapes in which False Analogy usually occurs are very numerous. They range from open reliance on Analogy in lieu of Proof, down to the finest shades of rhetorical suggestion by means of metaphor ; and even into the region where metaphor ceases to be distinguish- able as such, and where we reach the unavoidable short- comings of language. Taking first the more definite end of the scale, the following example will show to some extent the dangers of analogy. An eminent author, writino- on the work of the Enoiish Church before the Tractarian movement, contrasts the newer state of things unfavourably with the older, because the Church in those former days "taught us to use religion as a light by which to see our way along the road of duty. Without the Sun our eyes would be of no use to us ; but if we look at the Sun we are simply dazzled and can see neither it nor anything else. It is precisely the same with theological speculations. If the beacon lamp is shining a man of healthy mind will not discuss the composition of the flame." Here, of course, the resemblance between the Pro- testant religion and a light to lighten the road of duty is sufficiently striking, and (if it be granted, as for the purpose of this argument it may safely be, 260 FALLACIES. [Pap.t II, that the light is no mere will-of-the-^^dsp) no fault need be found with the metaphor so far. But in what respects do 'theological speculations' really resemble the process of ' looking at the light ' ? Whatever other faults the movement spoken of may have had, surely it was, in essentials, an attempt to look more closely at the road of duty as illumined by the light. To call this looking at the light is merely a loose and con- venient elliptical expression. At any rate, nothing is openly said by the writer to show that this latter employment of the metaphor is not a better one, and if we are to suppose such a denial covertly made, it comes very near to beggmg the most important question con- cerned. But in order to show more strikingly the worthless character of analogy as argument, it may be further noticed that in the second half of the sentence the metaphor is changed, b}^ its author himself, in a way that saves an opponent all trouble, inasmuch as it force.^- the first analogy to defeat its own j^urpose. Religion becomes no longer a Sun for lighting up the road, but a 'beacon lamp,' — a thing whose use and purpose is precisely to be looked at : and in order to save the argu- ment, theological speculation has now to be likened to 'discussing the composition of the flame.' Would not the Tractarians say rather that if they cared to discuss the composition of the flame at all, it was only so far as might enable them to be sure that this really was the ' beacon lamp ' of which they were in search ? Analogy used in this way is, no doubt, as things are, a powerful Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 261 rhetorical instrument ; but it is not one that is destined to extend its influence in the future. The remedy is so easy. Give a dealer in analogy rope enough and he will probably end as above ; but if not, and if it be considered too much trouble, or too difficult, or too slow, to inquire exactly into the real points of resemblance and difference, nothing is simpler than to change the metaphor and so turn the tables. One arguer can always assert covertly as well as another, and it requii-es no great intellectual strain to produce a happy simile or to ^x the attention of a busy or thoughtless audience on some ' striking likeness ' which is so neat and pretty that it seems to them it cannot be untrue. It is, however, solely when a supposed analogy is put (or accepted) in place of argument that harm is done. As mere illustration, or as re-assertion of a thesis in a more concrete form, only pedantry can object to it ; and as supplying the first vague hints for future verification it will always be the chief stepping- stone to good results. But the line between employing Analogy as argument and employing it with an open recognition of its dangers is so exceedingly fine that it becomes in practice almost impossible to over-estimate the need of keeping a jealous guard against neglected points of diflerence. It must also be remarked, that even where the analogy is plainly a false one, it is always possible that the person employing it has himself been under no delusion as to the gap requiring to be filled up, but has only overrated the discriminative power of his audience, — or foro^otten their readiness to be deceived. 262 FALLACIES. [Part II, Open reliance on Analogy as argument is rare. The analogical arguments that we find actually employed show a decided disinclination to express themselves in a quite straightforward fashion ; unless, indeed, as in some of the cases above quoted, the connecting link (or middle term) is fairly obvious, and the argument, therefore, already nearly deductive and easily raised to that higher rank. As a general rule, the more merely analogical (i.e, the less deductive) the argument is, the more will it naturally tend to avoid open and definite expression by means of this simplest formula : for the definite expres- sion of reliance upon the resemblance between S and ^ to prove a definite assertion regarding S, is apt to pave the way for inquiries that are then felt to be awkward. When the Analogy is a weak one (and equally when the points of resemblance are numerous or not easily summed up) nothing of course is more damping to the argument than any call for a clear statement of the exact points of resemblance relied upon ; and hence in many cases even the setting S and ^ clearly side by side, and reducing the reasoning to the above formula, becomes almost tantamount to a reduction of the whole argument to absurdity ; and is constantly employed for that purpose. Thus when a speaker in Parliament declared that — " To say that there was nothing in the nature of a compact or agreement between the Government and the gentlemen whom they had been keeping in confinement without trial, reminded him of the principal character in one of Moliere's comedies, who said that he had not sold anything, but had merely given it away to his friends and* they had given him some money in exchange — " Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 2G?> we find the other side makino- answer that— o " So far as the speech of the hon. member was not a mere baseless dream ... it contains at least this one statement, that hecause in Moliere there was a man who, having sold goods and received a price, pretended that he had made a present of the goods and received a pre- sent in return, the position of the Government is analogous to that man." And then comes a statement of the " essential differ- ence " between the two apparently parallel cases. As a general rule, then. Analogy has a tendency in practice to put itself forw^ard either as merely intended to raise a vague presumption, or else (and more com- monly), with an air of coming ex ahundanti, rather than as being in fact the sole evidence relied upon. It is usually given, however unintentionally, in such a manner that, if objections should be raised, it remains easy to claim that only an illustration was intended, and to grant with much candour that possibly as an illustration it fails to fit the case exactly; a process which closely resembles the parliamentary practice of first using and then ' withdrawing ' an ofiensive expression. The express words ' because,' or ' for,' or ' since,' are as a rule omitted by the speaker: the connexion will be amply supplied, as every experienced rhetorician must know, b}^ any average audience, and being thus voluntarily supplied by the audience, will probably be less exposed to their criticism. Whately, for example, did not write, " In- ductive Logic can never be a rival to the Aristotelian Logic, since a plough can never be substituted for a flail," but he wrote that Inductive Logic — 2CA FALLACIES. [Part II. " Would not . . . have the same object proposed with the Aristo- telian Logic ; nor be in any respect a rival to that system. A plough may be a much more ingenious and valuable instrament than a flail, but it can never be substituted for it." * Or again, Sir S. Northcote (speaking at Balham), did not say •' Mr. Gladstone, because he is fond of hewing down trees, will be likely to want to hew down our institutions," but he said — " We shall be abused by a great number of people because we hesitate to give to the Prime Minister exactly the facilities lie de- mands, but we shall endeavour to do our duty when those demands are made upon us ; and we may take to heart one of those wise fables on which our youth was nourished. You may remember how a cer- tain woodman went into the forest and asked the trees to lend him a bit of wood in order that he might make a handle to his axe. When they were unwise enough to give him a piece of wood, you recollect what happened to the trees themselves by the use the woodman made of the axe (cheers and laughter)." * These examples will be sufficient to show what is here intended. But the difficulty of deciding whether the Analogy Avas really relied upon as evidence, or genuinely and legitimately put forward as an illustration merely, or to point a quaint and semi-serious fancy, is not the only one to which we are exposed in practice, nor the most perplexing. This can, indeed, to a great extent be met (much as an unparliamentary expression may be met) by demanding a disclaimer on the spot. A far more difficult question arises when we attempt to ^x. the Kne between the metaphorical [and the direct use of names * The reader will notice that these cases are not given as examples of false analogy, but merely of the usual method of getting an analogy (true or false) accepted by an audience. Chap. YI.] THE EMPLOYMENT OF GUESSWORK. 265 And perhaps the most frequent manner in which covert analogy is used as argument, is by condensation into a name which just escapes being considered far-fetched or metaphorical. " It was observed by a sound thinker in those parts, that property- was ballast, and when once the aptness of that metaphor had been perceived, it followed that a man was not fit to navigate the sea of politics without a great deal of such ballast." That which to George Eliot and to most of her readers was clearly a mere metaphor, the aptness of which was all-important to the force of the argument, passed easily, she tells us, among the less educated electors of Treby Magna, as hardly distinguishable from a plain statement of fact. The power of recognising metaphor as metaphor is one of the latest and highest acquisitions (so far as it is yet acquired) of mankind ; an outgrowth of the accurate spirit which marks off modern science from the ancient reigTi of florid imagination. To some extent, however, we are all in the position of these electors. We smile at their simphcity, but future generations will smile at ours in turn. The schoolboy of the twentieth century may find a difficulty in realising that his ancestors were misled into supposing fleshiness of body to be "padding against the shafts of disease," or a glass of sherry taken just after a large and varied ^. In the first place, it must be remembered (as noticed at pp. 78-83) 268 FALLACIES. [Part H. that at the present stage of knowledge the propositions where such a statement can be in practice interpreted quite unreservedly are comparatively few in number. Here and there, certainly, we have discovered generalisa- tions which seem absolutely true, so far at least as our tests can yet try them and so far as all present practical pur- poses are concerned, — such as the Law of Causation itself, •or the law that human beings have human ancestors, or that all matter gravitates, or that decapitation causes death. But for the most part, even in Science, we are forced to be content with laws which express tendencies * merely. Often, indeed, we think ourselves fortunate if we can reach any shadow of a law at all. It is no ex- aggeration to say that the greater part of the knowledge •on which daily conduct depends for its rationalisation ■consists solely of generalisations which, however crudely and boldly expressed and at intervals believed, are really apprehended (so far as regards persistent or fruitful apprehension) in the dimmest and vaguest way. To go no fiu-ther than the popular maxim in favom- of speaking the truth, every thoughtful person will admit nowadays that the law as usually stated needs some qualification ; although most people feel the admission dangerous, since no one has yet been able to formulate the real law so ^s, while avoiding mere platitude, to take in all the exceptions. * The law of Gravity, it slionld be noticed, merely avoids this diffi- •culty in a verbal manner. It is absolutely true that all matter gravitates : but 'gravitates' is a word coined to exjoress the meaniog 'tends to fall.' Chap. YI.] THE EMPLOYMENT OF GUESSWORK. 2G0 Next, S (in general) may be asserted to indicate ^ (whether absolutely or reservedly) either as its cause, its^ concomitant, or its effect, — that is, either as ha^^ng ex- isted, as existing, or as to exist in the future. To assert that ^ is * the sole cause of S is to assert absolutely that S wherever found indicates ^'s past existence {e.rj. ' Life is always due to prior life ') : to assert the same indica- tion ' reservedly ' is to assert either that ^ is one cause but that there may be others ; or, in the most reserved form of all, that an observed sequence ^ foUow^ed by S was ' not purely accidental.' f To assert absolutely that S wdierever found indicates ^'s present existence, is to assert that every S w^ithout exception possesses the attribute, belongs to the class, deserves the name, or i& found in conjunction with, ^ : to assert the same re- servedly is to assert that S and ^ are more or less often found together (or that S is nearly always, usually, frequently, ^) — more often than mere coincidence wdll account for, — or again that the observed conjunction S and ^ in co-existence wdll at least tend to recur. To assert absolutely that S wherever found indicates ^'s future existence is to assert not only that S is a cause (or the cause) of ^, but that no other cause is ever capable of interfering with it, — a very large assertion : to assert the same reservedly is to assert that S, unless something unspecified interferes, may serve as a sig-n that * To say that S ^vas the sole cause generally bears a quite different meaning, namely that some other thing (perhaps vagiTely specified) wa& 9? of operative. t See note at p. 81. 270 FALLACIES. [Part II. ^ will happen, or that the observed sequence S followed Ijy ^ will tend to recur. In spite of these tangled variations there is, as it seems to me, a sufficient reason for framing the formula 4is above. This is the ideal type, by comparison with which any actual shortcomings may best be made apparent. If S does not indicate ^ quite absolutely, there is no better means of seeing why and how far it falls short of doing so, than an inquiry what are the dangers to which such certainty is exposed and what has been done to guard against them. And as for the time-element, that may be neglected, so far as a first out- lined view of the dangers is concerned. Just as the process may be generalised, so may the dangers. In spite of their surface variations their deepest meaning is the same. There is at bottom one primary source of fallacy in the inductive argument, call it by whatever name may be most convenient. We may name it, for instance, the danger of '' overlooking Plurality of Causes, or neglecting possible Chance or Counteraction," or " the possibility of unknown antecedents," or "arguing either jpost hoc ergo projyter hoc or per enurnerationein simpli- cem," or " neglecting to exclude alternative possibilities/' or " forgetting that facts may bear more than one inter- pretation," or " stating the law too widely," or " failing to see below the surface," or — perhaps on the whole best of aU — " unduly neglecting points of difierence." It may be well here to make a slight digression in order to show more definitely how ' undue neglect of dif- Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 271 ference ' is tlie main danger of direct generalisation just as of the argument from analogy. Concrete evidence for an abstract law consists, it has been said, of a case or cases brought forward, of which such law is asserted to be the best explanation. If then some better explanation is possible the theory as stated is impeachable. But what is meant by a Vjetter explanation ? Can there be degrees of explanation, so long as the facts are all explained ? Surely the facts relied upon either do or do not all form cases under the law asserted ? Surely the term ' better ' or ' worse ' is inappropriate ? B}^ the best explanation is meant, however, not only any law from which all the facts observed are deducible, — for w^e may often frame many different hypotheses, inconsistent w^ith each other, which will each explain all the facts ; but what is meant is, that solitary one out of all possible hypotheses which, while explaining all the facts already in view, is narrowed, limited, hedged, or qualified, sufficiently to guard in the best possible way against undiscovered ex- ceptions also. The wider the law^ the greater the danger, until precautions are taken : and it is in the strength of these precautions that the value of any Theory lies. It is a merely negative condition, or absolute sine qua non, that a Theory shaU at least explain the facts already in view : failing this, it is condemned, or seen to need qualification, on the threshold. But beyond and above the preliminary condition that no know^i fact as yet con- tradicts the theory, we need also the assurance, in some .shape or other, that if there ivere exceptions (or con- 272 FALLACIES. [Part IL tradictoiy instances) their existence would already have been discovered or inferrible. This assurance it is -which forms the turning-point of inductive proof. Hence the ' best ' explanation of the facts A and B and C is that explanation which while neglecting certain points of difference among them, and thus forming some generalisa- tion, neglects only those differences which are 'un- essential : ' the best explanation of {i.e. generalisation from) one solitar}^ sequence observed is that which neglects only its unessential elements or features. While all generalisation exists by neglecting points of difference, the soundness of any generalisation consists entirely in the completeness with which it balances out the relative importance of the points of difference concerned. The assumption at the bottom of all our explanation and pre- diction — of all our reduction of Nature to Law — is not only that the same antecedents will have the same con- sequents (for it seems hardly necessar}' to say that no two total sets of circumstances ever were or will be precisely alike *), but that whenever some of the observed circumstances recur, some of the same antecedents, con- comitants and consequents may be looked for. The problem is always to discover exactly which of the com- ponent circumstances of one total event are essential to any given portion selected from those of another. Every abstract proposition selects some only as being essential^ * Just as the members of every class of objects have their points of dissimilarity from each other, as well as the points of similarity which constitute them a class, so have the members of any class of events. Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 273 and it is through deep analysis of the actual circumstances that we avoid selecting too few. The two opposite modes of missing the ideal, then, are : — (1) to be content with too little repetition o£ circumstances — too broad a law, — as when we say in our haste '' All men are liars," and (2) to demand too exact a repetition of circumstances — too narrow a law, — as in the case of the Chinaman who burnt down his house in order to repeat as far as possible the exact circumstances in which he first obtained a certain kind of cookery. The former fault is the induc- tive fallacy proper : the latter may be a serious hindrance to knowledge, or may lead to a waste of time or money or trouble, but it makes no false pretence and thus runs less risk of failure in obtaining the immediate effect required. It is in every case, then, through undue neglect of the essential difference between the specific case or cases observed and the wider genus to which the assertion professes to refer, that we rise to a generalisation not sufficiently guarded against possible exceptions. The ideal is, to frame every generalisation unexceptionably, — so that no exception can be found, — and this whether the outward form that the statement takes is simple — as in "All matter gravitates," — or qualified, as in "All stones fall to the ground except when restrained in certain ways from doing so." It is either by far-reach- ing foresight or by growing experience that excej)tions come to light; and when they are recognised, the supposed law has either to be abandoned altogether (if 27 i FALLACIES. [Part IL they are numerous and important) or modified in order to take them in. The experimental methods are thus, in one aspect, methods for as far as possible anticipating the discovery of exceptions. The first and Aveakest remedy against stating as a law at all, what should properly be called a coincidence, is the employment of the Theory of Probabilities : an immense subject, and full of dangers of its own. Any full discussion of its details is here out of the question ; * nor, indeed, is it required for our purposes. It may, how- ever, be explained that, as regards Proof and Disproof — i.e. as regards the simple answer Yes or No, to a question raised and debated, — the chief operation of the doctrine is in enabling us to say in certain cases that S and ^ (e.g. sun-spots and magnetic storms) occur in conjunc- tion more frequently than can be accounted for by mere coincidence. In the absence of any knowledge of the causation concerned, such a result may, no doubt, have a certain value. But in pursuance of our plan, we shall confine attention to the more marked and definite end of the scale. The employment of the Doctrine of Chances must always be superseded by more stringent methods as soon as inquiry passes beyond its very earliest and most tentative stages. Since, then, for complete proof of a law from facts t\v^o things are necessary : — * Mr. Venn's Logic of Chance is generally considered the best English, work on the subject. See also Mill's Logic, bk. iii. chaps, xvii. xriii. and xxiii. ; and Bain's Induction, chap. ix. €hap. VI.] THE EMPLOYMENT OF GUESSWORK. '27o (1) The assurance that no contradictory instance has yet been found, and (2) The assui^ance that if a contradictory instance existed its existence would be known : it follows that negatively all turns on the finding of con- tradictory instances, while ■positively all turns on the completeness of the search for them. All positive proof depends not on the fact of observations having been made nor even on the fact of experiments having been per- formed; but on the care, the precautions, with which observation has been interpreted and experiment con- ducted. So far only as these exclude alternative possibilities, are they of real value. We have noticed, more than once, the danger of over- looking alternative possibilities. And it is true that every Theory set up has, in the first place, to show its preferability over all conflicting theories. This is pre- cisely what is meant by saying that the burden of proof remains. Just because Disproof is easier than Proof,* and because all positive assertion can only justify itself as a remainder when negative assertions are subtracted — when mistakes have been either one by one eliminate d or in a body prevented — the burden of doubt to be removed by evidence consists essentially in the group of alternative theories remaining undiscarded. The impor- tant point is always, to show that all other possible theories are weighed in the balance and found wanting : that is to say, that all precautions have been taken against ♦ See p. 250. ^7(3 FALLACIES. [Part IL that crudest kind of unchecked generalisation which the least trained mind possesses ever in greatest abundance. This objection against a theory — that alternative theories are not j^et discarded — appears, however, more directly applicable, more fruitful of results, against a concrete or an abstract-concrete thesis than ao^ainst a directly abstract one ; and as a method of attack on such theses, where for any reason it may be inconvenient to search for the supposed underlying Principles, it could no doubt be made useful. Accordingly I have thought it worth while to set out in an Appendix (A) a sum- mary of the alternative theories amongst which any observed concrete sequence or coexistence has to choose. Every observation or experiment interpreted is a case of the assertion of an abstract-concrete proposition. Find- ing S followed or accompanied by ^, under certain con- ditions, we assert causal connection between them. And the right of the theory chosen, over all its possible rivals, depends entirely upon the depth of our insight into the conditions under which the experiment or observation was really made. This is the main lesson of Logic, as regards Induction. The illogical person is content to produce, as evidence for a supposed instance of causation, the bare fact of succession in time, or unexplained con- comitance, — as, for example, in the case of quack re- medies, or again, in nearly all cases of superstitious belief; while inductive science always demands as full an analysis as possible, of all the circumstances. Failing this, as with all care it must sometimes fail, the proof is recognised as weak. Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 277 (c) The Empirical Methods. Of Empirical Methods the only careful classification yet made is, I believe, Mill's well-known list of five. While, as their author himself (and more lately, Professor Jevons) expended labour in showing, none of these is, except in an ideal sense, completely satisfactory as a guarantee, but in every case a further assertion is practically w^anted; yet the statement of the method employed in the given experiment or observation, to- gether with the precautions taken against its special ilangers, may be regarded as the answer given to the challenge of possible alternatives : in other words, as a means of shifting the burden of proof Since there may possibly be, in some quarters, a dis- position to take these methods for more than they were probably intended to be w^orth, there will perhaps be some use in reminding the reader that it is the guarding against the danger to which each method is liable, that is in every case the all-important circumstance — far more so than the mere employment of this or the other method. It is not, for instance, because a given experi- ment " proceeds according to the Method of Difference " that the evidence is strong, but because by means of certain precautions (often more easily taken under the Method of Difference than in the other cases) we happen to have approximately reached the ideal there set up. A careful employment of the " weakest " of the methods is often better than a loose employment of the strongest. 278 FALLACIES. [Part II. It seems unnecessary in this place to obscure our more general view by entering upon the Empirical Methods in detail and discussing their special liabilities to frustration.* It will be enough here to remark that ultimately the sole danger of fallacy in empirical proof is that of nesflectinof to take into account the differences between the Antecedent (or Consequent) observed in any actual sequence,! and that spoken of in the S (or ^) of our abstract proposition based upon it. In any sequence observed in Nature there are usually certain elements overlooked at first, and if one of these be important, our 'natural' inference is to that extent misguided. Thus for a long time the possibility was overlooked that the phenomena of fermentation could be due to germs floating in the air. From the most careful experiments that were made up to the beginning of the present century, the belief was held that since all the possible external sources were known and guarded against, the generation of the yeast-plant must take place in some ' spontaneous ' fashion within the fluid itself So again, until quite recently it was commonly believed that the carbon of vegetable produce must come from the soil : that it should be almost entirely derived from colourless air, seemed on the face of it unlikely. The same danger may be otherwise phrased by say- * I have, however, thought it well to set these out in the Appendix (B). f For brevity I here speak of sequence only ; since unless causation be a dream, co-existence may always be reduced to a complex result of" sequences. See also Appendix (A). Chap. YI.] THE EMPLOYMENT OF GUESSWORK. 279 ing that the empirical fallacy consists in resting our proof of a law or theory on conhi^matory {i.e. congruent) facts alone. If the facts around us do not fit our theories w^e have of course unanswerable disproof : but if the facts do fit them, the theories are not yet necessarily secure. We need besides such facts, in every case the further assurance that any contradictory facts, if existino-, would have come to light. And so far as this assurance is w^anting, so far the proof is weak. Mere number of confirmatory facts will sometimes yield us this assurance, but only so far as in the given case the special circum- stances guarantee this, is number of any avail. In many cases (e.g. in most chemical experiments) a single instance is more trustworthy than a thousand of another kind, since here the precautions are often enough to exclude ' unknown antecedents.' The assurance lies outside any inductive methods : for the various methods merely cor- respond to various forms which the same difiiculty takes on. It is analysis only that can enable us to know how far we have reaUy reckoned with unknown antecedents, — analysis of the complex facts presented to our obser- vation. The whole difierence between sound and un- sound generalisation lies in the care with which w^e seek for hidden elements in the cases observed, which shall modify our first rough guess at the law supposed to explain them. Accordingly the attack on a generalisation most usefully takes the shape of an attempt either directly to point out hidden circumstances in the facts observed. !>80 FALLACIES. [Part n. or at the least to point out that the analysis has not been a remarkably searching one. Thus Prof. Tyndall, attacking the theory that Bacteria are capable of 'spon- taneous generation/ sums up the chief faults of the argument as follows : — " The proof of Bacterial death at 140° Fahr. consists solely in the observed fact, that when a certain liquid is heated to that temperature no life appears in it afterwards ; while in another liquid life appears two days after it has been heated to 212°. Instead of concluding that in the one liquid life is destroyed and in the other not, it is assumed that 140'' Fahr. is the death-temperature for both ; and this being so, the life observed in the second liquid is regarded as a case of spon- taneous generation. A great deal of Dr. Bastian's most cogent reason- ing rests upon this foundation. Assumptions of this kind guide him in his most serious experiments. He finds, for example, that a mineral solution does not develop Bacteria when exposed to the air ; and he concludes from this that an organic infusion also may be thus exposed without danger of infection. He exposes turnip- juice accord- ingly, obtains a crop of Bacteria^ which, in the light of his assumption, are spontaneously generated. Such are the warp and woof of some of the weightiest arguments on this question which have been addressed by him to the Eoyal Society." Finding M (a component of Sj followed or accompanied by Z, whether in numerous instances, or in one instance where apparently no third circumstance has had time or opportunity to intervene, the natural impulse is to state the law as M — > Z. And, in every case, attack on the truth of such law consists ultimately either in the direct assertion that certain instances do in fact contradict it, or in the milder assertion that no steps have been taken to limit the sweep of the law as far as prudence would suggest; or in the still milder shape €uAP. VI.] THE EMPLOYMENT OF GUESSWORK. 281 of an inquiry whether or no such steps have been taken. If, in the case observed, M or Z was really qualified by the presence of N, it is always possible that the real law may be N — > Z, or MN — > Z, or M — > ZN, or MN — > ZN ; that is, N may be an important factor, and any statement of the law which neglects to mention it may accordingly be inexact and misleading. In the Appendix it is noticed that the five methods consist realty of variations upon two that are funda- mental. These two are the Methods of Agreement and of Difierence. It is questionable, however, whether the distinction even between these two is of real import- ance from our point of view. As regards observed coexistences, the Method of Difierence is plainly alto- gether inapplicable until they are resolved into sequences (which is often at present lyractically impossible) ; but as regards sequences the distinction depends merely on the fact that in employing the Method of Agreement ' unknown circumstances ' are eliminated chiefly by the Qiumher and variety of observations, while in employ- ing the Method of Difierence it is chiefly the immediacy of the sequence (known through our control of surround- ing conditions) that is relied upon for the same pur- pose. But in both w^e may be deluded, and by the same cause. The case or cases upon which we rest our theory may really belong to a narrower class than that which the theory contemplates. Their differentia over the genus about w^hich we make the assertion, may be an important factor in the behaviour of the things observed. 282 FALLACIES. [Part II. The Five Inductive Methods, with all their unlike- ness to each other, have thus one important point of similarity. They all consist in bringing cases, — claimed to be unmistakable on account either of their ' nature '' and circumstances, or their number and variety, — cases of the operation of the law set up as Thesis, and of no more complex one. And consequently the one point of vulnerability for all of them is the possibility that the cases relied upon were somehow different from those expressly covered by the . law ; that, in fact, there were special circumstances along with them, which should be generalised so as to find expression in the statement of the law, making it narrower than at present. The five methods are not in themselves a set of separate safeguards against inductive fallacy, or a com- plete exposition of the modes in which we ought to reason from fact to law ; but rather a generalised analysis of some of the most elementary modes in which we do (or perhaps, did originally) so reason ; each of these modes being liable to its own special dangers, and there- fore, unless properly guarded, each and all being illusory as a guarantee. Regarded simply as methods of Proofs they are in several ways not quite satisfactory. They are in this dilemma : either they are to be used as actual tests, to which we can bring the given experiment, — in which case they are certainly liable to ' frustration ; ' or else they are merely ideals to which in j^ractice we can never be sure that we attain. Moreover, they assume a greater simplicity of material than really ever exists, and CiiAr. YI.] THE EMPLOYMENT OF GUESSWORK. 28:> they assume too that the mind comes to its work of interpreting the facts of experience in a state of candour and virgin ignorance which is — ever since language took shape — very far from being the actual case. Their practical value, therefore, is rather as systematic hints for tentative discovery, than as methods of Proof at all. How then is our general knowledge proved from the particular facts of experience ? It can be disproved by experience easily (subject of course to the familiar possibility of our supposed experience being itself illusory), but proof of an abstract proposition can never be theoreti- cally complete, and the lines which we draw across the long scale between the highest practical certainty and the wildest guess-work are, like all our distinctions in continuous nature, useful up to a certain point but incapable of standing close scrutiny or careful refine- ment. The truth that destruction is easy and construc- tion difficult, is nowhere better exemplified than in our proof of general laws. A sequence in Nature is observed to happen frequently ; this perhaps sets some ingenious, inquirer on the track of a law ; experiments (we are speaking, of course, of modern times), are made with the view of testing the hypothesis, — of narrowing down the law into definiteness and limiting it as far as necessar}'. At last, after many struggles it comes forth as a recog- nised empirical law. But now it either remains in this^ condition, with the sword of possible contradictory instances ever hanging over its head, or by some further discovery it gets established under the protection of 284 FALLACIES. [Part IL some wider law with a greater prescriptive right. Noiu, if it be false, this wider law must be false also. Perhaps it is secure at last ? Perhaps it may be ; practically it ^ften is, but theoretically never. For every supposed law has merely served its purpose and stood its tests (such tests as we can apply) for a certain finite length of time. After centuries of life it may be upset in a moment, or at least found to be not universally true, to be true only under conditions, to be crude in its j)resent statement and to need further refining away. The longer it has stood its trial, the safer of course it is .against the fear of contradictory instances coming to light; in fact, it has probably been pared down already to accommodate such instances a dozen times, being of .course narrowed each time. It is an ungrateful task for any one who cares about the distinction between truth and error, to dwell on such facts as these, without some further apology. They seem at first sight to prove too much, — namely that there is no certainty ever attainable in interpreting Nature, but that ' unknown antecedents ' are as ubiquitous, and possibly as destructive to our best theories, .as the dangers to health in the midst of which our lives .are passed. Nor do I, in fact, see any way of denying this except by means of deliberate self-deception. But such apology as I can make for this view will come better in speaking, at the end, of some of the defences that can be made for Logic as a practical science. Of course, in the case of a great marny laws believed Chap. YI.] THE EMPLOYMEXT OF GUESSWORK. 285 in, the question is settled for ns Ly ancestral habits ; and in many other cases we shall accomplish more in the world by faith than by scepticism. But here we are merely trying, for the moment, to see the facts as they are, and not as practical prudence might suggest that we had better habitually view them. And two things, I think, w^e cannot help admitting : — First, that every supposed law, whether of succession or coexistence, may turn out to be too widely stated. If, as is probable, there is ' some truth in ' such law, yet the assertion it makes may be too wide and sweeping, and perhaps ought to be limited in some way, making it true only under certain conditions. Secondly, between mere guesses, hyjDotheses, theories, empirical law^s, and 'laws of Nature,' there are only continuous differences of degree in certainty, according to the nature and number of the tests they have stood, and the duration of their past invulnerability. In the case of Axioms, so far as their contradictory is incon- ceivable — i.e. makes nonsense of the words employed, — so far of course it is futile to speak of their uncertainty ; but wherever this is not the case, Axioms too come merely at the head of this same scale of credibility. The resemblance in uncertainty between a fanciful guess and a proved law may be less important than the difference in degree of certainty : but the fact cannot be safely hidden that the resemblance exists. The distinction often made between valid inductions and ' merely empirical laws ' is then, strictly speaking. 280 FALLACIES. [Part II. not absolute, though roughly useful; the line between them will not bear close inspection. For 'empirical' means ' true so far as we can yet see, but, inasmuch as inexplicable at present by a higher law, possibly liable to further limitation ; ' and. this may be said of every Law of Nature we possess. The method of proving laws is one and the same whether they be the merest wildest supposition or the soundest explanation of the facts of Nature. In the first place it is a sine qua non that no contradictory instance shall have yet been found. It hardly needs expressly stating that one single discovered exception is sufficient to break down an asserted law. The absence of such an instance, however, it must be equally obvious, is not sufficient for proof But, in the second place, the positive strength of our evidence de- pends upon the extent of our right to claim sufficient knowledge of all the attendant circumstances of the •observation or experiment. IV. The Dangers of the Argument by Sign. Under Deductive Proof, it will be remembered, we have elected to leave aside the case of complete Demon- stration, since to supply a missing premiss correctly is at least as difficult as to pass it for sufficient when .already expressed. It is not, however, with the whole problem of supplying missing premisses that we are now concerned : that belongs by right to the method for reducing to absurdity. Chap. YL] THE EMPLOYMENT OF GUESSWORK. 2^87 What is here called the argument by sign, as opposed to the argument by example, consists of the cases where the major premiss is either itself given as Eeason, or is only suppressed through its extreme familiarity, not through any doubt as to its truth or any hesitation as to what the law may really be. When, e.g., we attempt to prove innocence by means of an alibi, we refer no doubt to the principle (^vhich hardly needs express statement) that a man cannot be in two places at once ] and so, in a large number of instances, where the application alone is expressly given, the argument is really intended for deduc- tive. In all cases of attempted proof, it is experience in some shape or other that is relied upon, whether already generahsed experience or not ; experience crystallised into names and propositions, or experience not yet so formulated. The difference between empirical and de- ductive proof may be further brought out by saying that in the former we deal more directly with the facts expe- rienced, while in the latter we rely largely on mere for- mulas. The chief diihcidties in summing up the dangers peculiar to the Argument by Sign lie partly in the fact that faulty deduction may be due to so many different causes, and that, through disclaimino- one cause while allowing another to operate, the fallacy has so many facilities for escaping open conviction ; and partly in the fact that according to our own definition, it is only when both Principle and Application are clearly apprehended as such, that any argument can be rightly called deduc- 288 FALLACIES. [Part IL tive, and that consequently if an attempt is made to employ a Principle that does not strictly apply, it may easily be pleaded against the charge of faulty deduction^ that strict deduction (Demonstration) is not intended. Nevertheless something may, I think, be done, by recognising clearly that the danger against which every argument 'professedly deductive has to guard is the ac- ceptance of a Principle which does not apply ; and this, whether caused through ignorance of syllogistic require- ments, or through verbal ambiguities, or through suppos- ing the reciprocal of either Principle or Application to be its equivalent. Against the easy plea that demonstration is not intended, may be brought the reminder that in such case the Thesis, so far as definitely asserted, is at first a pretender to qualities which it afterwards confesses to be wanting. So far as it really cannot be rationalised, — by bringing the underlying principle and its application into shape for rigid investigation, — so far its truth must of course remain untested, and belief in its truth either a careless or a semi- voluntary act. It may be well, then, to glance at the operation of the three causes of faulty deduction just above enume- rated. And first, of the ignorance of syllogistic require- ments. By this is meant solely the ignorance, when Reason and Thesis are given, of the fact that a further assertion is implied, and of the nature and limits of such further assertion, — what must be said by it, in order to complete the deductive proof It may be held, and it may be true, that in actual Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 28D practice purely syllogistic fallacies very rarely occur. What on the face of them appear like syllogistic fallacies may in most cases be found on further inquiry to be really due either to false belief as to the matter, or to the tyranny of names, or to ignorance of the law of Counter- Indication, whereby the reciprocal of some true Principle is accepted as equivalent in meaning. Thus if any one argues that the prisoner is guilty, from the fact of his confusion when arrested, it is, no doubt, more probable that he believes in the truth of the further assertion ' confusion — > guilt,' or in the equivalence of this with the less questionable law that ' guilt causes (and there- fore — >) confusion,' than in the formal sufficiency of the latter assertion as completing the Syllogism. Still, easy and indeed self-evident as the formal requirements of reasoning are, we are bound to suppose that people are occasionally liable to look upon insufficient premisses as formally binding. In fact, there is probably one class of persons who have really acquired some power of con- fusing themselves in this matter, namely, those who, having learnt the moods and figures by rote for an examination, have not as yet quite succeeded in forget- ting them again. Nothing could well be more confusing than an attempt to apply the cumbrous machinery of the Syllogism to arguments met with in real life. And whoever has tampered with his mother-wit by substi- tuting for it a clumsy Logic depending on elaborate mnemonics, must no doubt pay the penalty in loss of power, so long as the mischief remains. u 290 FALLACIES. [Part II. It is well, therefore, to remember tliat the Syllogistic requirements may always be clearly shown either by viewing the middle term as a sign, the universal trust- worthiness of which sign is all-important to the proof; or, where the middle term is difficult to find, by viewing E as itself the affirmation of the antecedent (or the denial of the consequent) of a hypothetical proposition of which T (or the denial of T) forms the other term. It is not necessary in this place, however, to enter fully into the details of this operation, since in the chapter on Reduc- tion to Absurdity (p. 298) we shall find a better opportu- nity for doing so. In the mean time, apart from igno- rance of syllogistic requirements, and from the possibility that our supposed knowledge relied upon may be mis- taken, there remain two other, and commoner, sources of error. As regards the acceptance of the reciprocal as equiva- lent, not much more remains to be added to that already said. Either the Principle or the Application may be wrongly supplied in this manner, with the result that we then accept an express principle, together with an express supposed application thereof, when in fact the latter is merely the application of a very difierent prin- ciple, — and one, it may be, very much easier to prove. Especially is this the case, as pointed out above, in the disjunctive (or dilemmatic) argument : M — > non-^ is nearly always easier to establish than non-M — > ^ ; and accordingly, wherever in a deductive argument the E, states that S — > non-M, we need to be especially on •Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 291 guard. But in all cases of attempted deductive proof, this fallacy is a constant source of danger. And its in- sidious nature and the facilities for escape "which, even when detected and aiTested, it presents, mark it out as deserving very careful attention. So great are the facilities for escape that it is difficult to find instances which will be unhesitatingly accepted as such, even by a respectable minority of readers. The danger is so simple, so obvious when pointed out, that those who have not had occasion to study the causes of fallacy in actual operation will be loth to accuse the human intellect in general of ever being in the least affected by it : while even those who have watched the action of erroneous reasoning most carefully must hesitate to say in the given case that this cause was solely, or even mainly, operative. The logician is in fact here placed in much the same difficulty as so frequently occurs in all interpretation of riiotives : several motives have had a share in some action, and amongst them, in the vaguest and most unconscious manner, one motive less noble than the rest ; a motive which the person accused will be not only sure to deny, but which, if he had been conscious of it at the time of acting, he would at once have dismissed as unworthy. As a matter of fact it may have had con- siderable weight, and yet if the ease is brought forward as an instance of its operation, a feeling of perfectly honest virtuous indignation is aroused. So it is with o this deductive fallacy. A person who has really been partly misled by it will be almost sure to declare, when 292 FALLACIES. [Part II, the fallacy is pointed out, either that he meant the Principle to cut both ways, or else that he only intended to make a suggestion or to raise a presumption, — " com- plete demonstration being unattainable : " and quite probably both of these intentions were really present to his mind m a vague way, along with some uncertainty as to what the requirements of complete demonstration might be. For just as a man is seldom conscious of his own motives at the time, while on after reflection the nobler motives are apt to rise into undue prominence, so our view of what constitutes complete demonstration is often clearer on after reflection than in the heat of argument or during the first glow of belief Nevertheless, there is on occasion something gained by forcing even the most unworthy motives into promi- nence, in order that they may be definitely disclaimed and the disclaimer registered for future use ; and so with this kind of fallacy. Where the argument is plainly intended for deductive, time may often be saved by searching first for any slackness in the view of what de- ductive proof really demands. If on inquiry it turns out that the intention was merely to raise a loose presumption in favour of the view, the looseness of the presumption may be thus made fully evident : while if the reciprocal of the express principle is believed to be also true, this belief can then be placed on its trial. The remaining source of danger in deductive argu- ments may be described as that of forgetting part of the jDOstulated meaning of the names employed, or again, of Chap. YI.] ' THE EMPLOYMENT OF GUESSWORK. 293 reading into them meanings which they are not intended to bear. So far as significant names are employed in Proof (whether as M or S or ^) the two liabilities to error are at bottom the same as those already men- tioned, — undue neglect of difference or of resemblance. The meaning of every name, we have seen (p. 108) contains two elements, — the diflferential and the generic, — and either of these may be unduly overlooked. We may, in other words, unduly neglect the negative or the positive meaning, the points of difference from other things or the points of resemblance to some of them, to which the name refers. This double chance of error is one that was treated at some length by Aristotle, under the name of the Fallacia Accidentis, or confusion of the accidental with the essential. It is true that if we interpret Fallacia Accidentis as widely as possible, it will include far more than these merely verbal errors, namely, the errors also to which empirical proof, as such, is liable. When we reason by false Analogy, or when we expKcitly frame too sweeping a generalisation, we are taking 'accidental' resemblance for essential (or essential difference for acci- dental) ; and vice versa when we fall shoi't of the ideal on the other side ; but it was the interpretation of names that Aristotle seems to have had chiefly in view. There is another phrase also sometimes applied to the same double chance of error ; the possibility of arguing a dido svnipliciter cul dictum secunduon quid, or cc dicto secun- durii quid ad dictum sionpliciteo' ; and perhaps this supplies the more really descriptive title. 294 FALLACIES. [Part II. Everything that can be named may be viewed as existing at once smijjliciter and secundum quid (or as belonging to a genus and also possessing a difference). Everything belongs to certain classes, the narrower * of which possess difference over and above the broader, and beyond the narrowest of all remains any real individual peculiarity of the thing in question. Accordingly any general name we give to a thing neglects of necessity more or less of its secundum quid, and yet in order to employ deductive proof we are obliged to use general (i.e. significant, or indicating) names. S may be rightly called M, but it is also always something more : all depends (as we have seen in speaking of Analogy) on whether the something more is important or unimportant (essential or accidental) for the purpose in hand. But suppose that the] difference is ruled unimportant and that M is decided to fairly deserve the name of §,. that name in turn has a differential and a generic meanino^, either of which may be unduly overlooked ; and so on for ever. Take the name ' man.' Because a man is certainly an animal, or a ' creature,' or even a ' thing,' or a ^ figure,' or an ' object,' we do not thereby gain the right to forget the differential qualities due to his human nature: nor on the other hand does the fact of his rationality do away with the chain that binds him to the wider class of ' animals,' or with the consequences (such as mortality) therein implied. If men, through developing their diffev- * I.e. narrower by direct limitation, not merely those -wliicli happen to have the fewest members. Chap. VI.] THE EMPLOYMENT OF GUESSWORK. 295 entia from beasts still further, should eventually manage to conquer death, some of our old nomenclature would reqmre remodelling, but the logical law would of course remain unaltered. The traditional examples of this fallacy are valuable rather as being unmistakable than as really representative of the difficulty involved. "You are not a man; for a man is what I am, and you are not what I am," or " You ate raw meat to-day ; for you bought raw meat in the mar- ket yesterday, and to-day you ate that which you bought yesterday in the market." Practically such catches as these are obvious to any child, and in order to exemplify the working of the real danger we must choose a finer shade of it. For this purpose the best examples of neglecting difference are perhaps the cases where some judgment is based upon what may be called a partial or one-sided view of the S : where the name with which the S is labelled is incompletely defined, defined by genus, without the full differentia ; as where a soldier is said to be " a man who makes a contract with his country to kill anybody Avhom his country wishes to have killed." In reality, of course, the soldier does not make this contract simpliciter, but there are other elements in it, which when taken into account may perhaps alter radically our opinion of his merits. Or again, voluntary death is some- times heroic ; and suicide is certainly always voluntary death, — but with a difference added. Voluntary death is the genus under which ' suicide ' comes, but the specific difference is just the fact that the motive is merely 296 FALLACIES. [Part II. to escape, for ourselves, something which, rightly or wrongly, we regard as worse than death, not a ' heroic ' thoughtlessness for ourselves and regard for the good of others. For examples of neglecting resemblance we may take the cases where difference is believed to be thorough- going or fundamental, merely, or mainly, from the fact of different names being used. Readers of Newman's GraTiimar of Assent will remember, for instance, the importance there given to the difference between an assertion and a conclusion. The two names are different, and the two things are certainly so far different that an assertion may sometimes be made "without grounds," while a conclusion (by its definition) presupposes grounds, weak or strong. But a conclusion means, of course, an assertion and something more : it belongs to the genus assertion, but possesses also the differentia " reasoned." Newman indeed prefers to say (p. 2) that an assertion has "got beyond being a mere conclusion," but by this it appears (p. 4) he means merely that unhesitating faith is stronger than faith which (p. 1) consciously depends on a prior condition being true. His interest, however, is to make out that a conclusion is radically different from {i.e. does not even belong to the genus) assertion, and for this purpose he dwells at some length on the specific difference (the presence, and the absence, of reference to grounds).* * It should be mentioned, however, that at the end of the section (p. 6) this is felt to be hardly sufficient, and another supposed point of Chap. YI.] THE EMPLOYMENT OF GUESSWOEK. 297 difference has to be brouglit forward, resting on a less interesting or important verbal confusion. " We cannot give onr assent to the proposi- that ' X is y ' till we are told something about one or other of the terms " [I should rather say, hoth the terms] ; " but we can infer, if x is y, and y is z, that X is z,' whether we know the meaning of x and z or no." The merest beginner in logic will recognise at once that ' x is z ' does not stand here for a single, meaningless, proposition, but merely for an indefinite variety of possible propositions with a meaning. All that is said in saying that in such a case we recognise the reasoned truth of ' X is z ' is that (with these premisses admitted) we see clearly that X, y, and z may mean anything whatever, without affecting the validity of the conclusion. CHAPTER VII. EEDUCTIO AD ABSURDUM. Having thus spent some trouble over the inquiry what can be done to improve our methods of finding offhand the source or cause of a piece of faulty reasoning, it is with a feeling of relief that we now turn away from the difiiculties of guesswork, treading again upon firmer ground. Any discussion of the best means of promptly discovering the actual seat of a fallacy is likely to raise more difficulties to the mind of the thoughtful reader than it can settle for him. He will feel, at the end, that educated tact and insight are of higher value for such a purpose than any number of condensed rules can be. The special circumstances encountered in actual argTi- ments are plainly too various to admit of hard and fast legislation, and the most that can be hoped is that some aid may have been given in clearing away preliminary confusion; rendering it to that extent more easy for further small advances to be made. But now there remains the question, Where guesswork fails, what then ? The answer has been briefly given already, — once, and Chap. TIL] EEDUCTIO AD ABSURDU^I. 299 directly, on p. 174, and on other occasions (as on pp. 27, 114, 213) by implication : but it now becomes necessary to deal more fidly with it, and to show what is meant by "applying the method with sufficient fairness and caution." ' The Keduction to Absurdity, it was also said above, is a method of raising objections which is ultimately appli- cable in all cases without exception; and the plans of attack already hinted at are only to be preferred to it on the oTound of their neater directness in certain cases. It should, however, be at once explained that the name ' Reduction to absurdity ' is here to be employed in a somewhat narrower sense than usual. To reduce any assertion, — simple assertion or argument, — to absurdity is always, at bottom, to bring it somehow into conflict with observed or admitted fact ; and this may of course be done in various ways. For example, to produce a contradictory instance might fairly be called a mode of reduction to absurdity : or again, more widely still, to bring to light the absurd consequences of any hypothesis. But, as applied to arguments, rather than to assertions in general, we may define the process of reducing to absurdity more narrowly, restricting it to one special method, in default of a better nam.e to use for the purpose. In all arguments as a last resource — and in some even as the most direct attack — we have the power of com- bining R and T, inquirmg what they together imply, and then comparing such further assertion with observed or admitted facts. For simplicity let us denote " required oOO FALLACIES. [Part IL further assertion" in every case by the letter F; then the reduction of an argument to absurdity (as the name will here be used) means the objection that, T and E, being given, F is untrue* The fact that every Thesis deductively proved, — every ^syllogistic conclusion — rests upon some law, or Prin- ciple, from which its deduction takes place, has been already sufficiently noticed, the two premisses of every Syllogism being respectively : — (1.) The major premiss, — the statement of such law : and (2.) The minor premiss, — the application of it to the case in hand : and whichever o£ these be given as R, the other is implied before R's 'formal adequacy' is complete. But now it remains to be said that every R must be translatable into one of these, — major or minor premiss, — before we can proceed to fully test the argument.! This was in fact the meaning of saying that all Proof, so far as really Proof, is deductive, and that the Syllogism is "perfectly * It must be noticed that F is not contained in the meaning of T and R together in the same way exactly as T is contained in the mean- ing of R a.nd F; but it is as truly implied by them nevertheless. And if that which T and R together imply be found untrue, the argument is clearly overthrown : for R, regarded as a firm support for T, is found to require as true a proposition which is in fact (or by admission) not so. It makes no difference whether F be Principle or Applica- tion : unless both of these are true, T remains without the required foundation. t Hence a prior condition to the employment of the method is agree- tnent as to the meaning of the assertions made in T and R. Chap. VIL] EEDUCTIO AD ABSUEDUM. 301 general in its operation : applies to all Proof whateveiv and is not an engine to be used in deductive inference merely." That is to say, whenever any Reason is given for any Thesis, a knowledge of syllogistic requirements will enable us to see how far such attempted Proof falls short of Demonstration ; or, in other words, to see what further assertion must in every case be added to E, before its formal adequacy is complete ; — before all has been done except to inquire whether E, is true in fact. Wherever any Eeason is given for any Thesis, and the special dangers of the argument are not immediately apparent, hostile criticism falls back at once on the inquiry. What are the gaps in the reasoning that possibly require to be filled? The Axiom of the Syllogism, whether stated in ' ex- tension ' (i.e. with direct reference to the ' things ' spoken of), in the famous Bictmn cle orani et nullo, — which being rendered into English says in effect, " Whatever is asserted (affirmed or denied) of a class is asserted of any part of that class," — or in comprehension (i.e. with direct reference to the judgment made) in the equally famous JS^ota notce, which we may translate, — " A sign (S) of a sign (M) of ^, itself indicates ^ " ; — the Axiom of the Syllogism requires, for purposes of Proof, to be postu- lated true in its 'reciprocal' form. The statement so obtained might be not improperly named the Dictum de singulo or the JS^ota rei ifsius. It says that in order lo prove anything true of a single thing (whether object, quality, event, or whatever the thing may be) 302 FALLACIES. [Part IL it must also be shown to be true of a whole class of such things, a class including the one observed. Or, stated in comprehension, — In order to prove that S — > ^, S must be shown to indicate M, a sign of ^. Let no one think these postulates either a valuable discovery in Logic, or an unwarranted and presumptuous innovation. They are merely another way of making the familiar assumption that "Nature is uniform," or that there are 'laws' of sequence and coexistence. It is on this assumption that all explanation, classification, and prediction necessarily proceed. Without it the Universe would be a chaos of exceptional cases, — if 'exceptions' can be pictured apart from 'rules' at all. Every individual thing represents a class, of which it is a member; everything belongs to some genus, besides possessing a differentia. Accordingly, whenever any fact is appealed to as reason for believing any assertion, the important matter is to get the supposed underlying law (or laws) clearly stated; and the central difficulty in- volved is that of really rising above the individual case while at the same time avoiding the unfairness, or the pedantry, of insisting that a wider, and therefore more vulnerable, law is implied than the assertor really in- tends. It is true that R is sometimes, though seldom, the statement of the law itself, — as in the argument that *' Protective duties are economical : for whatever brings in money enriches : " or again, " The farmers will not pay in rent more than the net produce of their farms, for no trading class will continue a losing business." But here €hap. YII.] REDUCTIO AD ABSURDUM. 303 no real difficulty can arise, except through verbal ambiguities, and, sometimes, through uncertainty as to the Law of Counter-indication, The findiug of the Application when the Principle is clearly expressed must, from the nature of the case, be always an easy matter. Supposing that, in the first of the two instances just given, — their truth or cogency does not interest us here, — " enriches " and " are economical " are used in the same sense, it needs no Logic to tell us, at this stage of the work at least, that the formal adequacy of the Reason depends on the further assertion that " Protective duties bring in money." If a Principle is laid down as Reason, even a child can seldom fail to see that its force as Reason depends on its being connected, in the only way possible, with the Subject of the Thesis. Of course there are cases conceivable, where, through accepting the reci- procal as equivalent, a wrong application may be made. But this danger has been already sufficiently discussed. We need not here go back to the pons asinoriiin of Logic. We have to deal, then, solely with the case where R, if relevant at aU, is not itself the Principle, but is either (1) directly, or (2) remotely, the Application. By a ' remote ' Application is meant the case (briefly referred to on p. 210) where the S of the thesis is not expressly mentioned by the Reason. But first of the case where the Application given is as direct as possible. That is, where something is distinctly said about S as a reason for believing the assertion made of it ; as in ' Gold can- 204} FALLACIES. [Part II, not be produced artificially, for it is an elementary sub- stance/ or ' Whales are not fishes, for they breathe by lungs/ or ' He must be in London, for he is not at his country house.' The whole difficulty here is as to the extent of the Principle really involved. Is it, for example, ' To be an element — > incapability of artificial production,' 'To breathe by lungs — > not to be a fish ' (the counter equivalent of 'To be a fish — > not to breathe by lungs '), ' Not to be at one's country house — > to be in London' (i.e. 'All who are not at their country houses are in London ') ; or is it the narrower assertions, ' Gold, if an elementary substance — > incapability of, etc.,' ' Breathing by lungs, when found along with the other attributes of a whale — > non-fish,' ' If he is not at his country house, he must be in London ' ? The answer to this question furnishes the key to the distinction between fair and unfair emplo3Tiient of the method for reducing- to absurdity. The difierence between what Logic might be, and what it too often is (what perhaps its less thought- ful enemies suppose it always to be), is much like the difference between fair and unfair caricature : a difference not so much in the thing itself as in the manner in which it is interpreted, and the occasions on which it is employed. It is chiefly the inability to keep this dis- tinction clear which has made it possible for orators to describe the Syllogism as "a contrivance for catching you in a trap and holding you fast in it/' Just as the middle term in a Syllogism (the term Chap. YIL] REDLXTIO AD ABSURDOI. 305 appearing in both premisses) may always be viewed as a sign, or mark, possessed by S, — a mark which, abstractly indicating (or being a universal sign of) ^, is employed to prove the conclusion; so, conversely, that which is asserted by E as indicated (abstractly or concretely) by S, may always be viewed as the middle term of a Syllo- gism which has yet to be completed. If S is only known to be ^ because it is M, M is (according to the Dicturit de singulo) thereby asserted to be universally a sign of ^. If S is only known to be ^ because, being iV^, it is M, M, when specially limited in this mamier by N, is thereby asserted to be universally a sign of ^.* The proposition MN — > ^ is of course just as truly ' universal ' as M — > ^, though of narrower sweep. Are we then, whenever we meet, put forward as Reason for any Thesis, a minor premiss which is bare of special limitation, to assume that no special limitation was present to the mind of the person so putting it for- ward ? Yes, and No. For the purpose of getting the principle expressly defined, it is often highly desirable to assume, provisionally and fictitiously, that the ^vide Prin- ciple, as strictly implied by the reasoning, was believed to be true. By this means wavering uncertainty as to its falsehood may often be destroyed, and even where no shade of such hesitation existed it is a clear gain to get the real principle reduced to definiteness. But if we go beyond this employment of the method, we ourselves * E.g. ' S is gnilty (5) ; since, (N) though the charge is one that au innocent person Avould readily contradict, it Las (M) never yet been expressly contradicted.' X . 306 FALLACIES. [Paet 1L commit probably the greater error of the t^yo. Thus while no objection would perhaps be raised to demanding, as Principle for 'Gold caimot be produced artificially, since it is an element/ the assertion that 'all elements are incapable of artificial production/ it is obviously un- fair to demand as the Principle strictly involved by ' He must be in London, since he is not at his country house,' the assertion that ' All who are not at their country houses' — still less 'All who are not at his country house ' — ' are in London,' thus neglecting the fact that other alternative places of residence exist. The absur- dity, if we made such a demand, would rather lie with ourselves. In such a case as this, since there could not be any hesitation as to the suggested Principle being un- true, we should probably dispense with even the ficti- tious and provisional assumption of it, cutting the process short by asking at once what the special circumstances are which are supposed to limit liirii (not 'all men') to one place or the other. But there are plenty of really doubtful cases. Take further the argument 'He must be ill : for he has lost his appetite.' Here the principle really believed as foundation might be that 'loss of appetite universally indicates illness ; ' or, on the other hand, it might be merely ' if he has lost his appetite he must indeed be ill,' — the special circumstance thereby indirectly hinted being of course that S's appetite is known to be of a particularly unfailing kind. If the latter were the true explanation, we should of course make a grave mistake in attempting to lay upon the €hap. YII.] REDLXTIO AD ABSURDUM. 307 assertor the burden of supporting the truth of the wider assertion; but we should be quite right in giving him the choice between doino- so and narrowino- it down into o o a shape that will fit the facts. The method of reducing to absurdity should, then, be regarded rather as a method of putting questions than of making a direct assertion that an absurdity is necessarily implied. We can never really get so far behind the scenes of another person's mind as to attain complete security in guessing what the exact Principle relied upon has been. We can only say that the Principle which appears to us to be implied by the express statement is so and so, and that we presume he hardly intends, in fact, to rely on any such plain absurdity. He must either narrow it for our benefit, or be content to leave us unconvinced: we certainly cannot accept the argument -as it stands. So far as the Principle fails to attain some generality wider than the T itself, so far the T remains imrationalised, — i.e. without a logical foundation : so far as the principle sacrifices security for the sake of gene- ralisation, so far the foundation is unsound. We do not ■catch the assertor in a trap : we merely show him that he has chosen to place himself in a dilemma : and Ave then request him, for our enlightenment, to choose which- ever alternative he himself prefers. If for any reason he does not like to rationalise his thesis by committing him- self to any definite Principle, it is always open to him to Idc content to leave us unconvinced. But there is a sense in which this may be called 308 FALLACIES. [Paet IL stating the alternatives a little too baldly. In a certain sense there may be a flaw in our con^dction, and yet not a serious chasm. There is a middle ground between complete Demonstration and total failure to justify belief. There are, in a sense, different shades of certainty ; evidence varies in strength. Where we cannot get an assertion completely demonstrated from a definite and faultless principle, the next best thing is to demand that the Principle shall, if vague, be as unexceptionable as possible ; if sound, as simple as possible ; and that we shall know, even incompletely, what the Principle really is, and to what extent it may be trusted. Knowledge, even when in the empirical stage, is often better for practical purposes than pure ignorance would be. And this leads us to speak of the sole remaining case, — where the Reason is ' remotely ' the Application. When, for example, I argue by Analogy, and equall}' when I base a law on facts observed, nothing at all is- said in the Reason about precisely the S of the Thesis. In the former kind of argument, as already seen, the Reason speaks of a supposed ' parallel case ; ' in the latter kind, of ' This (or these) S ' only, not of ^ All S ' as in the Thesis. So again in such (very common) deductive argu- ments as ' A storm is brewino- for the elass has fallen rapidly,' or ' My friend is out, for there is no light in his window ; ' here the respective theses speak of ' a storm ' and ' my friend,' Avhile the Reasons speak of ' the- glass,' and ^ a light in the window.' In perhaps the- majority of actual arguments we cannot say, without €hap. VIL] REDUCTIQ AD ABSURDUM. 809 great circumlocution;* that tlie S of the Tliesis is directly spoken of by the Reason, and in the process of translating into and out of the clumsy phrases required for doing so, there are endless opportunities for verbal error to creep in. In the analogical and the inductive arguments, it is probably in most cases the simplest plan to try directly for unsuspected and essential difference; but there can be no harm in pointing out the longer method of arriving at the further assertion involved. The com- pletely definite underlying Principle differs radically in the two cases (Analogy and Induction), being alike only in the one point of being often highly complicated and extremely difficult to state with any exactness. In the argument from analogy the S of the Principle implied is the inventory of the (often vaguely felt and numerous) points of essential resemblance between the two parallel cases : these points of resemblance are im- plied by the argument to indicate Z, either universally or at least indifierently in the two cases before us. In the inductive argument the full underlying Principle is the statement that certain precautions in observation or experiment are sufficient to warrant the inference. These, it must be confessed, are nearly always too numerous for concise summation. In the presence of the almost infinite diversity of the circumstances in which observation and experiment may take place, we * Cj. Jevons, Elementary Lessons, p. 164. — " The circumstances of tliG barometer falling are the circumstances of bad weather coming." 310 FALLACIES. [Part II. have not yet got far towards generalising the sufficient safeguards. Mill's five methods were an attempt in this direction, but, as we have seen, it is only as ideals that they are satisfactory, and the point of practical import- ance is always to know how near to the ideal the given experiment approaches ; for Avhich piece of ' special " knowledge an enlightened review of innumerable cir- cumstances, and of their bearing on the case, is needed. But if we cannot in these cases arrive at any full; and definite statement of the Principle, still the method of reducing to absurdity may be of service in another way. Whatever be the S of Thesis or of Reason, the truth of the Reason as a whole is given as indicating- that of the Thesis, and consequently (by counter-indi- cation) the untruth of the Thesis as indicating that of the Reason. In other words, it is always asserted that iveve the Thesis untrue, the Reason ivoidd he untrue also : and this, if the Reason be given as true, is clearly absurd. In other words again, every argument asserts that no theory except the thesis is compatible with the reason. In yet other words, that all possible rival theories have been examined and found wanting. Here we touch again upon the difficulties surrounding the burden of Proof. This last statement may at first almost appear as if, after all — to quote a former passage (p. 149) "the sole concern of the assertor were to frustrate, one by one, attempts at disproof made by the other side." The real case is however ver}^ different. Until he has shown that cdl such attempts are worthless, he Chap. Til.] EEDUCTIO AD ABSURDUM. 311 may have an underlying Principle indeed, but it must l>e one whose material truth has not yet passed our examination. In proportion to the extent of rival theory still remaining undestroyed, is the weakness of the evi- dence brought forward. Often these rival theories may all be summed up in one concise expression, and may in this shape be discarded en bloc. Thus in the analogical argument we may say that there was perhaps ' some cause ' for ^ being Z, which cause is inoperative in the case of S. That is to say, if the assertor can show some probability to the contrary, he has done more to support his assertion than if such alternative has never occurred to him or has been half-consciously suppressed as in- convenient. So in the inductive argument we may sum up the alternatives by saying that perhaps the law is stated too widely, and here again there are ways of showing what has been done to limit its sweep as care- fully as possible : and also ways of letting out the secret that we have gladly caught at the first explanation, and afterwards obstinately refused to see its obvious faults. In this employment, however, of the Reduction to Absurdity, as well as in the easier case first noticed, the attitude of fair investigation is still the same. The essential characteristic of it is that it avoids dogmatic assertion, and merely asks to see what has really been done to stop the gaps in the reasoning or to minimise the opportunities of error. It is noteworthy that in other matters also the same negative, anti-dogmatic tendency has always been observable in Logic. Even when Logic .SI 2 FALLACIES. [Part II. undertook to interpret to some extent the meaning of words and phrases off-hand, we find at least a strong- inclination to bind them down to the least amount of positive assertion Avhich the words could be supposed, to contain. ' Some ' meant ' not-none ' instead of ' some only ; ' the universal affirmative could not by itself be taken to express reciprocal indication ; the Principle of Logical Division treats A and not-A as equal in import- ance ; and quite recently we have had, in Mr. Venn's Symbolic Logic, a more consistent following out of the plan of interpreting statements merely by what they deny, than had ever before been openly and distinctly attempted. Logic is in far more danger of losing its operative power in hesitation and inactivity through extreme desire for fairness, than of lending any aid to unfair quibbling, or of trying ingeniously to make the worse appear the better reason. An additional circumstance, another straw helping to show the direction in which the current of Logic sets, may be found in the fact that so often its enemies are merely talkers who dislike the check that reason always gives to ready dogmatism ; reasoners who care more to do their reasoning easily than correctly, or who have not yet become aware that any great need for caution exists. It is chiefly because they lack the calm- ness and strength required for looking difficulties in the face, and because Logic contents itself with asking whether they have really done so, that they dislike its methods. I do not mean, however, that the wish to Chap. VII.] REDUCTIO AD ABSURDUM. 313 assert without foundation is the only explanation of all possible objections to Logic, and before quitting the subject it may be worth while even briefly to notice some of the more disturbing things that can be genuinely urged against the science. As akeady sufficiently ex- plained, however, I can here attempt to notice only those objections that may arise before Philosophy, — as cut loose from all merely practical considerations, — is brought to bear upon the question. CHAPTER VIII. SOME OBJECTIONS TO LOGIC. The practical objections to Logic, other than those merely felt without the trouble of thought or inquiry, seem ta me broadly divisible into two groups : those which claim that the logical attitude is on the whole useless, or worse ; as for instance that, consistently held, it means pure stagnation or scepticism, and that even a partly inconsistent holding of it is apt to leave us too long- undecided : and those which admit that the end is good^ but declare that the means are clumsy. The former of these is certainly the more serious of the two, and, as said above, I can in fact only provide a half-satisfactory answer. It seems impossible to deny that even our most careful reasoning may lead us into mistaken views ; and strictly speaking, the more we re- cognise this fact, the less room must there be for active faith. But it is one thing, after all, to admit the fact and quite another to admit the hasty inference sometimes drawn from it. It is not true that because every sup- Chap. YIIL] SOME OBJECTIONS TO LOGIC. 315 posed fact is ultimately uncertain, therefore there is no useful distinction to be made between a careful induc- tion and a hasty guess. There are endless shades of difference here, and nothing is gained, except the cheapest sort of peace of mind, by shutting our eyes to them. If there are, strictly speaking, no degrees in fallibility, yet there are differences of the highest im- portance betAYcen the results of care and carelessness in reasoning. It is for the most part mere sloth, or even sometimes a kind of pettishness, that leads us to resolve to reason carelessly because with all possible care we may still make mistakes. Perhaps, indeed, it will be said that no one ever really "resolves to reason care- lessly," and this may be granted at once. The pro- cess is commonly described in finer language. It is '•'humility," not slackness of purpose, that prevents our asserting positively that black does not mean white. It is "in a spirit invincibly calm" (nor can I quarrel mth the epithet) that we claim a vision of " loftier than mere material verities and wider than purely physical laws." Or we contradict ourselves, and then caU the result a " Mystery," or an " Antinomy of Eeason," wash- ing our hands of all responsibility, and content to lay it on the Powers that designed the faulty human intellect. The humble mind has an easy command of numerous humble phrases. Practically the surest defence against Scepticism lies, not in claiming infallible revelations, but in patiently making the best of the truths that have stood the test 316 FALLACIES. [Part II. of time. Not, of course, only tlie few that exist now in the shape in Avhich they were originally put forward, but also the many that have been graduall}^ narrowed down iind pared into lasting shape by persistent hostile forces. On these we 'ancients' build, as on a basis always growing firmer : — though in recognising the fact, we of <30urse admit that our basis is never completely firm. But just in this recognition lies the life and strength of science ; for the admission gives a power to discover and correct mistakes, and also tends to weaken the natural petty desire to pose as supernaturally knowing. Free. from the fear of being found an impostor, science is able to challenge — and to court — correction : more than it loses in influence by being proved mistaken, it gains by being known as honest, and it adds a further gain by registering the mistake. Knowledge is built upon a mass of prejudices, possibly, but one difference between scientific and unscientific prejudices is that the former are chiefly recognised as provisional merely. If it were not for these strong provisional prejudices. Science would hardly liave reached the results already won. Until they prac- tically fail these may be trusted, and where they are proved in any case fallacious we only learn a further piece of knowledge, and so really add to, not weaken, our old foundations. Logic is fond enough of reminding us that " All men are fallible : " but the rider must be added that it depends largely on ourselves to say to what extent we choose to live under the sway of fallacy. And as to unpractical hesitation, again we may appeal Chap. YIIL] SOME OBJECTIOXS TO LOGIC. 317 to results. It is easy of course to assert that these have been reached by Common Sense in spite of Logic, and in one sense possibly this may be true. But that is an objection to a name, and not to a process : "whether ' logic ' or not, it is consistency of thought, deep analysis- of supposed simple phenomena, and recognition of possible unknown antecedents, to which the results have been mainly due. To refuse all belief until we reach absolute demonstration would of course be an unpractical habit ; but between doing this and merely recognising the possible loopholes of error, there is all the difference that exists between standing still and moving cautiously. It is clear too that these more fundamental objections to careful inquiry would come with greater force if they were once for all to declare their exact position unmis- takably. At present they are apt to shift their ground too fast to hold it firmly. Science finds itself between two apparently contradictory objections, both often coming from the same objector, — that it is too dogmatic^ and also not dogmatic enough. Either on the whole, or on ajiy given point, one or other of these charges may be true ; but it would at least tend to enable us to correct our errors, if the charges were to cease to destroy each other. A more insidious form that this objection to Logic, and defence of Fallacy, sometimes takes, closely resem- bles the attitude of loose, good-humoured Optimism towards the problem of Evil. Since Fallacy is a fact in Nature, let us recognise it as part of the wisely-ordered :31S FALLACIES. [Paet IL scheme o£ things, without which Nature would be 'in- complete.' To hold it merely for an enemy is 'narrow' and 'one-sided.' Or let us view it, at the lowest, as useful manure to raise the crops of reason. Nearly all the more important theories we possess have been preceded by a number of false ones, and without the latter the former could never have been attained. Only the slug- gard never commits a fallacy. A touch of madness is usually found along with the highest genius, and no one is good for much who lacks a spice of the fool. This is, of course, an unduly brief account of the view here spoken of; and it is eminently a view that will hardly bear so definitely stating, Ijut needs as much dilu- tion as possible. Perhaps, however, it will serve to show what is intended, more especially as the statement given above does mix up — ^just as the easy optimists commonly do — two quite distinct, and mutually destructive, de- fences, neither of which would be found so satisfactory by itself. The first of these, — that Fallacy is a part of our total nature, and therefore worthy of our respect, rests on a merely verbal confusion, and one which no man has ever yet quite l^een able to preserve consistently. If Fallacy is a part of our nature, so, surely, is the power to recog-nise Fallacy as unprofitable, and the wish to avoid it as far as we can. There is hardly any element of human nature really stronger than the wish to dis- criminate between truth and error, — except perhaps the wish to keep the still wider distinction of good and evil clear. While we are about worshipping our instincts. €hap. YIII.] some OBJECTIOXS TO LOGIC. 319 why neglect the most fruitful and persistent of them all ? That the view has a certain charm, over and above the mere refreshing effect of the paradox, will be readily admitted by most people. It is often a great relief, and sometimes has a healing and strengthening effect, to feel free to relax our wakefuhiess a little. But the thing can be very easily pushed over into an absurdity, — or, what is worse, can be accepted as a serious theory by minds that might otherwise have kept or attained some vigour. To yield to it to any great extent is as enfeebling to the mind as long-continued sensuous luxury to the body : the comfortable sentiment, ''I am sufficient as I am," may be of use now and then as a piece of rather open self-deception, but a mind that truly and firmly held such belief for any considerable length of time would -miss the bracing effect of a struggle for improvement. The second defence, — that error often leads to truth, — has this advantage over the first, that it does preserve the distinction between the preferable and the unprefer- able. And so long as this is clearly and consistently done, I do not see that we need at all object to recognise the fact. But this is certainly no argument for remaining in an error longer than we can help. By all means admit that liability to error is part of the price we have to pay for forward movement ; but are we to pay the price and then contentedly forget to carry home the purchase ? The transaction needs again to be viewed from both sides instead of from one only. Eather than stop short at the fact that fallacy has its uses, we need to remember that 320 FALLACIES. [Part II. it is only justifiable when it has really led to the good results; and this is apt to be sometimes forgotten. There is, however, one purpose for which the view in question seems to me to have considerable value, and that is, to force us to see that a man who commits even a large number of fallacies is by no means necessarily a fool. I do not mean that this is an advantage only so far as it leads us into charity towards opponents, but also, and chiefly, that it tends to weaken the weight of mere authority as regards any given question : a man may have all the wisdom and learning of an Aristotle, and yet be quite mistaken on a given important jDoint. The recognition of this fact tends to make us value conclusions more on their ovni merits and less on the merits of those who advance them. Such, in rough outline, are the chief objections of this class. On the whole, I think we may say, that when viewed as mere protests against the opposite extreme, they often have a value. But they are too seductive in themselves, too gratifying to common vanity, and too open to employment as simple excuses for idleness, to remain always in their proper place, and as a rule their professed exponents appear by no means conscious of the needed limitations. As regards the objection that Logic is too slow and clumsy to be of the highest practical service, there seems little to be said, except to admit the fact, and even to urge it as a reason for doing all we can to improve the methods of fighting fallac}'. It seems undeniable Chap. VIII.] SOME OBJECTIONS TO LOGIC. 321 that there is an artificial rigidity about all definition, a false simplicity about analysis, a standing failure in all attempts to cram the universe into labelled nutshells. Where Proof depends on many intricate special circum- stances taken together, the analytical habit of mind may often be disastrous. There are plenty of valuable facts too shadowy for Proof, and plenty of occasions where, if we had to wait for logical investigation, the opportunity would be gone, — "there being," as Bishop Warburton expressed it, " no worse practical men than those who require more evidence than is necessary." If common sense is rough. Logic, at least, is far from ready, and sometimes its pretended deeper insight is practically either futile or misleading : for Logic is bound by language, and language always hangs a little behind the newest glimpses of truth. The facts being admitted, it is much easier to find this fault with any existing system of Logic than to supply a better system : and if the objection Avere brought solely, or mainly, by those who know something of the difiiculties to be encountered, every one who cares about the matter would welcome it gladly. Unfortu- nately this cannot be said to be the case. The alterna- tive everywhere suggested by these objectors is one which growing experience has always been steadily finding, on the whole, untrustworthy. Whether we call the alternative ' common sense ' or ' intuition,' its fault is the same, — that, where it really exists, it is so truly a better instrument than slow and deliberate reason, Y 322 FALLACIES. [Part IT. that people are apt to claim, or to imagine, they possess it, when they really possess it not. It is open to any lunatic to know by intuition that he is the angel Gabriel, just as it was formerly open to common sense to see that the Sun went round the Earth, or to feel that the Antipodes were a plain absurdity. In the face of omnipresent illusion, and of possible lunacy, it seems that we must often be content to sacri- fice speed, at least, in the attempt to get the most objective standard possible. Whether breadth of view need really be sacrificed depends chiefly on the time at disposal in the given case, partly also on our power of employing highly general words or symbols. But what is here contended is, that whatever be the sacrifice required, it is safer to make it than to imagine the other alternative really pre- ferable on the whole. It is not claimed that whenever we are called upon to reason we shall gain by deliberately reducing the process to formulas. But what is claimed is that unless we have the power to do so, we have nothing else to keep our reasonings straight. There are two distinguishable states of mind in which slow and deliberate reasoning is now and then dispensed with, — one the reasoned belief that in a given case, or set of cases, it is better to trust to rapid insight, doing this, however, with all the care available and with a clear recognition of the danger ; and the other, the far com- moner state of mind, composed partly of mere easy-going ignorance of the difficulties, partly of dim and floating views of important truths, and largely perhaps dependent Chap. VIII.] SOME OBJECTIONS TO LOGIC. 823 on more purely physical conditions. These are, at least, the two ends of the scale : no one is, quite consistently, either an angel or a fool, either a doubter or a seer; and even the man who follows his ' moods ' has a reasoning mood amongst others. But still we may class men broadly in two opposite camps, according as, on the whole, they are for or against the deliberate use of reason. In the former case, we occasionally make a compromise and voluntarily accept what seems to us in the special instance the smaller of two evils ; in the latter case, — and hence, no doubt, its popularity, — we know little or nothing of evils or of danger, but merely glow with faith in our penetration, and with honest anger at any attempt to call the results in question. If, as so often happens in the latter case, we are also gifted with eloquence, it lies in our power to do much harm to those who have not yet declared for either side. It is easy enough to paint Insight in florid and striking colours, Reason as cold and dismal : and the weaker brethren are always glad of a powerfully phrased excuse. There is, no doubt, much to be said against the careful employment of reason; but it is not the whole story, nor even the most important part of it. The practical problem is, how to make use of logic without spoiling our common sense, or how to make use of our common sense with rather less common discretion. Im- patience with logical method may no doubt here and there be justified, whether in Philosophy or in looser 324' FALLACIES. [Part IL regions of thought ; but far more often it is merely an expression of the unchecked desire to run before we have learnt to walk. Here and there it is plain that the impatience springs from a genuine wish for improve- ment in our methods, but far more often it flows either from idleness or from being unaware that there are any methods to improve. And in any case, though we may appreciate the good intention shown, as yet the fruits are wanting. If logical method as at present kno^vn is insufficient, the sole alternative is unmethodic speculation, which on the whole is less sufficient still. It is open to any one to sit down and dream that to him alone has been given the key of all knowledge — or of any given piece of knowledge, — without any laborious precautions. And perhaps he may be right. But how is he, after all, to be sure of this on reflection, and how are his friends to know it, and the other people with different dreams of their own ? Whether the seer needs an objective standard or not, he will hardly deny that rival seers need one : and in their case, at least, he finds, just as the scoffers do, that the calm security of inspiration is difficult to distinguish from a child's untroubled conceit. CONCLUSION. SUMMARY. To challenge attack is of the essence of ' real ' assertion, and the kind of challenge depends on the confidence with which the assertion is made. Sometimes we speak as having fully considered the question ; sometimes as rather waiting to hear, as a novelty, what may be said on the other side. It is with the former case only that we have been here concerned, and for convenience in describing this kind of assertion we have employed the ancient name of Thesis. The first of the dangers that a Thesis has to rmi, we found to be that of containing the empty form of asser- tion without the substance. If no real meaninsr be understood by the hearer, to him the thesis is non- existent, whether for acceptance or attack. And the hearer alone can decide how far the meaning is real. When the meaning is real and clear — or sufficiently clear for its purpose — the second danger is that of sup- posing that a thesis, to be left unaccepted, stands in need of Disproof. And here the distinction between Disbelief 326 FALLACIES. [Part II, and Unbelief is all-important : or, however the states of mind be named, the thing to remember is that so long as a thesis is unsupported it has not yet been shown to be either true or false ; that although it claims to be true, its claim is not yet made out. The attempt to support an assertion by asking what can be said against it, may be met by replying that at present we know nothing against it, but this much against accepting it — that we see no reason to believe. He who asserts may choose between the two alternatives — producing reasons to satisfy the inquirer, or lea\T.ng him unconvinced. And lastly, when reasons are brought forward, the question at once arises, how far the proof comes short of being conclusive : or what are the gaps remaining before Demonstration is complete. And having found these (as they appear to the inquirer), the safe and fair attack i& still to ask for information : not necessarily to accuse the assertor of absurdity ; only to force him to take care that he in fact avoids it. But to view the office of Logic as consisting purely in sceptical attack, is itself a kind of artifice, undertaken with a far more useful purpose in view. It is not the seizing of firm positions in verbal controversy that is the chief aim of logical method, but the power thus gained may be used as a means to a further end. Since a 'priori any belief may be erroneous, and especially since we have abeady often found ourselves and others mistaken, there is a certain use in learning to treat ourselves as the wary debater would treat a less wary opponent. The Conclusion.] SUMMARY. 327 attack on any erroneous belief must come either before or after its acceptance has led us into actual error. The practical purpose of Logic is to enable us to forestall the possible attacks, and so to guard against the consequences of credulity. Logic thus aims at the adoption only of those beliefs that cannot fairly be avoided, and its opera- tion is in the first place mainly to restrict the natm^al exuberance of belief. It is not necessary here to repeat in any completeness of detail all the separate points of doctrine on which the science of Logic depends : nor can I, indeed, pretend to be able to sum them up in the most concise available form. Apart from metaph3^sical difficulties, the latter operation would demand both a wider symbolic language than is at present accepted, and also a more universal practice of handling symbols easily and reading their application. Expressed in more highly general language than we have, the logical doctrines that are of chief importance from the practical point of vieAv would prob- ably be few in number, simple in nature, far-reaching in their application, and true under all conditions of their use. Such as we have abeady are, when wrongly inter- preted, open of course to easy caricature — as every pun and every verbal puzzle bears witness : but, interpreted fairly, we need never be afraid of trusting our Aveight upon them. Like Science in general, Logic exists for a pur- pose, and wherever it fails to attain that purpose the failure merely needs incorporation into our statement of its laws. Thus we may use, for example, the law of Con- 328 FALLACIES. [Part II. tradiction, while fully admitting that the line between A and not-A is a contrivance of our own : or we may use the Reduction to Absurdity while recognising that it only asks a question. But without attempting here to draw Tip the list of doctrines, it may be of use to select as land- marks for memory some of the salient features of the science. The first of these I hold to be the negative attitude above spoken of. And the second, all that is included under the name Consistency. As already shown, this contains much more than what is commonly meant by ' abiding by our assertions,' namely the whole problem of bringing to light the hidden implications underlying a thesis, and especially the large assertion implied in every confident theory — that all possible conflicting theories are to be discarded. That this demand, if strictly enforced, would be a bar to all belief, may be freely admitted. What Logic is concerned to do is, not to remove all theoretical doubts, but to force us into recognising as clearly as possible their actual extent and power in the given case. As a first means of pointing out the dangers, it sets up an ideal type of Demonstration, and then demands not that we shall reach this but that we shall know clearly how far short of it we fall: for it finds that until the distinction between proven and not-proven is apprehended -with some real distinctness, there is no chance of dealing successfully with the endless complica- tions due to varying degrees of strength in evidence. The more we inquire into the main sources of error, the Conclusion.] SU30IARY. 329 more clearly we see that ignorance of danger is at once the commonest and the only one that we can certainly remove. Hence the central purpose, for practice, is to find the gaps in Proof remaining to be filled. The definable term, the abstract proposition, and the argument, have this in common, that each is capable of being viewed as expressing an indication. Given the general name, and any of the essential attributes follow ; given the S of an abstract proposition, and the ^ follows ; given the Reason and the Thesis follows. And to each of the three the rule of counter-indication applies : deny an essentia] attribute and we deny the name ; deny ^ and we deny S; deny the Thesis and the relevant Reason is denied. In the attainment of Consistency the Law of counter- indication has two chief uses ; first that of restraining us from taking two distinct assertions as equivalent, and secondly as a means of helping to bring to light the hidden implications. In the former, or negative, aspect it operates chiefly by preventing us from proving some easy proposition under the belief that we thereby prove its reciprocal also. In the positive aspect the chief value of the law is in helping to explain the syllogistic process. But such explanation demands — Next, the assumption that every isolated fact comes imder a wider law. This doctrine lies at the root of Proof and of Explanation equally. To prove a thesis, we need to show it as a case under some Principle — just as, to explain a name we have to mention a genus, 330 FALLACIES. [Part II, * or as to explain a fact we have to bring it under a law. And o£ that Principle the thesis may be either a denial of the antecedent (S), or an affirmation of the consequent (^) • while the Reason either denies the consequent or affirms the antecedent. By means of Thesis and Reason together we can thus find the law implied. Lastly, there is the doctrine that every isolated fact is further analysable — that besides belonging to a genus, it possesses also a specific difference. And that, in order to view such fact correctly we need to bear its difierential qualities in mind. The eye for genus thus leads us to ~ attempt to establish our thesis deductively, while the eye for differentia becomes the main safeguard of induction. While, then, we continue to assume, as a basis for practical proof, that all 'things' belong to classes, the names of which may be used as in- dicating certain facts about them. Inductive Logic teaches us to cultivate the eye for difference, — to keep refining away what passed at first sight as indivisible, and breaking down ancient barriers that perhaps have served some useful purpose but were better suited to clumsier needs than ours. Deductive Logic insists that conclusiveness depends on indication, — the trustworthi- ness of laws ; inductive Logic leads us to revise the laws themselves, and put us on guard against accepting them too widely. The power of seeing finer shades of differ- ence is on the whole the best and most lasting result of logical training, and affords most help in the rapid detection of fallacy. CoxcLusiox.] SUMMARY, 331 These seem to be, in briefest outline, the more im- portant points to keep in mind : but as thus shortly stated they can only be of use as memoranda, not as in themselves by any means sufficient statements of all that is required for practice. Nor, certainly, would such sufficient statements be easy to frame. It is not theory alone that can ever fully enable us to preserve the golden mean between faith and hesitation. So commonly is this fact recognised, however, that it will be well if we can avoid going far beyond it and accept- ing the easy view that Theory and Practice must for ever carry on a hopeless warfare, and that, so often as our weak attempts at theory fail to fit the facts, it is sufficient to plead the possession of a Iiighly practical spirit. Perhaps one chief source of red precipitate." We will not ask how far these methods, and the subordi- nate variations of them, can be trusted for proof of absolutely universal laws of sequence, whether of backward or of for- ward reference, — laws, e.g., such as " Wherever S is found, ^ must have been before," or " Wherever S happens, ^ is sure to follow." Practically, as already said, we are for the * Mill's Lorjic, vol. i. p. 450. (8th Ed.) 34?2 APPENDIX. most part obliged to be content, in our knowledge of causal sequences, with mucli less than these completely universal assertions. The mass of our propositions regarding causal laws are of the milder type, " ^ is one cause of S," or " S, unless counteracting circumstances interfere, will cause <$ to follow." It is necessary, therefore, to inquire how far the empirical methods vhb.j be relied upon for the support of such comparatively timid assertions as these. The Metliod of Agreement. Caxon. — If two or more instances of the phenomenon under investigation have only one circumstance in common, the circum- stance in which alone all the instances agree is the cause {or effect) of the given phenomenon. It is obvious, in the first place, where the simple Method of Agreement fails. Its ' characteristic imperfection,' as Mill himself took care to show, is due to our necessity of admitting that the ' same effect ' may be produced by ' dif- ferent causes.' Of course, as Mr. Carveth Eead puts it, an effect particularised to the full can never arise from different causes ; but the very essence of these abstract propositions is that they particularise to the full neither S nor <^, and so far as they fall short of describing an effect " in the minutest detail," so far they leave an opening for vicarious causes. The manner in which the vicariousness (' Plurality ') of causes interferes with the cogency of the method is easily seen. Assume, for instance, that I have made ten observa- tions as to the apparent ' effects' of eating salmon ; having- ten times observed this antecedent to be followed by indisposi- tion. On each of these occasions there have been many other circumstances combined with it, — the other things eaten and drunk during the same period, to go no further. In order to THE METHOD OF AGEEEMENT. .343 put the most favourable case possible for tlie operation of the method, we will also suppose that the salmon was the only- antecedent common to all the cases of indisposition. But if vicariousness of causes be once admitted possible, there is nothing to prevent A having been the real cause on the first occasion, B on the second, C on the third, and so on; S (the salmon) having been perfectly harmless all the while, — just as harmless as some other circumstance which, though not part of the food, is invariably present in all the cases, — say the fact that Bismarck is still alive. Unless, in short, we have some further reason to suspect the element in question to be the guilty one (in the case supposed, e.g., we may rely on popular belief, or doctor's advice, or family tradition) — un- less we can bring deduction from some accepted truths to aid us, the mere method of agreement by itself can give, in such cases as these, no solid support at all. There is, however, it will perhaps be said, one class of cases in which the unsupported method of agreement must be allowed to be practically sufficient ; namely, where the cases observed are not counted by tens, but by hundreds or thousands or more. But putting aside the difficulty of set- tling where the sufficient number begins, and also the diffi- culty of finding an unmistakable instance of such a case, — for where the observations are numerous either the joint method^or that of concomitant variations is usually appli- cable,* — what is there to prevent these thousands being all under the same limitation ? " We might," as Mr. Fowler says, " pass through a field containing thousands of blue hyacinths, but this would not justify us in expecting that the next time we saw a hyacinth it would be a blue one " [say rather, ' this * Certain axioms, e.g., sometimes quoted in tliis connexion, seem to me to be more dependent on concomitant variations than on strict and mere agreement. 344 APPENDIX. Avould not jQWve that all hyacinths are blue']. A large numher of minor differences may be thus eliminated, and yet some important limitation may remain so as to constitute a differentia common to all the cases observed. In other words, besides mere number we need the assurance that these in- stances are fairly representative of all that exist. The field of our observation may be a large one, but there may also be other fields outside of it, — until such possibility is excluded. The Joint Method. These difSculties are partly met by the Joint Method, but not entirely. The Joint Method compares two sets of instances independently, and combines the results. Its canon is, in Mill's words : — If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance ; tlie circumstance in which alone the two sets of instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. The canon itself is axiomatic, but its application is far from being secure. To test it, let us suppose the most favour- able conditions ; namely, that the instances observed are considerably more than two in number. Mr. Fowler again provides us with a good example — " I have observed that a certain plant is invariably plentiful on a particular soil : if, with a wide experience, I fail to find it growing on any other soil, I feel confirmed in my belief that there is in this particular soil some chemical constituent, or some peculiar combination of chemical constituents, which is highly favour- able, if not essential, to the growth of the plant." It is clear that if the one set of instances agree in THE METHOD OF DIFFERENCE. 345 nothing but the presence of the two circumstances, and if the other set agree in nothing but their absence, there is of course no room for a vicarious cause. But it is just this further assurance which lies outside any possible application of the canon, and which must be added to it to complete its cogency in a given case. To refer to Mr. Fowler's ex- ample, we need assurance that besides the chemical consti- tuents of the soil no other surroundings are invariably present and absent together with the soil, — such as climatic condi- tions, for example. A wider experience may always, until the contrary be shown, lead to the necessity of qualifying (ji.e. limiting) the law arrived at. Instead of being simply " This plant, in general, — > these chemical constituents in the soil," the law may be, " This plant, under certain conditions (of climate or otherwise), > these chemical constituents." In its simpler form the law remains liable to contradictory instances being found on a wider search. TJie MetJiod of Difference. Canox. — If an instance in whicJi the pihenomenon under in- vestigation occurs, and an instance in luhich it does not occur, have every circumstance in common save one, that one only occurring in the former ; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon. The Method of Difference may be called the sheet-anchor of empirical proof. "It . . . appears to be by the Method of Difference alone," says Mill, " that we can ever, in the way of direct experience, arrive with certainty at causes." Elsewhere we frequently hear of its " rigorous cogency." An example has been already given, — an example which shows the strength of the method but not its weakness : o4!G APPENDIX. when we add iodide of potassium to cliloride of mercury, we may no doubt be tolerably sure of the substances Ave are handling : inside a test-tube unknown antecedents have small chance of entry. Granting, however, that this method has a practical ad- vantage, in many cases, over the other methods ; and that its results are often practically beyond cavil ; on what does its certainty depend ? Not, in any way, on the method 2^61' se but on the fact that in certain departments of inquiry (^e.g, in chemical experiments) we are fairly in a position to obtain the external certainty that all the antecedents are known. So far as we can be sure that we vary only one circumstance at a time, so far we attain this external certainty : so far as we cannot get this assurance the method of Difference is no more safe than any other suggestive source of inference. Where, as in a chemical laboratory, we have practically entire control over surrounding circumstances, such as light, air, and temperature ; where we can obtain any element, or com- bination, we require, in the utmost possible purity and in the exact proportion desired ; there is no doubt this method may be trusted almost absolutely. But the certainty is due to the laboratory apparatus and not to the method of Differ- ence by itself. When we come outside these highly artificial conditions, and attempt to apply the method of Difference in circumstances over which we have no control, we find our- selves constantly brought up against the fallac}^ jpos^ hoc ergo ^7'Ojpter hoc. To show simply that in a given case when S was added to existing circumstances ^ followed, cannot prove that S — > ^, unless we show at the same time that no other alteration in the existing circumstances took place, — a universal negative which in practice it is often hard to prove even approximately. In all the more complex questions, such as those of politics, cliaracter, or daily life in general. THE METHOD OF EESIDUES. 347 firm proof by raeans of the direct raetliod of Difference be- comes nearly impossible. Witness the argument that because the addition of Free Trade to England's commercial system has been followed by periods of depressed activity, therefore the former is the cause of the latter. And the possibility of conjuring tricks is perhaps the clearest example that can be given of the effects of unguarded confidence in the direct method of Difference. "When the conjurer j^roduces startling effects by apparently insignificant causes, there are ' un- known antecedents' up his sleeve or elsewhere convenient, whose presence it has been his business to make us overlook. The Method of Besidues. Canox. — Subduct from any phenomenon such part as is Jcnoicn by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining ante- cedents. It is seldom that the Method of Kesidues can, or rather need, be employed at all as a method of proof, though, as a source of inference it has often been fruitful and important. Astronomical discovery especially is full of striking results obtained by means of it : so, too, certain other departments of science. But of attempted proof by means of Eesidues merely, we are rather hampered in finding true examples. Mill himself gives no instance of its working, except in symbols, and every instance given b}'- Professor Fowler is an instance of discovery, not of proof. Most of those given by Professor Bain are also cases where suggestive hints have been first given by this method, to be verified in other ways. Here it is clear at once, even without examples, that all must turn upon the exhaustiveness with which the residue is narrowed down by the hiown causes and effects in the case- :34S APPENDIX. The difficulties of the method of Difference are therefore here repeated, and are further increased by the fact that the required isolation of the phenomena is not actually attained, but only seen by the light of imagination. The negative instance is obtained by deduction, not by direct experience. In the last two paragraphs of Prof. Bain's exposition of the method, we obtain what seems to me a valuable hint as to its true importance for purposes of proof; namely, that it may be employed to prove a negative result, — to disprove some supposed explanation by showing that the effects can all be accounted for in other ways. Thus, if it can be shown that the known forces of inorganic matter, operating in the special collocations of organic bodies, will account for the phenomena of life without leaving a residuum, the theory of a vital force, or vital principle, becomes unnecessary. Such cases as this are perhaps those for which the method is most adapted ; but here too all turns upon the " if it can be shown." This condition, and not the mere fact of employing the method at all, is the important matter. Tlie Metliod of Concomitant Variations. Caxox. — Whatever 'phenomenon varies in any manner loJien- ever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. ' Concomitant Variations ' is perhaps the most commonly applied of all the inductive methods. Its application, ac- vcording to Mill, is in proving " the laws of those Permanent Causes, or indestructible natural agents, which it is impossible either to exclude or to isolate ; which we can neither hinder from being present, nor contrive that they shall be present alone." And it may be added that in almost all those vague THE METHOD OF COXCOMITAXT VARIATIONS. 34:9 and large assertions so common in daily life, the method of Concomitant Variations is continually employed in proof. More than this, it seems (as already said) not impossible that certain Axioms, snch as those of Geometry, find their best support in this method rather than in the method of Agree- ment. The more nearly our actual lines approach paral- lelism, or our magnitudes equality, the more nearly do the axioms fit the facts observed : the more one set of antece- dent circumstances resembles another, the more do their respective consequents agree.* In certain cases such as these, perhaps, ' unknown antecedents ' can be shown to be as im- probable as a pest of mice to the mounted knight. But even here we are never quite secure against their interference, and what security we have is, as in all the former cases, gained from external sources. Good examples, usually given, of the employment of this method are to be found in the thermometer and the pen- dulum. We cannot deprive a body of all heat, and we cannot entirely remove the Earth from the pendulum, nor the pendulum from the Earth; but by observing the variations we may often obtain a law which is practically as secure as if it were really obtained by the direct method of Difference. We get abundant evidence tending to show that if the direct method of Difference could be applied (which, by the hypothesis, it cannot), we should have all the cogenc}' which that method could give us. We should have all that cogency, but no more. For in this case, as in the case of all the other methods, we require, over and above the employment of the method itself, a further assertion on which its actual cogency in the given case shall * Cf. also the use made by tlie late Prof. Jevons of liis principle of the " Substitution of Similars," where " likeness or equivalence " is treated as purely a matter of degree. 350 APPENDIX. depend. For Concomitant Variations, tliis further assertion has been expressly formulated by Prof. Fowler, as a ' rider ' to the canon : — If ice can assure ourselves that there is no third phenomenon varying concurrently with these two, toe may affirm that the one phenomenon is either a cause or an effect of the other. The theory may in fact hold good only up to a certain point, — namely, so far as that third phenomenon (which let us call Z) is present ; and instead of S — > ^, the law should be accurately expressed S (when Z is present) — > ^. A well-known example of this is the contraction of water by cold, down to 39°, after which it begins to expand again. Here the limitation ' above 39° ' must be added to the first crude statement of the law ' water contracts with cold.' I may add a further difficulty to which the method of concomitant variations is liable : namely, that the supposed law guaranteed by it may be a case of varepov Trporepov. Finding that the size of towns varies concomitantly with the size of the rivers on which they are built, an incautious reasoner might conceivably arrive at the law that the size of the river was due to the size of the town. Hearing the cuckoo call its own name, he might conceivably put this down to the cleverness of the bird. Finding Hamlet full of * quotations ' he might suppose that Shakespeare was sadly wanting in originality. Of course, these extreme cases are mainly useful as affording food for the comic papers ; but in serious inquiries such as that of the concomitant varia- tions between new organic structures and the need for them, the fallacy is perhaps not quite unknown. Or agaiij, take as an example the good old farmers' theory that ' blight ' was either itself a kind of disease, or at least a sign of existing disease, in plants. They pictured the plant 'becoming diseased,' — much as a man's digestion might get out of THE METHODS, IX GENERAL. 351 order; and, as an effect of tliis, the blight was supposed to ' come out,' — much as the man might break out in a rash, or pimples. But it seems to be now completely established that the true explanation is that blight is a kind of fungus, the spores of which take root equally in the leaves of healthy plants and unhealthy ; but that, however healthy the plant may have been, the parasite drains its life, and so causes disease, — stunts the growth of the plant, or taxes its fruit- bearing powers, or in some way interferes with the normal state of things. It is thus often an exceedingly difficult matter to say which of two things, varying concomitantly, is cause and which is effect ; and the common-sense view, based perhaps on some loose analogy, is as likely as not to reverse the sequence. The Methods, in general. This, then, is the difficulty attending the application of all the methods, — the possible presence, unsuspected, of a third phenomenon (or ' unknown antecedent ') in the cases observed : so that the real law, instead of S — > ^, should be either Z — > ^, or SZ — > ^. The first of these two alternatives (namely that S is purely accidental to 5) may be for practical purposes excluded by the Doctrine of Chances : the second alternative must remain in every case possible, imtil removed by special evidence outside and beyond the mere fact of ' employing the method.' To sum up : — Where the Method of Agreement is employed, evidence should be further produced, to show (1) either that every element but S and ^ has been eliminated, or (2) that those remaining are accidental to <§ ; and also that the Plu- rality of Causes does not here interfere. Where the Joint [Method is employed, we require to know 352 APPENDIX. further that no other operative antecedent was present in the positive set of cases and absent in the negative ones. Where the Method of Difference is employed, we, must be sure that onlj^ one circumstance has been added. Where the Method of Eesidues is employed, we require the same external evidence as for the Method of Agreement. Where the Method of Concomitant Variations is employed, we must be further assured, (1) that nothing besides S varies concomitantly with <^ ; and (2) that whichever (S or <§) is supposed to be the cause of the other, is not in reality the effect. In each case the real cogency of the argument depends upon the certainty obtainable on these points : obtainable by any external (and especially instrumental) correction of our observations, and by searching analysis of the phenomena observed. The mere statement of the method employed is not by itself a sutficient guarantee : at most it may serve to point out the special direction in which we should look for dangers, and guard against them. The two main modes of Inductive fallacy known by the time-honoured names of Inductio per enumerationem simjplicem, and Post hoc ergo p-ojpter hoc, correspond essentially to failures in guarding against the dangers of the unaided methods of Agreement and Difference respectively. Valid induction often enough begins by simplex enumeratio ; and post hoc often sets us on the track of a law : indeed it is difficult to suppose any other beginnings that can be called beginnings of know- ledge. But it is when the attempt is made to TQ&t proof on these alone, that the characteristic imperfection of all the methods comes to be important. Unaided by special know- ledge of the circumstances, they are suggestive guides hut uncertain tests. THE MOODS OF EXCEPTIVE DISPROOF. 353 THE ilOODS OF EXCEPTIVE DISPROOF. Before tracing in detail the reduction of the fourteen syllogistic moods in I and to the two formulas given on p. 242 above,| there is a less wide and general view that may be taken for a moment with advantage ; and that is, the view of them as reducing a generalisation to absurdity by means of the modes of positive deductive proof. In every valid syllogistic mood there must be at least one positive indication among its premisses, and if such premiss be com- bined with the contradictory of the thesis {i.e. with the posi- tive assertion which such Thesis just denies) we get as a new conclusion either the contradictory or the full contrary of the other premiss. If, then, both premisses be in fact true, the contradictory of the Thesis cannot be true : that is the Thesis itself must be so. Thus in the mood BaroJco, the Thesis being S -j — > ^, its contradictory is S > <^ : combine this with the positive premiss ^ > M, and (b}' Barbara) we get the conclusion S > M. But this contradicts the remaining pre- miss of BaroJco, namely S -\ — >• M, and accordingly one of the premisses in our Barbara must be materially false. But the premiss ^ — > M is given true : thus the fault is shown to lie in the remaining premiss S > ^ : and this being false, our Thesis is necessarily true. It is needless to set out all the forms, but if the reader cares to trace the process in them, he will find that BoJcardo also employs Barbara: that Festino and Disamis employ Celarent : Ferio emjoloys Cesare : Darii, Felapton, and Ferison employ Camestres ; while the four moods belonging to the fourth figure employ Camenes. * See p. 241. t And sec formula; (1) and (11) on p. 355. 354 APPENDIX. In practice, however, any metliod based on this view of the argument from exception would, I think, be found intricate and unwieldy. The only purpose of mentioning it is in order to admit that on occasion the arguments from sign and from essential difference (and even the almost non- existent form Camenes) maij be thus utilised in Disproof by exception. But since all are also translatable into one or other of the two forms above given, which two are in a sense typical and fundamental ; and since, in fact, the amount of translation necessary in order to bring them under the appropriate formula is of the easiest possible description, it seems better worth while to follow the inquiry in this direction. If we take the fourteen s^^llogistic moods whose conclu- sions are in I and 0, it will be seen that these two formulas are generalised from them, by omission of the distinctions of quality in M and ^ respectively, by free employment of the law of counter-indication, and by confining attention to the smallest amount of assertion necessary. There is only one, for example, which exadlij corresponds with our first formula, namely BaroJco, and only one which exactly corre- sponds with our second, namely Bokardo. All the others may be viewed as varieties of these tv/o. Thus, in the first place, with M negative instead of positive, we get Festino ; with M and <^ both negative and with the counter-equivalent of the required non-^ — > non-M (namely M — > <^) we get Darii. With these differences and also with the counter-equivalent of the required S -\ — > non-M (namely M H — > non-S) we get Datisi ; and if instead of merely M H — > non-S in this latter mood we can make the positive assertion M — > S, we get Darapti. With M nega- tive and with the counter-equivalent of the required ^ > non-M (namely M — > non-^) we get Ferio ; with the same THE MOODS OF EXCEPTIVE DISPKOOF. 355 differences and also the counter-equivalent of the required S H — > non-M (namely M H — > non-S) we get Ferison ; and if here we can make the positive assertion M — > S, we get Felapton. Finally, with M negative, and only the minor premiss reversed (namely M -\ — > non-S instead of S H — > non-M) we get Fresison ; and if this be strengthened into 31 — > S, we get Fesapo. Similarly, in the second class, with <^ negative we get Disamis : with the same difference and also with the counter- equivalent of the required M H — > non-^ (namely ^ H — ^ non-M we get Dimaris ; and if this be strengthened into the positive assertion ^ > M, we get Bramaniij). A table may be of service to the reader in verifying these details : — (1) Baroko . S -^^ 5 for S +> M and 5 ^ M ^ (2) Fe&tino . Ditto S -f^ uon-il „ 5 — >■ non-M (3) Bar a S+> non-S „ S -1^ non-M ,. M^-S (4^ Datisi . 1 Ditto M -{-> non-S ., M— >S (5) Bar apt i . Ditto M-^S „ M ^ S First (6) Ferio S-f^S S -f^ non-il „ M ^> non-S formula. (7) Ferison . Ditto M -f^ non-S „ M -^ non-S (8) Felapton Ditto M-^^S „ 31 -^ non-S C9) Fresison Ditto M -t^ non-S „ S — ^ non-M (10) Fesapo . Ditto M^-S „ S — ^ non-M (11) Bokardo . Ditto M->S ., M+>S \ (12) Disamis . S-|-> non-S „ M^S „ M -f-> non-S Second 'formula. (13) Dimaris 1 Ditto M-^S „ S -f^ non-M (14) Bramantip Ditto M->S „ 5 -^ M It will be se( 3U that the s;; dlogistic moods corresj: ending ooi^ APPENDIX, to our first formula are nearh' three times as numerous as those corresponding to the second ; but the second is not on this account at all less important, or even less frequently met with in practice. All the syllogistic moods are possible^ indeed, but some are no more than possible, and certainly not all these fourteen forms are equalty employed. Probably the seven commonest are BaroJco, Festino, Darii, Ferison, Datisiy BoJcardo, and Bisamis. Of these the six last form three pairs, differing onlj' in the quality of ^ ; the reason that BaroJco has no kindred form in I is that for such form the disjunctive non-,^ — > M would have been required, and the disjunctive had no place amongst the moods of the scholastic scheme. D.* INVARIABLE SUCCESSIOX. In accordance with the plan proposed in this book, I have tried to keep away from all the deeper problems in the theory of causation. This was partly on account of their difficulty, but also because, whatever other elements may be involved in the notion of causal sequence, the element of invariabilitij appears strictly sufficient for the purposes here aimed at. The ' cause ' of a thing comes now more and more to mean its ' history.' The assumptions seem more and more justified, that if past events had been at all different this present event or thing would not have been precisely what it is ; that if they had been ' essentially ' different this^ would have been essentially different also ; and hence, that if the essential part of this event be fixed by definition, to * Sec p. 81. INVARIABLE SLX'CESSIOX. 357 sucli essential part there corresponds a 2^0.1-1 of the antecedent history, which not happening the event in question (happen- ing there and then) would have been too different to deserve its present name. But, as noticed elsewhere, the fixing of a definition is never " particularisation to the full." Hence, within the limits allowed by the name, there is room also for difference in the antecedent circumstances (i.e. for Pluralit}^ of causes), and therefore we are led to read the essentiality only from effect to cause (the indication from cause to effect), and to use the concept ' invariable law ' in preference to that of the * identity ' of cause and effect. In all cases of ' invariable ' sequence in which S and S are not regarded directly as cause and effect, the assertion of invariability is either expressly stated as conditional, or intended as tentative (or ' empirical ') only. In the often- quoted case of day and night, for example, experience tells us not only that da}^ always follows night, but also that night follows day, and, further, that day always follows sunrise and night sunset. We thus get a double observation (under the joint-method) in favour of the commonly received explana- tion of the phenomena, while the supposed assertion, * night causes day,' could only rest upon the method of agreement, and, even in the absence of the other explanation, would be of very uncertain tenure, — being no explanation of more than half the facts observed. It would be an empirical law, entirely unconnected either with wider laws which might explain it, or with other facts which itself might explain; and it would also be open to the obvious ciiticism that nothing had been shown to prove that the dependence was not exactly the reverse way, — day causing night, as daily exertion (it might be suggested by the poetic mind) causes nightly sleep. So 8 APPENDIX. Invariability of succession is then what, in assertions of causation, we always do mean to express, whether we also include Unconditionality (or Efficacy), or keej) our assertion close to the facts from which these highly abstract notions, take their rise. The sequence of night and day, viewed merely as sequence, and apart from all question of efficacy, is not contradicted by the establishment of the surer sequence " Earth's revolution in sunlight > day and night alter- nately," but is merely merged in this, and loses thereby' whatever independent value it might otherwise have had a& an engine of explanation and prediction. So far as it is for these two purposes only that we need, or use, the notion of Causation, Invariability is sufficient. Nor, on the other hand, if we picture caiises as liable to ' counteraction,' need the absence of actual invariabilitj- present a stumbling block. Although, for example, the majority of seeds never actually come to anything, our knowledge of the causes of failure permits us to infer that but for certain obstacles that may be classed and numbered, they would do so. So far only as the definite possibilities of counteraction remain unknown, so far we admit an element of uncertainty in any predictions based on our causal law. In such a case the statement of the law itself is felt to need some further limitation. APPENDIX. .359 E. TABLE I.* Concrete, Affirmation and Denial. bol of indication ; -f-^ for exceptive and simple id . — ' for the assertion of dift'erence.] Real. >enial. Concrete. Assertive (or afBrmative). This S — > S-. {e.g. ' This was due to carelessness.') Denial. Assertion of difference. S. — ^5. {e.g. 'Whales are not fishes.') Simple. This S -|-> S'. {e.g. 'This was not due to carelessness.') Assertion of difference. This S , ■ S. {e.g. 'This case differs from that.') * See pp. 41-78. E. TABLE I.* ' Concrete, Affir: [-^ being the symbol of indication ; -|-^ for exceptive and simple inial of indicatioiu and , — ■ for the assertion of difference.] Denial. Assertive DoqIhI. ) Exceptive Assertion of Simple. Asecrtlo S-f^S. differcDce. ThisS-&S. differen 1 1 APPENDIX. 360 TABLE II.* SSIOX AND CO-EXISTENCE. Real Propositions. » Crete, assertive or negative : the symbol -t-^- d to generalise — > and -f^.) Predictive. future S. Lcient education vours crime.' 3 law will not acify Ireland.' Of co-existence. Descriptive, classifying, and connecting. S -J^ present £>. S % — present &. 'Gold is an elementary sub- stance.' ' Business qualities and the san- guine temperament generally go together.' ' This man is guUty.' ' Whales are not fishes.' 'This case differs from that.' [eaves out of consideration the further dis- ly roughly true : ' for these, see Table III.] * See pp. 79-83. Succession and Co-exisi Re4i. Propositions. ■ This law will not •This case differs ft APPENDIX. 361 TABLE III.* xs, eegarding ixdication, to one of which every Thesis gites the answer Yes or No. being spoken of in the ab- stract. S in the past re- ■ latively to S. S in the present relatively to S. The asserted in- 'j (Is S dication being ( sary to S as strictly inter- [ cause ?) preted. ) "With unex pressed quail V fication. /Strictly. (Is S> one cause - ) (Is S -V ofS.' With unex- pressed quali- r Strictly. S in the future J relatively to S. ) With imex- pressed quali fication. (Does S always co-exist with S?) (Does S usually co-exist with S?) (Is S the in- evitable effect of S .') (Does S tend to produce S' ?) being spoken of in the con- • Crete (i.e. as particularised by its indivi- dual peculi- arities and environment). * (Was the actual sequence or co-existence, S followed or accompanied by S, other than accidental ?) -^Utivel/S's":'" }(D"1 -S happen, causing S?) ■ * ieVtivertot } CDoes S coexist wift S .-) See pp. 4l-b3. _StemB.pokeii APPENDIX. 362 TABLE IV.* E Types of Argument. Arguments. By Sign. Proof by Sign. (S -^ Distinction by Exceptive Point of Disproof. Difference. I for "j '}\ . ^C^^^,,^ By Sign or ^0 ^— ^non-M.) Difference. for 5 -^ M.) By Example. * See pp. 224-252, TABLE 1V.» The Types of Abcumk APPENDIX. 363 TABLE v.* CULIAR TO THE SPECIAL TyPES OF ARGUMENT. In the ArPTument : — ■ id essential By Sign. (Danger : acceptance of a Principle which does not apply. 2) Generalisation. (Danger : essen- tial differencehe- f^ween This Sand All S.) ance that (4) Acceptance of the nciple and reciprocal of ilication are either Principle led: or what or Application as I should be. equivalent. Un suspected difference or resemblance be- ticeen the ' thiyigs ' spoken of, through the influence of names. (5) Difference between things named alike. See pp. 252-297. I (6) Resemblance be- tween things named differ- ently. Tbe Dangebs Pecuh I ,,(«.,««/ a Pritrci.!. 'f^ £^3^HP INDEX. A. Absence, indication bj, 84, 92 ; and presence, speciallj defined, 85. Abstraction, in general, 72, 333 ; abstract propositions, 66, 76, 78, 80, 112, 235, 272, 276, 339 ; ab- stract terms, 72. Absurdity, reduction to, 298, 174, 251, 286, 307, 326, 328. Accident. See Essence. Accidentis Fallacia, 293, 176. Adequacy of Eeason given. 111, 102, 300, 26. Admissions, appeal to, 114, 181 note, 207. AflBrmation and Denial, 6i, 68, 223, 243. Agreement, Method of, 342, 281, 339, 351 ; as to meaning, neces- sity of, 16, 57, 65, 145, 183. Alternative theories, need for con- sidering, 39, 40, 164, 177, 270, 275, 276, 310, 311, 328; list of, 333. Ambiguity, verbal, 124, 133, 177, 184, 189. Analogy, as argument, 226, 252, 179, 212, 214; and metaphor, 198 note, 259 ; and essential re- semblance, 227, 247, 267; and deduction, 229 note, 231, 232, 234, 254 ; dangers of, 252 ; vital point of, 267; usual modes of employing, 262 ; analogical con. sisteucy, 110, 104. Analysis, value of, 258, 237, 273, 279, 317 ; and synthesis, 259. Analytical proposition, 42 note. Antecedent and Consequent, 222, 290. Antecedents, unknown, danger of, 270, 279, 284, 349, 351. Application, of Principle, 111, 113, 103, 109, 204, 208; remote and direct, 303, 308, 210. Argument, real and verbal, 204; special types of, 202 ; as com- plex proposition, 100, 58, 64, 310 ; and rules for debate, 160, 163 ; by example, 224, 220, 252 ; by sign, 239, 286, 220; hypo- thetical and categorical, 221 ; ad hominem, 61, 181 note, 205; by analogy, 226, 252, 179, 212, 214; inductive, 234, 267; de- ductive, 242, 286; chain, 210, 303, 308; obstruction of, 50, 128, 167; a list of objections to, 178. Aristotle, 174, 176, 179, 193, 209, 293. Assertion, in general, 41 ; and denial, 64, 68, 223; and con- clusion, 33, 18, 41, 150 ; unsup- ported, 147, 326; of difference, 68, 246 ; of doubt, 153 ; implied by Thesis and Eeason, 99, 26, 27, 114, 288, 300 ; goal and start- ing-point of, 54 ; degrees of reality in, 146 ; suggestive and tentative, 151, 227, 252, 259, 2Qi) INDEX. 162, 188 ; vagueness of, 49, 187, 251 ; and meaning, 26, 60, 63, 183. See also Proposition. Associations, gathered, in names, 184, 191, 199. Assumptions, covert and open, 180, 181 note, 194, 198 note ; neces- sary for language, 13, 46, 106, 134; for explanation and pre- diction, 13, 272, 302. Attack, successful resistance to, 37, 38, 249, 273. Axiom, and undeniability, 285 ; and theory, 207, 285 ; and plati- tude, 80; proof of, 343 note, 349 ; of Syllogism, 301 ; of Causation, 272, 302. Axioms, of Consistency, 105, 14, 21, 46, 122, 208 ; for the induc- tive methods, 340. B. Bain, Professor, 56, 87, 89, 105, 125, 134, 142, 222, 274, 347, 348. Belief, reasons and causes of. 33 ; rationalisation of, 111, 213 ; ditficnlties of grounding, 33, 46, 48, 149, 309; repression of, by Logic, 20, 314, 326 ; in Mystery, 48, 140, 315; unbehef and dis- belief, 153, 326 ; provisional, 94, 164; and opinion, 162, 151, 98, 325 ; fluctuation lietween con- tradictory beliefs, 120, 140. Bentham, George, 190. Bentham, Jeremy, 198. Berkeley, 72. Bulls, 129. Burden of Proof, 148, 247, 277, 310, 325. C. Casuistry, 132, 258. Categorical proposition, 73 ; argu- ment, 221. Causation, metaphysics of, 14 ; axiom of, 272, 302 ; propositions asserting, 54, 79 ; and indica- tion, 79, 82, 268, 356 ; and counteraction, 80, 270, 342, 358; and uniformity of nature, 272, 302, 356 ; causal dependence, 63 ; and efficacy, 358 ; kinds of cause, 334, 269 ; identity of cause and effect, 357; vei-a causa, 238,347,348; plurality of causes, 80, 270, 342, 351; ancestral cause of coexistent events, 336, 278 note ; cause and history, 356. Chain arguments, 210, 303, 308. Chance, tendency, and law, 81, 268 ; elimination of, 274, 351, - 270; necessity of recognising, 337, 81. Circle, 120, 169, 213. See also Petitio Principii. Circular definition, 123, 142. Circumstances, essential, 272, 340; control of, 281, 346 ; exact simi- larity impossible, 272; circum- stantial evidence, 221, 224. Classification, 63, 64, 171 ; aiid see Names; of fallacies, 170, 171, 176 ; classifying i^ropositions, 53, 54, 79, 83. Co-effects, 335. Co-existence, 64 ; and succession, 78, 46, 278 note, 281, 325, 337 ; incomplete indication of, 82 ; and ancestral cause, 336. Coincidence. See Chance. Common sense, untrustworthiness of, 2, 4, 5, 77, 98, 160, 169, 317, 321, 323. Compartmental view of proposi- tions, 53. Complex proposition, only gradu- ally distinct from simple, 56 ; argument as, 58, 64, 100, 310. Conclusion, 33, 41 ; and thesis, 18, 150. Conclusive proof, 40, 114, 157, 204, 220, 275, 285, 300, 329. INDEX. 3G7 Concomitant Variations, method of, 348, 339, 343, 352. Concrete. See Abstraction. Confusion, fallacies of, 170, 173, 177. Congruent facts, as Proof, 219, 224, 215, 279. Connotation, 53 note, 107. See also Meaning. Consistency, 103, 109, 114, 207, 317, 328; Axioms, Maxims, or Postulates of, 105, 14, 21, 46, 122, 208; deductive and analo- gical, 110, 103, 104. Continuity of Xature, 336, 133, 14. Contradiction, law of, 105, 106, 109, 328. Contradictory instance, 250, 271, 275, 283. Contraposition, 84, 87. Conversion, 84, 87. Copula, 54. Counteraction, of law, 82, 270, 342, 358. Counter-indication, law of, 84; and contraposition, 84 note, 87; gives the sole equivalent form, 86, 208; table of, 87; use of, 84, 89, 310, 329 ; value chiefly nega- tive, 90; and the disjunctive proposition, 92; applied to con- crete propositions, 95 ; as re- gards past and future, 96. Criticism, value of hostile, 33, 39, 60, 204, 232, 301, 315. Crucial instance, 235 note. D. Deduction, 110 note, 330; and Syllogism, 113, 212, 300; and Induction, 212, 177, 330, 204; and Proof, 213, 217 ; and Petitio principii, 194; and Analogy, 231, 229, 234, 254 ; and Inference, 216; principle required for, 213, 245, 287, 288, 290; deductive consistency, 110, 108 ; deductive argument, kinds of, 242; dangers of, 286, 287. Definition, consists in exclusion, 39, 93 ; limits of, 140; per genus et differentiam, 108 ; ordinary, best, and special, 125, 127, 137 ; as remedy for unreal assertion, 119, 127, 134; difficulties of, 124, 127, 133; ch-cular, 123, 142 ; ignotum per ignotius, 142 ; definitions as postulates, 122. Demonstration, as an ideal, 301. 195, 232 ; how far conclusive, 205; and Keal proof, 203; im- mediate and mediate, 95, 208 ; demonstrative arguments rare, 209. De Morgan, 92, 93, 130, 150, ] 59, 180, 193, 194, 251. Denial, 64, 68, 223, 243 ; exceptive, 68, 249. Denotation, 107. Dependence, 63, 74. Descriptive proposition, 54, 83. Dictum de Omni, 301. Difference, 108, 135, 255, 281, 294, 302, 330, 341 ; power of seeing, 256, 193, 330; essential, 247, 248, 356; indistinct, 246; as- sertion of, 68, 246 ; points of, 69, 228, 246; neglect of, 108, 254, 256, 270, 293 ; method of, 345, 277, 281, 339, 352 ; distinc- tion by point of, 246, 241. Dilution of Fallacy, 130, 196. Disbelief and unbelief, 326, 154. Discovery. See Inference. Disjunctive proposition, special danger of, 92. Disproof, and absence of proof, 151, 165 ; as means to proof, 113; exceptive, 249, 353, 241, 242; frustration of, 149, 310: use of syllogistic moods in, 243, 248 ; easier than proof, 250, 275, 279 ; under Method of Residues, 348. 368 INDEX. Distinction bv point of difference, 246, 241. Division, line of, 133, 39, 93, 106, 124. Doubt, assertion of, 153. E. Efficacy in causation, 858. Elements of an event, 237, 272, 340, 348. See also Analysis. Elimination of Accident, 274, 351, 270, 340. Ellijosis in expression, 189, 210, 260. Empirical law, 285, 286, 357; proof, 234, 19, 204, 212, 215, 217 ; methods, 277, 339. Enumeratio simplex, 270, 352. Epigram, 45, 129, 132. Error, reduction to minimum, 117; psychology of, 14, 22. Essence, and accident, 83, 293, 335, 336 note, 338; essential resemblance, 229, 64, 253, 254 ; ditto asserted in every analogical argument, 266 ; essential dif- ference, 247, 248, 356; essential elements of an event, 237, 272, 340, 348 ; essential and acci- dental propositions, 42, 125. Establishment by testing, 37, 39, 249. Etymology, use and abuse of, 37, 105, 190. Events, as abstractions, 333 ; ana- lysis of, 237, 272, 340, 348. Evidence, 21, 148 ; varies in strength, 40, 308, 311, 328; relevancy of, 101, 111, 182; hearsay, 148, 221 ; circumstan- tial, 221, 224; aid of special knowledge in judging, 22, 25, 26, 310. Example, argument by, 224, 220, 252. Exception, and rule, 36, 249, 273, 271, 279. Exceptive denial, 68 ; disproof, 249, 353, 241, 242. Excluded Middle, law of, 185, 105, 106. Exclusion and definition, 39, 93. Expei'imental (inductive, or empi- rical) Methods, general discus- sion of, 277 ; in detail, 339 ; as means of discovering exceptions, 274 ; as shifting burden of proof, 277; as ideals, 282, 310; re- ducible to two, 281, 339; un- satisfactoriness of, 282, 339 ; fundamental resemblance of all, 282 ; further evidence required in, 279, 351 ; experiment, pre- cautions in, 277, 309, 352. Explanation, the counterpart of^ Proof, 111 ; assumptions required for, 13, 272, 302 ; and reduction to law, 74 ; limits of, 128, 142 ; the 'best,' 250, 271, 272; ex- planatorv propositions, 83, 123,. 219. F. Fact, and law, 66, 61, 224, 219, 215 ; and theory, 161, 207, 225, 279, 76, 157, 213, 306; con- gruent, 219, 224, 215, 279. Factor overlooked, 201, 181, 252, 278. Fair presumptions, 158, 94. Faith and hesitation, 162, 285, 314, 331. Fallacy, and Sophism, 9 ; study of, 8, 22; real and verbal, 214, 204; avoidance, detection, and con- viction of, 22, 23, 31, 118, 200, 287, 291, 298; classification of, 170, 171, 176; dilution of, 130, 196 ; various senses of, 172 ; may be due to several causes, 170, 289. Fluctuation of belief, 120, 140. Formal adequacy of Reason, 26, 111, 102, 300. INDEX. ;gi) Fowler, Professor, 237, 340, 341, 34-3, 344, 347, 350. Further assertion implied hv The- sis and Eeason, 26, 27, 99, 114, 2b8, 300. G. Gaps in reasoning, 114, 210, 310, 311, 326. Generalisation, and abstraction, 72, 333; attack on, 279; rests on neglect of difference, 254, 272 ; and exception, 273, 279 ; implied in concrete proposition, 76; danger of, 270, 256. See also Law. General Names, use of, 107, 190; and symbols, 96; and definition, 124, 133, 141. (ienus, and Differentia, 108, 135, 255, 281, 294, 302, 329, 344; summum, 141. Grammar, and Logic, 15, 57, 65, 73, 183,221, 223; and Language, 4, 64, 66, 69, 73, 97, 183. Goal of an assertion, 54. Guesswork, employment of, in de- tecting Fallacy,*'l69, 218. Guidance of reasoning, 17. H. Hamilton, Sir W., 18, 42. Hearsay evidence, 148, 221. Hesitation, 162, 285, 258, 314, 331. Hypothesis, 164, 215, 271, 283, 285 ; hypothetical proposition, 67, 73 ; hypothetical argument, 221. I. Identity, law of, 105, 106, 109, 122 ; of cause and effect, 357 ; identical propositions, 42. Ignorance, profession of, 154, 156. Ljnoratio elenclti, 182, 121, 150 note, 177, 178, 197 ; finer shades of, 189. Icjnotumpev ignotiiis, 142. illicit process, 173, 223. Illusion, 181, 207, 322. Immediacy of sequence, 281. Immediate inference, 95, 208. Implication, and Logic, 21, 25, 107; and Indication, 60. See oho Meaning, and Consistency. Import of propositions, four views of, 53. Impossihile, diictio per, 174 note, 353. Inconceivability of opposite, 285. Inconsistency. See Self-contradic- tion. Indication, the most general rela- tion, 59; and sign, 79, 107, 113, 239, 245, 301 : and names, 107 ; contrasted with implication, 60 ; chief difficulty of the name, 61 ; abstract and concrete, 61, 62 ; incomplete, 80, 268 ; lasv of counter, 84; in concrete propo- sition, 61; in induction, 214, 309 ; time-element in, 96 ; of Thesis by Reason, 99, 204, 211, 244, 310, 329 ; and causation, 79, 82, 268, 356; and meaning, 60, 63, 107. Indistinct difference, 246; resem- blance, 226. Individuality, and differentia, 254. Induction, and Logic, 276, 330 ; and neglect of difference, 270; contrasted with deduction, 212, 177, 204, 330; dangers of; 267, 270 ; and incompleteness of Principle, 214, 308, 309 ; induc- tive inference and proof, 215, 234, 272 ; inductive methods, 277, 339 ; and unknown antece- dents, 270, 279, 284, 349, 351. Inference, ambiguities of the name, 32, 34; and Proof, 17, 31, 68 note, 94, 97, 214, 217, 227, 347, 352; immediate, 95, 208; de- 370 INDEX. pendence on deduction, 21G ; fallacies of, ] 77. Inquiry, stifling of, 154. Instance, contradictory, 250, G9, 271, 275, 283 ; crucial, 235 note. Intention of speaker, 16, 65, 69, 70. Interpretation, and Logic, 16, 21, 183; and counter-indication, 89; of Principle, 103, 109. See also Meaning and Misinterpretation. Interval between self-contradic- tory assertions, 130. Invariable succession, 356, 80. Irrelevant Reason. See Ignoratio elenchi. J. Jevons, Professor, 91, 92, 183, 277, 309, 349. Joint method of Agreement and Difference, 344, 357. Judgment, and Thesis, 41, 97; degrees of completeness in, 41, 97, 325; presumption involved in, 162; reservation of, 150. See also Belief, a^id Proposition. K. Keynes, 96. Knowledge, growth of, 75, 212, 258; need for special, in judg- ing evidence, 22, 25, 26, 310; generality of, 76. See also Be- lief, and Proof. L, Language, and Grammar, 4, 64, 66, 69, 73, 97, 183; Logic limited by, 45, 47, 132, 187, 321; assumptions required for, 13, 46, 106, 134: difficulties of, 133, 136, 189, 259, 264; snares of. 174, 176, 186 ; and hidden differ- ence, 258. Law, in Nature, 14, 71, 81, 285, 272, 302 ; and Fact, 66, 61, 224, 219, 215 ; and explanation, 74 ; and counteraction, 82, 270, 342, 358; and contradictory instance, 249, 275, 283, 69, 271; empirical, 285, 286, 357 : chance and ten- dency, 81, 268 ; reference to in concrete propositions, 76 ; re- quired for all rationalisation, 111, 213, 255. See also Principle, Generalisation, Abstract pro- position. Laws of Thought. See Axioms of Consistency. Line of division, 133, 39, 93, 106^ 124. Logic, and Philosophy, 2, 3, 12, 46, 142, 313, 323; and Common Sense, 2, 4, 5, 77, 98, 160, 169, 317, 321, 323; and Physical Science, 2, 3 ; and Grammar, 15, 57, 65, 73, 183, 221, 223; and Ehetoric, 15, 8, 23, 180, 200, 259, 263; and Psychology, 14, 22, 41, 97, 120; and Scepticism, 20, 284, 314, 326, 128; and im- plication, 21, 25, 107 ; practical purpose of, 2, 3, 6, 8, 10, 13, 17, 112, 117, 276, 326, 331 ; disputed points of, 7, 8, 11 ; clumsiness of, 9, 320; negative character of, 19, 327 ; xoons asinorum of, 81, 303 ; province of, 12 ; limita- tions of, 10, 13, 25, 26, 38, 102, 117 ; objections to, 7, 314 ; in- ductive and deductive, 19, 110 note, 212, 276, 330; logical dependence, 63 ; logical out- come, 103; logical necessity, 207. M. MacColl, H., 60, 84, 101. Margin, doubtful, in names, 134. Material obverse, 89. INDEX. 371 Maxims of Consistency. See Axioms. Meaning, laAvs of interpretation, 21 ; agreement postulated as starting-point, 16, 57, 65 ; and indication, 60, 63, 107; and gathered associations, 184, 191, 199 ; and definition, 39, 107, 141, 185 note ; best, usual, and special, of a name, 125, 127, 137; part forgotten, 126, 292; gradual change in, 184, 189 ; re- lative to standard, 191 ; of Thesis contained in Reason, 26, 204 ; meaningless term, fallacy of, 47, 138 ; meaningless questions, 45, 46, 47, 131, 185 note. Mediate inference, 95, 208. Metaphor, as argument, 179, 259, 265 ; in names, 189 ; change of, 261 ; difference from analogy, 198 note, 259; inclination to- wards, 257, 259, 265. Metaphysics. See Philosophv. Middle term, 222, 229, 234^ 239, 244, 290, 304, 305 ; as sign, 234, 239 ; undistributed, 173, 222. Mill, J. S., 15, 19, 53, 107, 170, 172, 174, 177, 230, 274, 277, 310, 339, 341, 342, 344, 345, 347, 348. Miracles, 157. Misinterpretation, 182, 169, 173; by opponent, 188; and law of Excluded Middle, 185; of motives, 171, 175 ; accusation of, 183 ; avoidance of, 186. See also Meaning, and Interpreta- tion. Modi ponens, tollens, etc., 240, 241. Moods of Syllogism, 223, 240, 355. Mysteiy, belief in, 48, 100, 315. N. Names, twofold use of, 107 ; as labels, 109, 245; loose applica- tion of, 83, 124, 133, 184, 189; question-begging, 198, 264 ; negative, 65, 71, 93 note; gathered associations of, 184, 191, 199; ancestors' mistakes ill apjDlying, 187. See aJso Mean. ing a??ci Metaphor. Nameable things, 13, 53. Nature, continuity of, 133, 336, 14 ; explanation of, 302, 272, 13 ; natural laws, 14, 61, 71, 81, 285, 272, 302. Necessary truth, 207. Needs of Practice, 4, 13, 20, 38^ 154, 162, 169, 331, 336. Negation, in propositions, 64, 6S, 223, 243; in names, 65, 71, 03 note. Negative, proof of, 250, 346. Newman, Cardinal, 66, 296. No7i Sequitur, 168, 179. Nota Nota;, 245, 301. Number of confirmatory facts, 279,. 281, 343. O. Objections, to an assertion, 24; to an argument, 178 ; to Logic, 7t 314. Observation. See Experimental Methods. Obstruction, of argument, 50, 128, 167. Obverse, material, 89. Opinion, prevailing, 159 ; and be- lief, 162, 151, 98, 325. Opponent, misinterpretation bv, 188. Opposite, inconceivability of, 285. Over-generalisation, 177, 256, 270, 293. Paradox, 45, 130. Parallel cases, 104, 110, 219, 226, 233. Paralogism, 173. Particular propositions, 68, IXDEX. Fetitio Pvincipii 193, 177, 181 j note, 195, 198, 206, 260, 264; j and deduction, 191; and tauto- j logy, 120 ; in names, 198, 261. Philology, and unsusi^ected differ- ence, 258. Philosophy, and Logic, 46, 2, 3, 12, j 14, 142, 213, 323. Platitude, 120, 198. Plurality of causes, 80, 270, 342, 351. Point at issue. See Ignoratio Elenchi. Points, of difference, 69, 228, 246 ; , distinction by, 246, 241 ; of re- semblance, 228, 253, 300. j Pons asinorum of Logic, 84, 303. j Positive assertion. See Affirmation. | Post hoc, fallacy, 270, 346, 352. j Postulates. See Assumptions. | Practical certainty, 38, 94, 205, \ 308. I Practice, needs of, 4, 13, 20, 38, I 154, 162, 169, 331, 336. Precautions, in experiment, 277, 1 i-s 309, 352. I Predicate, 54. Predication-view of propositions, 53, 54, 231. Prediction, and explanation, 13, 74, | 219, 272, 302; liredictive pro- positions, 83. I Premisses, 32, 100; major and minor, 113, 173, 300. Presence and absence, specially defined, 85. Presumption, fair, 158, 94 ; in- volved in all judgment, 162 ; of ^ weakness, 165; raising of, 209, j 263. Prevailing opinion, 159. ' Principle, as required for Proof, 111, 113, 204, 208, 213, 287, 309, 329 ; interpretation of, 103, 109 ; formation of, 104; extent of, 304, 309, 329 ; in inductive proof, 213, 214, 226, 267, 309; in deductive proof, 213, 245, 287, 288, 290. Probability, 274, 133, 351. Proof, in general, 99, 97, 111, 113, 214, 329 ; meaning and aims of, 31; etymological meaning of, 36; subject-matter of, 41; and testing, 35 ; and explanation, 111 ; and resistance to attack, 37; and inference, 17, 31, 68 note, 97, 214, 217, 347, 352 ; and disproof, 113, 151, 165, 250, 275, 279; and principle. 111, 113, 204, 208, 213, 287, 309, 329; degrees of, 40, 308, 311, 328; unavoidable incompleteness of, 38, 40; need for, 143, 42, 149, 165; demand for, 165; conclu- sive, 220, 40, 114, 207, 275, 285, 300, 328 ; empirical and deduc- tive, 111, 113, 204, 212, 213, 214; 215, 217, 272, 300; circum- stantial, 221, 224 ; by sign, 244 ; real, and demonstration, 203 ; of axioms, 343 note, 349 ; of nega- tive, 250. 346; concerned with complete assertion only, 41 ; ex- cuses for absence of, 166 ; often not demanded, 50, 165. Propositions, Subject, Predicate, and Copula of, 51 ; four views of the import of, 53 ; best excuse for predication-view, 54 ; start- ing-point and goal of, 54, 55 ; real and unreal, 41 ; unreal and verbal, 42 ; apparently unreal, 48; tautologous, essential or identical, 43 ; synthetical and analytical, 42 note ; self-contra- dictory, 44 ; simple and complex, 56 ; argument as comjDlex pro- position, 100, 58, 64,310; affirma- tive and negative, 64; abstract and concrete, 66 ; abstract-con- crete, 77, 276; notienal and real, 66 note ; exceptive denial, and assertion of difference, 68 ; particular, 68; categorical and hypothetical, 73, 67 ; of succes- sion, 79 ; naming, classifying, or descriptive, 54, 79, 83 ; explana- tory, 83, 123, 219; predictive. INDEX. io 83 ; reciprocal, 89, 88 ; disjunc- tive, 92. Proverbs, employment of, 26G. Province of Loc^ic, 12. Provisional beliefs, 94, 164, 316. PsjcliologT, and Logic, 14, 22, 41, 97, 120." Q. Question-begging. See Petitio prmcipii. Questions, meaningless, 45, 46, 47, 131, 185 note ; verbal, 144. E. Eationalisation, of thesis, 111, 213, 255, 288, 307. Eead, Carveth, 53, 80, 342. Eeality, in propositions, 41, 42, 204, 214 ; degrees of, 146. Eeason given, and Thesis, relation between, 99, 26, 204, 211, 244, 288, 300, 310, 329; material truth of, 25, 26, 101, 195 ; formal adequacy of, 26, 102, 111, 300 ; real and verbal, 204; reasons and causes of belief, 33. Eeasoning, and rationalisation, 111, 213, 255, 288, 307; guidance of, 17 ; direct and reflective, 18, 31 ; chain of, 210 ; gaps in, 114, 210, 310, 311, 326. Eeciprocal proposition, 89 and note, 88 ; acceptance as equiva- lent, 91, 173, 288, 290. Reductio ad ahsurdum, 298, 174, 251, 286, 307, 326, 328. Eeflective reasoning, 18, 31. Eelation-view of propositions, 53. Eelevancy of Eeason, 101, 111, 182, 191. See also Ignoratio Elenchi. Eelevant fact overlooked, 181, 252, 278. Eesemblance, striking, 227, 256, 261 : essential, 229, 64, 253, 254, 266 ; neglect of, 108, 257, 293 ; indistinct, 226; points of, 228, 253, 300; degrees of, 227; of circumstances, 272. Eeservation of judgment, 150. Eesidues, Method of, 347, 339, 352 ; disproof by, 348. Eesistance to attack, 37, 38, 249, 273. Ehetoric, 15, 8, 23, 180, 200, 259, 263. Eival theories. See Alternative. Eobertson, Professor Croom, 84 note. Scepticism, 20, 128, 285, 314, 315, 326 ; as an artifice, 153, 326. Science, physical, and Logic, 2, 3. Self-contradiction, 103, 129, 44, 317, 328; contrasted with tau- tology, 129, 130 ; and epigram, 129, 45, 132; requires dilution, to be dangerous, 130; interval between contradictory asser- tions, 131; in form of question, 131; opposite causes of, 132 ; and difficulties of language (sorites), 133; verbal, not real, 139, 140. Self-deception, 284, 319. Self-evident truths, 46, 149, 207, 285. Senses, deception of, 207. Sequence. See Dependence, Suc- cession, and. Causation. Sign, and indication, 62, 74, 79, 90, 107, 113, 239, 245, 301 ; and symptom, 63, 79, 270, 308; and naming, 109 ; and middle term, 234, 239; by presence and absence, 86 ; a special sense of the name, 79 ; argument by, 239, 220, 286 ; proof by, 244, 240. Similarity. See Eesemblance. Simplex enumeratio, 270, 352. Simpliciter et secundum quid, 293, 294. 374 INDEX. Sole cause, 269, 334. Sorites, fallacy, 133. Special circumstances, influence of, 67, 68, 72, 282. Special knowledge, required in judging evidence, 22, 25, 26, 310. Species, 255. Spencer, H., 20, 47, 53, 130, 190, 156. Starting-point of an assertion, 54. Stephen, Sir Jas., 150, 159. Subject, of a proiDOsition, pro- visionally defined, 42 ; and " things," 51 ; two in a proposi- tion, 52. Substitution of Similars, 349 note. Succession, and co-existence, 78, 96, 278 note, 281, 325, 337; in- variable, 356, 80 ; immediacy of, 281 ; incomplete indication of, 79. Suggestive assertion, 162, 188, 151, 227, 259, 252, 325. Sully, J., 14, 181. Summiim genus, 141. Superficiality of view, 201. Syllogism, uses of, 114, 181 note, 289, 300, 304 ; Axiom of, 301 ; moods of, 223, 240, 355; and proof, 111, 113, 212, 204, 207, 254, 300 ; syllogistic fallacy, 209, 288, 289. Symbols, danger of, 91, 96 ; need of, 322, 327; explanation of those here employed : — S, 51 ; J, 51; 5, 54; -^, 62; -f^, 68; ^,68; T and R, 99. Synthesis, 259; synthetical pro- position, 42 note. T. Tautology, 120, 43, 204 ; causes of, 121 ; resemblance to Petitio principii, 120; chief forms of, 123 ; harmless when used as Postulate, 122 ; finer shades of, 124; Bain's view of verbal pre- dication, 125 ; dependence on ex- tent of remembrance of mean- ing, 126, 292 ; remedy for, 127 ; contrast with self-contradiction, 129, 130. Tendency, 81, 268. Tentative assertion. See Sugges- tive. Terms, 51, and see Names ; mean- ingless, 138, 47; abstract and concrete, 72. Test. See Proof and Exception. Testimony, 221, 225. Theorv, 219, 252, 271; and fact, 76, 157, 161, 213, 326, 207, 225. 279 ; and axiom, 207, 285 ; alter- native theories, 39, 40, 164, 177, 239, 270, 275, 276, 310, 311, 328, 333. Thesis, defined, 18, 41 ; and con- clusion, 18, 150 ; and suggestion, 122, 325 ; and judgment, 41, 97 ; and Eeason combined, 26, 27, 99, 114, 288, 300 ; indicated by Eeason, 99, 204, 211, 244, 310, 329. ' Things,' 13, 51, 52. Truth, accepted, 26, 102, 205; necessary, 207 ; self-evident, 46, 149, 207, 285; material, of Eeason, 25, 26, 101, 195. Tyndall, Professor, 158. Types of argument, 202. U. Ultimate questions, oiu' neglect of^ 46, 3, 12, 142, 171. Unbelief and disbelief, 326, 154. Unconditionality, 358. Undistributed Middle, 173, 222. Uniformity, 14; and see Law. Universe of discourse, 93 note. Universal. See Abstract proposi- tion. Unknown Antecedents, danger of, in induction, 270, 279, 284, 349, 351. INDEX. 375 Unreal propositions, defined, 42; remedy for, 119, 127, 134; degrees of unreality, 146. . 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