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Thoae too large to be entirely included in one expoaura are filmed beginning in the upper left hand comer, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Lea cartea, planches, tableeux, etc., peuvent Atre filmte A des taux de rMuction diffirents. Lorsque le document est trop grand pour Atre reproduit en un seul ciichA, il est fiimA A partir da i'angia supArieur gauche, de gauche it droite. et de haut an baa, an prenant le nombre d'Images nAcessalre. lies diagrammes suivants illustrant la mAthoda. 1 2 3 1 2 3 4 5 6 'f^^V ^1^; - * '"■'' -m.- '^^ w ^; ) '" 1*» •V 5-fS -^ %T' V :'C' '^.-1 ■^4* ^ ^'^ ■^^ • ' ^ V EASY LESSONS ON REASONING. REPRINTED FROM "THE SATURDAY MAGAZINE." NEW EDITION. TORONTO: COPP, CLARK & CO. ib72. St ai 01 01 o t i 1 . ^ PREFACE. The gubject treated of in the following pages is one which has not usually been introduced into the course of elementary studies for young persons of all classes. It is supposed by some, that the difference between a better and a worse reasoner depends either wholly on natural ability ^ or on that combined with practice, or on each man's greater or less proficiency in the tuhjects he is treating of. And others again consider a systematic study of the prin- ciples of Reasoning as suitable only to a few persons of rare endowments, and of a peculiar turn of mind ; and to those only in an advanced stage of their education. That this branch of study is requisite for all, and is attainable by all, and presents not, necessarily, any greater difficulties than the rudiments of Arithmetic, Geometry, and Grammar, — all this cannot be so well evinced in any other way as by experi- ment. If the perusal of these Lessons, or of the half of them, fail to satisfy on this point any tolerably attentive reader, it is not likely he would be convinced by any distinct argument to the same effect that could be offered. The work has very little claim to novelty, except as to tho limplicity and familiarity of its form. But without making any IV PREFACE- diacoverif, strictly so called, of anything previously altogether unknown, it is possible— since ''discovery" is a relative word — to be, practically a discoverer, by bringing within the reach of thousands some important branch of knowledge of which they would otherwise have remained destitute all their livea. And in regard to the present aubjeot, a familiar introduction to the study is precisely what has been hitherto wanting. The existing treatises upon it may be compared to ships well freighted, but which can only unlade at a few wharfs, care- fully constructed, in advantageous situations. The want is of small boats drawing very little water, which can carry ashore small parcel i of the .^argo on ev :ry part of the coast, and run up into every little creek. Should the attempt to supply this deficiency prove as ?\ic- cessful, as there is reason, from the trial that has been already made (in the Saturday Magazine)y to hope, an addi- tion by no means unimportant will have been made to the ordinary course of elementary education. To frame, indeed, a system of rules that should equalize persons of all varieties of capacity, would be a project no less ' chimerical in this than in other departments of learning. But it wouhl certainly be a great point gained, if all persons were taught to exercise the reasoning faculty, as well as the natural capacity of each would permit; for there is good reason to suspect, that, in this point, men fail quite as often from want of attention, and of systematic cultivation of their powers, as from natural deficiency, .xud it is at least worth trying the experiment, whether all may not be, in some degree, trained in the right exercise of a ficulty which all in some degree, possess, and which all mitst^ more or less, exercise, whether they exercise it well or ill. It was at one time contemplated to subjoin an Index of the technical terms, with brief definitions of them, and references to the Lessons and Sections. But, on second thoughts, it has been judged best to omit this, and to recommend each student PREFACE. V to draw up such an index for himself. It is for stiuUnU^ strictly so called, — that is, persons employed in acquiring an elementary knowledge of the subject, — that the work i;-i chiefly designed : and for these no exercise could be devised more calculated to facihtate their study than that of carefully com- piling an Index, and also expanding the Table of Contents, so as to give a brief summary of the matter of each Lesson. And this being the case, it would not bo any real saving of labor to the learner, to place before him such an Index and Table of Contents already drawn up. It may be worth while to sugj:,est to the Teacher to put before his pupils, previously to their reading each Lesson, Bome questions pertaining to the matcer of it, requiring of them answers, oral or written, the best they can think of without consulting the book. Next let them read the Lessons, having other questions, such as may lead to any needful expla- nations, put before them as they proceed. And afterwards let them be examined (introducing numerous in the )ns,) to terms ; d other lar, are remem- g much :ending aing or ^uman ent on truths Dwever '. One bodiiy- uld in- t once. , or to )rofess to lay down a system of rules to teach all these at once^ anfl also the business of a shipwright, and a musician, and a watchmaker, and everything else that is done by means of the bodily organs, you would teach, in reality, nothing at all. And so it is on all subjects. It is better to undertake even a little, that it is possible to accomplish, than to make splendid professions, which can only lead to dis- appointment. After all, indeed, it cannot be expected, that, in Reason- ing, any more than in other mental exercises, men of very unequal degrees of intelligence should be brought to the same level. Nor is it to be expected, that men will always bo brouifht to an agreement in their conclusions. Dif- ferent men will have received different information re- specting facts ; or will be various^ biassed, more or less, by their early prejudices, their interests, or their feelings. But still, there is something gained, if they are taught in respect of the lleasoning-process itself, how to proceed rightly and to express themselves clearly ; and if when they do not agree, they can be bro\ight at least to under- stand wherein tliey differ, and co state distinctly, what is "the point at issue" (as it is called) between them; that is, what is the real question to be decided. And it is just so, in the case of Arithmetic also. Two persons may differ in their statements of an Account, from their scttinf? out with some difference in the nuinhers each puts down;— in the Items (as it is called) of the Account. And no rules of Arithmetic can prevent such a difference as this. But it is something gained if they are guarded (as arithmetical rules do guard us) against differences arising out of errc rs in the calculation itself. LESSON ir. § 1. We have said that in all subjects, and on all occa- sions, the Reasoning-process is in itself the same Whether you are occupied in refuting an opponent, or in conveying 18 ANALYTICAL INTRODUCTION. [Part I. '•^^ ":i 'h instruction, or in satisfying your own mind on any point, — and again, whatever kind of subject-matter it is that you ar© engaged on, in all cases, as far as you are (in the strict sense of the word) reasoning, — that is, employing Argument — it is one and the same process (as far as it is correctly conducted) that is going on in your own mind. And what this process is, must be the next point to be inquired into. Although (as has been said) all men do occasionally reason, they are often, at the time, as unconscious of it as of the circulation of their blood, and of the various other pro- cesses that may be going on within the body. And even when they do, knowingly and designedly, use arguments, or are listening to those of another, they will often be as much at a loss to explain why one argument appears to them strong, and another less strong, and another utterly worthless, as if the whole were merely a matter of taste ; like their preference of one prospect, or one piece of music \o another. In order, then, to obtain correct rules for forming a judgment on this subject, and clear expressions for explain- ing such judgment to others, it is necessary to analyse, — as it is called, — that is, take to pieces) the Reasoning- process. And for that purpose, we should begin by examining the most plain, short, and simple arguments, and enquiring on what it is that their validity [or con- clusiveness] depends; examining also, some of those apparent-arguments which are not valid, and therefore not, in reality, arguments at all ; though they are often passed off for them, as counterfeit coin is for genuine. § 2. You will perceive, on examination, that what is called a '* Conclusion," — that is, a proposition proved by Argument, — is drawn, in reality, from two other Proposi- tions. And these are called its "Premises;" from their being (in natural order) ^^premised" or put before it. At first sight, indeed, some might suppose that a Conclusion may follow from one Pi-emise alone. For it happens, oftener than not, that only one is expressed. But in this case, there is always another Premise under- stood, and which is suppressed, from its being supposed to be fuU^ admitted. ■:*HJ«S»m-.l#g(!*S LoMson ii.] tiir rkasoxtng-process. 19 Thfit this is the case, may easily be made evident by sup[>osin^ that suppressed Pi-eniiac to be den'ml ; wliicb will at one destroy the force of the Argument. For instance, if any one, from ])erceiving that "the World exhibits marks of design," infers [or concludes] that " it had an intelligent Maker," he will easily jKirceive, on reflection, that he must have had in his mind another Premise also, namely, thiit "whatever exhibits marks of design had an intelligent maker :" since if this last pro- position were denied^ the other would prove nothing. It is tiiie, that in some cases one proposition implies iinother by the very signification of the words, to every one that understands those words ; as "negroes are men ; therefore they are rational-beings," now, "rational-being" is implied in the very name "man." And such examples as this have led some pp-ople uito tlie idea that we reason — or that we may reason — from a single Premise. But take such a case as this; some fossil-animal is discovered, which Naturalists conclude to have been a "ruminant," from its "having horns on the skull." Now the laborers who dug up the skeleton could not draw this inference, supposing they were ignorant of the general law, that "all horned animals are ruminant :" — and they might be thus ignorant, though using the name "horned animal," in the same sense as the Naturalist : for the name itself does not imply " ruminant," as a part of its signification ; and again, a Naturalist at a distance, who knew the general law, but who had heard only an imperfect account of the skeleton, and did not know whether it was horned or not, would be equally unable to draw the inference. In all cases of what is properly called "Argument," there must be two pre- mises assumed, whether they are both expressed or not. § 3. Such an argument as the above, when all the three propositions are stated at full length, and in their natural order, is called a "Syllogism." And this is the form in which all correct reasoning, on whatever subject, may be exhibited. When one of the Premises is supjiressed [or under- stood], which, for brevity's sake, is usually the case, the argument is called, in technical language, an " Enthy- meme;" a name derived from the Greek, and denoting it 20 ANALYTICAL INTRODUCTION. [Part I. k that tliero is sometliiiii^ \oSi out, which is to be supposed [or understood] as l)eni/jf woll-kuowii. It is to bo observed, that, whori aii argument, statcnl in this hast form, is met by opponents, their objection will sometimes lie against the assertion itself that is made ; Bometimes, against its force as an argument. They will say either, "I deny wliat you assume," or "I admit, indeed, what you say, but I deny that it proves your conclusion." For instance, in the example above, an atheist may be conceived either denying* that the World does exhibit marks of design, or again, denyingt that it follows from thence that it must have had an intelligent Maker. Now you are to observe, that these are not in reality objections of different kinds. The only difference is, that, in the one case, the expressed Premise is denied ; in the other, the suppressed Premise. For the force as an argu- men, of either Premise, depends on the other Premise. If either be denied, the other proves nothing. If both be admitted, the Conclusion regularly drawn from them, must be admitted. § 4. It makes no difference in respect of the sense of an argument, whether the Conclusion be placed last or first ; provided you do but clearly mark out what is the Conclusion. When it is placed last (which is accounted the natural order), it is designated by one of tht)So conjunctions called ^'illative" such as "therefore," — "thence," — "con- sequently." When the Conclusion is put first, the Premise is usually called the "Reason;" and this is designated (whether it come last or first) by one of the conjunctions called *^causal," such as "since," — "because," &c. And here it is to be observed, that each of these sets of conjunctions have also another sense; beiug used to denote, respectively, sometimes " Premise and Conclu- sion," — sometimes " Cause and Effect." And much error and perplexity have often been occasioned by not attend- ing to this distinction. * As many of the ancient atheists did. t An luoiit cf the modcru atheists do. Lesson ii.] the reason ino-procesb. 21 \Vlion I say *'thia ground in rich; becaiiso the troos oii it arc ilouriHliiiig;" or again, when I exprosH tlio same sense in a ditterent form, saying, "tlio trees on tliis ground are flourishing, and tlieretbro it nuist bo rich," it is plain that I am emph^ying those conjunctions to denota merely the connexluii of J^remise and Conclusion ; or (in other words) I am implying that the one m.ay ho inferred from the other. For it is evident, that the flourishing of the trees is not the cause of the ground's fertility, Init on!/ i\iQ cause of my believing it. The richness of tho soil Jollows as an inference from the luxuriance of tho trees ; which luxuriance follows as an effect [or, natural consequence] from tho richness of the soil. But, if again, I say, *' the trees flourish because the ground is rich," or (which is the same in sense) "the ground is rich, and consequently [or therefore] the trees flourish,' I am using the very same conjunction in a dif- ferent sense; namely, to denote, tlie Connexion of Cause and Effect. For in this case, the luxuriance of tho trees being a thing evident to the eye, would not need to be proved', and every one would understand that I was only accounting for it. § 5. But again, there are many cases also in which the Cause is employed as an Argument, to prove the existence of its effect. So that the Conclusion which follows, as an Inference, from the Premise is also an Effect which follows naturally from that same Premise as its Cause. This is the kind of argument which is chiefly employed when we are reasoning about the future, : as for instance when, from favorable or unfavorable weather, any ono infers that the crops are likely to be abundant, or to be scanty. In such cases, the Cause and the Reason [or Proof] coin- cide ; the favorable weather being at once the cause of the good harvest, and the cause of our expecting it. And this circumstance contributes to men's often con- founding together "Cause" and — what is strictly called — "Reason;" and to their overlooking the different senses of such words as "therefore," "thence," "consequently,'* &c., and again, of such words as "because," "inasmuch as/ (kc, and also, of the words "follow,'' "consequence," s >! I 22 ANALYTICAL INTRODUCTION. [Part I. and Hevoral others ; which have all of thorn that double meaning which has just been explained. J.li^Su^' 111. § 1. In such an iirgunient as that in the example above given, (in § 2, Lesson ii.) it is clearly impossible for any one who admits both Promises to avoid admitting the Conclusion. If you admit that " Wliatover exhibits marks of design had an intelligent Maker," and also that *' the world exliibits marks of design," you cannot escape the Conclusion that "the world had an intelligent Maker." Or again, if I say "All animals with horns on the head are ruminant; the Elk has horns on the head ; therefore it is ruminant;" it is impossible to concei\'c any one's doubting the truth of the Conclusion, supposing he does but allow the truth of each Promise. A man may perhaps deny, or doubt, and require proof, that all animals thus horned do ruminate. Nay it is conceivable that ho may even not clearly understand what *Wumhiant,^^ means, or he may have never heard of an *^Elk;'^ but still it will not be the less clear to him that supposing these Premises granted, the Conclusion must be admitted. And even if you suppose a case whore one or both of the Premises shall be manifestly false and absurd, this will not alter the concltisiveness of the Reasoning; though the conclusion itself may perhaps be absurd also. For instance, "All the Ape-tribe are originally descended from Reptiles or insects : Mankind are of the Ape-tribe ; there- fore Mankind are originally descended from Reptiles or Insects ; here, every ono* would perceive the falsity of all three of these propositions. But it is not the less true that the conclusion follows from those premises, and that •y they were true, it would be true also. § 2. But it oftens happen that there will be a seeming * Except certain French Naturalists. LesBon iii.] FALLACIES. 01 connoxioii of certain in'omisos with a coiicluHion which does not really follow fi\)iii them, although, to the inat- tentive or iinHkiliul, the argument will a|)[)ear to be valid. And this is most especially lik(^ly to occur when such a seeming argument [or Fallacy] is dressed up in a great quantity of line-sounding words, and is accompanied witli much vehemence of assertion, and perhaps witli expres- sions of contempt for anyone who presumes to entertain a doubt on the matter. In a long dechimatory speech, especially, it will often happen that almost any proposi- tion at all will be passed off as a proof of any other that does but contain some of the same words, by means of strenuous assurances that the proof is complete. Sometimes again, sound arguments will be distrusted as fallacious; especially if they are not clearly expressed; and the more if the conclusions are such as men are not willing to admit. And frequently also, when there really is no sound argument, the reader or hearer, though he believes or suspects that there is some fallacy, does not know how to detect and explain it. § 3. Suppose, for instance, such seeming-arguments as the following to be proposed: — (1.) *' Every criminal is deserving of punishment ; this man is not a criminal ; therefore he is not deserving of punishment :" or again, (2.) "All wise rulers endeavor to civilize the People; Alfred endeavored to civilize the People; therefore he was a wise ruler." There are perhaps some few persons who would not perceive any fallacy in such arguments, even when thus briefly and distinctly stated. And there are probably many who would fail to perceive such a fallacy, if the arguments were enveloped in a cloud of words, and conveyed at great length, in a style of vague indistinct declamation; especially if the conclusions were such as they were disposed to admit. And others again, might perceive, indeed, that there is a fallacy, but might be at a loss to explain and expose it. Now the above examples exactly correspond respec- tively, with the following; in which the absurdity is manifest : — (1.) " Every tree is a vegetable ; grass is not a tree; therefore it is not a vegetable;" and (2.) "all vA t 24 ANALYTICAL INTRODUCTION. [Pai-t I, vegetables grow ; an animal gi'ows ; therefore it is a vegetable." These last examples, I say, correspond exactly (considered in respect of the reasoning) with the former ones ; the conclusions of which, however true, no more follow from the premises than those of the last. This way of exposing a fallacy by bringing forward a similar one where a manifestly absurd conclusion professes to be drawn from premises that are true, is one which we may often f nd it needful to employ when addressing persons who have no knowledge of technical rules ; and to whom, consequently, we could not speak so as to be understood concerning the principles of Reasoning. But it is evidently the most conveiiient, the shoiijest, and the safest course, to ascertain those principles, and on them to found rules which may be employed as a test in every case that comes before us. And for this pui-pose, it is necessary (as has been above said)to analyse the Keasoning process, as exhibited in some valid argument expressed in its plainest and simplest form. § 4. Let us then examine and analyse such an example as one of those first given: for instance, "Every animal that has horns on the head is ruminant ; the Elk has horns on the head ; therefore the Elk is ruminant." It will easily be seen that the validity [or "conclusiveness;" or "soundness"] of the Argument does not at all depend on our conviction of the truth of either of the Premises ; or even on our understanding the meaning of them. For if we substitute some unmeaning Symbol (such as a letter of the alphabet) which may stand for anything that may be agreed on — for one of the things we are speaking about, the Reasoning remains the same. For instance, suppose we say, (instead of "animal that has horns on the head,") "Every X is ruminant;" "the Elk is X; therefore the Elk is ruminant;" the argument is equally valid. And again, instead of the word "ruminant," let us put the letter "Y:" then the argument "Every X is Y; the Elk is X; therefore the Elk is Y;" would be a valid argument as before. And the same would be the case if you were to put "Z" for "the Elk:" for the syllogism "Every X is Y ; Z Lesson iii.] ARBITRARY SYMBOLS. 25 is X; therefore Z is Y," is completely valid, whatever you suppose the Symbols, X, Y, and Z to stand for. Any one may try the experiment, by substituting for X, Y, and Z, respectively, any words he pleases ; and he will find that if he does but preserve the same form of expres- sion, it will be impossible to admit the truth of the Pre- mises, without admitting also the truth of the ConcluBion. § 5. And it is worth observing here that nothing is so likely to lead to that — very common, though seemingly strange — error, of supposing cirselves to understand distinctly what in reality we understand but very imper- fectly, or not at all, as the w^t of attention to what has been just explained. A man reads — or even writes — many pages perhaps, of an argumentative work, in which one or more of the terms employed convey nothing distinct to his mind: and yet he is liable to overlook this circumstance from finding that he cleanly understands the Arguments. He may be said, in one sense, to understand what he is reading; because he can perfectly follow the train of Reasoning^ itself. But this^ perhaps, he might equally well d:o^ if he were to substitute for one of the wor(^ employed, X, or Z, or any other such unknown Symbol ; as in the examples above. But a man will often confound together, the understand- ing of the Arguments, in themselves, and the uridersta/nding of the words employed, and of the nature of the things those words denote. It appears then that valid Eeasoning, when regularly expressed, has its validity [or conclusiveness] made evident from the mere ybrm of the expression itself, independently of any regard to the sense of the words. § 6. In examining this form, in such an example as that just given, you will observe, that in the first premise (" X is Y,") it is assumed universally of the Cla^ss of things (whatever it may be) which "X" denotes, that " Y" may be affirmed of them: and in the other Premise, "Z is X") that **Z" (whatever it may stand for) is referred to that Class, as comprehended in it. Now it is evident that whatever is said for the whole of a class may be said of anything that is comprehended [or "included," or "oon- B 'i lt(>:i y-t . II 26 ANALYTieAL INTRODUCTION. [Part I. tained,"] in that Class : so that we are thus authorized to say (in the conclusion) that "Z" is "Y." Thus also in the example fii-st given, having assumed iinivei"sally, of the Class of '^Things which exhibit marks of design," that they " had an intelligent maker," and then, in the ether Premise, having referred "The world" to that Class, we conclude that it may be asserted of "The world" that "it had an intelligent maker." And the process is the same when anything is denied of a whole Class. We are equally authorized to deny the same of whatever is comprehended under that Class. For instance, if I say, " No liar is deserving of trust ; this man is a liar ; therefore he is not deserving of trust :" I here deny "deserving of trust," of the whole Class denoted by the word " liar;" and then I refer "this man" to that Class; whence it follows that " deserving of trust" may be denied of him. § 7. This argument also will be as manifestly valid, if (as in the former case) you substitute for the words which nave a known meaning, any undetermined symbols, such as letters of the alphabet. " No X is Y; Z is X; there- fore Z is not Y," is as perfect a syllogism as the other, with the affirmative conclusion. To such a form all valid arguments whatever may be reduced : and accordingly the principle according to which they are constructed, is to be regarded as the Universal Principle of Reasoning. It may be stated, as a general Maxim, thus : " What- ever is said, whether affirmatively, or negatively," [or " whatever is affirmed or denied"] "of a whole Class may be said in like manner," [that is "affirmed in the one case, and denied in the other,"] " of everythii^g compre- hended under that Class." Simple as this principle is, the whole process of Rea- soning is embraced in it. Whenever we establish any Conclusion, — ^that is, show that one thing may allowably be affirmed, or be denied, of another — this is always in reality done by referring that other to some Class of which such affirmation or denial can be made. The longest series of arguments, when fully unfolded, step by step, will be found to consist of nothing but a LesBon iv.] APPARENT-ARGUMENTS. 27 repetition of the same simple operation here described. But this circumstance is apt to be overiooked, on account of the brevity with which we usually express ourselves. A Syllogism, sit ^h as those in the examples above, is seldom given at fall length ; but is usually abridged into an "Enthymeme."* (See Lesson ii. § 3.) And moreover what is called "art a/rgument^^ is very often not one argu- ment, but several compressed together; sometimes into a single sentence. As when one says: "The adaptation of the instinct of suction in young animals to the supply of milk in the parent, and to the properties of the Atmo- sphere as well as other like marks of design, show that the world must have had an intelligent maker." For most mer are excessively impatient of the tedious formality of stating at full length anything that they are already aware of, and could easily understand by a slight hint. LESSON IV. § 1. We have seen that when an argument is stated in the regular form (as in the foregoing examples), which is what is properly called a " Syllogism," the validity [or conclusiveness] of the reasoning is manifest from the mere form of the expression itself, without regard to the sense of the words ; so that if letters or other such arbitrary anmeaning Symbols, be substituted, the force of the argument will be not the less evident. Whenever this is not the case, the supposed argument is either sophistical and unreal, or else may be reduced (without any alteration of its meaning) into the above form : in which form, the general Maxim that has been laid down will apply to it. What is called an unsound [or fallacious] argument (that is an c^/?/)are?^^argument which is in reality none) cannot, of course, be reduced into such a form. But when it is stated in the form most nearly approaching to this that is possible, and especially when unmeaning symbols (such as letters), are substituted for words that have a meaning, its fallaciousness becomes evident from its want of conformity to the above Maxim. ♦ That is, an argument with one of the Premises understood. 28 ANALYTICAL IKTRODUOTION. [Part I. I L i I II. 1 i! m § 2. Let us take the Example formerly given: "Every criminal is deserving of punishment ; this man is not a criminal; therefore he is not deserving of punishment;" this, if stated in letters, would be, "Every X is Y ; Z is not X ; therefore Z is not Y." Here the term (" Y") "deser- ving of punishment" is affii-med universally of the Class ("X") "Criminal;" and it might therefore, according to the Maxim, be affirm ed of anything comprehended under that Class ; but in the instance before us, nothing is men- tioned as comprehended under that Class ; only "this man" ("Z") is excluded from that Class. And although what is affirmed of a whole Class may be affirmed of anything which that Class does contain, we are not authorized to deny it of whatever is not so contained. For it is evident that what is truly affirmed of a Class, may be applicable not only to that Class, but also to other things besides. For instance, to say that "every tree is a vegetable" does not imply that "nothing else is a vegetable." And so also, to say that "every criminal is desei ving of punish- ment" does not imply that "no others are deserving of puni'jhment:" for however true this is, it has not been asserted in the proposition before us. And in analysing an argument we are to dismiss all consideration of what might have been asserted with truth, and to look only to what actually is laid down in the Premises. It is evident, therefore, that such an apparent-argument as the above does not comply with the rule [or Maxim] laid down ; nor can it be so stated as to comply with it ; and it is consequently invalid. 5 3. Again, let us take another of the examples formerly given; '' 4.11 wise rulers endeavour to civUize the People; Alfred endeavoured to civilize the People ; therefore he was a wise ruler." The parallel example to this was, "All vegetables grow; an animal grows; therefore it is a vegetable." And each of these, if stated in Symbols, would stand thus: every "Y is X," [or the thmg denoted by Y is comprehended under the Class for which X Bt nds,] "Z is X; therefore Z is Y." Now in such an example, the quality of "growing" ["X"] is, in one Premise, affirmed univei-sally of "vege- table," [" Y"], and it might therefore have been affirmed of Lesson iv.] APPAREITT-AROUMENTS. 29 .>» anything that can be referred to the Class of "vegetable" as comprehended therein : but then, there is Twthing re- ferred to that Class in the other Premise; only, the same thing which had been affirmed of the Class " vegetable," is again affirmed of aaother Class, " animals" (Z); whence nothing can be inferred. Agaiii, take such an instance as this ; " Fruit is pro- duced in England; dates are fruit; therefore dates are produced in England." Here "produced in England" is affirmed of "fruit," but not universally; for everyone would understand you to be speaking not of " all fruit," but of ^'some fruit," as being produced in England. So that, expressed in Symbols, the apparent-argument would stand thus: "Some X is Y ; Z is X ; therefore Z is Y ;" in which you may see ihtt the Rule has not been com- plied with ; since that which has been affirmed not ol the whole of a certain Class, [or, not universally] but only of part of it, cannot on that ground be affirmed of whatever is contained under that Class. § 4. There is an argument against miracles by the well- known Mr. Hume, which has preplexed many persons, and which exactly corresponds to the above. It may l>e stated thus: "Testimony is a kind of evidence more likely to be false than a miracle to be true;" (or, as it may be expressed in other words, we have more reason to expect that a witness should lie, than that a miracle should occur); " the evidence on which the Christian miracles are believed is testimony ; therefore the evidence on which the Christian miracles are believed is more likely to be false than a miracle to be true." Here it is evident, that what is spoken of in the first of these Premises is, "j^ome testimony;" not "all testimony," [or any whatever,] and by "a witness" we understand, ^'some witness," not ^^ every witness;" so that this apparent- argument has exactly the same fault as the one above. And you are to observe, that it makes no difierence (as to the point now before us) whether the word "some" be employed, or a different word, such as '^7nost" or "many," if it be in any way said or implied that you are not speaking of ^^all" For instance, ^^ most birds can fly; and an ostrich is a bird," proves nothing. ♦ n 30 ANALYTICAL INTRODUCTION. [Fart I. § 5. In order to understand the more clearly, and to describe the more accurately, the fallaciousness of such seeming arguments as those of which we have just given examples, and also, the conclusiveness of the sound arguments, it will be necessary to explain some technical words and phrases which are usually employed for that purpose. This is no less needful (as was remarked in Lesson i.) than for an Artisan to have certain fixed and suitable names for the several instruments he works with, and the operations he performs. The word " Proposition!^ (which we have already had occasion to use) signifies "a Sentence in which something is said — [or predicated] — that is wffirm,ed or denied — of another." That which is spoken of, is called the ''Sub- ject" of the Proposition : and that which is said of it, is called the "Predicate;" and these two are called the " Terms" of the Proposition : from their being (in natural order) the extremes [or boundaries] of it. You are to observe, that it matters not whether each of these Terms consist of one word, or of several. For whether a Proposition be short or long, there must always be in it, one — and but one — tning of which you are speaking; which is called (as has been just said) i}he Subject of it : and there must be (in any one Proposition) one thing, — and only one — that is affirmed or denied of that Subject: and this which we thus affirm or deny of the other, is called — whether it be one word or more — the Predicate. § 6. You are to observe also, that though (in our lan- guage) the Subject is usually placed ^rs^, this order is not at all essential. For instance, "it is wholesome to rise early, ' or "to rise early is wholesome," or "rising early is wholesome," are only three ways of expressing the same Proposition. In each of these expressions "rising early," (or "to rise early," for these are only two forms of the Infinitive) is what you are speaking of; and "wholesome" is what you say [or predicate] of it. When we state a proposition in arbitrary Symbols, as "X is Y," it is understood that the first term ("X") stands for the subject, and the last ("Y") for the Pre- dicate. But when we use terms that are significant, [or, have a meaning] we must judge by the sense of the words .^ Lesson v.] PROPOSITIONS. 31 which it is that is the Subject, and which the Predicate ; that is we must ask ourselves the question, "What am I speaking of; and wliat am I saying of ifi" For instance; "Great is Diana of the Ephesians;" here "great" is evidently the Predicate. Again, "Thou art the man ;" and "Thou hast given occasion to the enemies of the Lord to blaspheme;" by asking yourself the above question, you will perceive, that in the former of these examples, "Thou" is the Predicate, and in the latter, the Subiect.* § 7. That which expresses the affirmation or denial, is called the *' Copula." For instance, if I say, "X is Y," or "X is not Y," in each of these examples, "X," is the Subject, and "Y" the Predicate; and the Copula is the word "is" in the one, and "is not," in the other. And so it is, in sense, though not always in expression, in every Proposition. For either the Affirmative-copula, "is" or the Negative-copula, "is not," must be always, in every Proposition, either expressed in those words, or implied in some other expression. Any sentence which does not do this — in short, which does not affirm or deny — is not a Proposition. For in- stance, of thes^ sentences, "Are your brothers gone to school?" "They are not gone;" "Let them go," the second alone is a Proposition [or "Assertion"]; the first being a Question, and the last a Gommcmdf or Request. m >'JI LESSON V. § 1. We have seen that in every Proposition there is something that is spoken of; which is called the subject; and something that you affirm or deny of it ; which is called the Predicate. And it is evidently of great import- ance to understand and express clearly, in each Proposi- tion, whether the Predicate is said of the whole of the Subject, or only oi part of it: — in other words, whether it is predicated ^^ universally,^^ or ^^particularly" [partially.'\ * The Predicate is the emphatic word or words in each proposition, and marked as such, by the voice, iu speaking, and sometimes by Italics or under- scoring in writing ; as you may perceive from the examples above. 32 ANALTTICAL INTRODUCTION. [Parti If, for instance, I say, or am nnrlerstood to imply, that '*all testimony is unworthy of credit," this is a very differ- ent assertion from saying or implying, merely that ^'some testimony is unworthy of credit." The former of these is called a " Universal" Proposition ; the Subject of it being taken universally ^ as standing for anything ami everything that the term is capable of being applied to in the same sense. And a term so taken is said (in technical language) to be ^^distributed." The latter of the two is called a ** Particular Proposition;" the Bvibject being taken j)arti- cularlyy as standing only for part of the things signified by it: and the Term is thjn said to be ^'u')idistributed" The technical word "distributed" (meaning what some writers express by the phrase "taken universally" is used, as you perceive, in a sense far removed from what it bears in ordinary language. But, — for that very reason, — it is the less likely to lead to mistakes and confusion. And when once its technical sense is explained, it is easily re- membered. When I say "birds come from eggs," and again, "birds sing," I mean, in the former proposition, "all birds" [or "every bird"]; in the latter proposition I mean, not "all," but "sonie" birds. In the former case the term "birds" is said to be "distributed;" in the latter, "undistributed." You must be careful also to keep in mind the technical sense (already explained) of the word "particular." In ordinary discourse, we often speak of "ihw, particular person" or thing; meaning "this hulivi- dual." But the technical sense is different. If I say, "this city is large" the Proposition is not "Particular," but is equivalent to a Unive/rml; since I am speaking of the whole of the Subject; which is "this single city." But *^some city is large," or "some cities are large" is a parti- cular proposition; because the Subject, "city" is taken not universally, but partially. The distinction between a "Universal" proposition and a "Particular," is (as I have said) very important in Reii- soning; because, as has been already remarked, although what is said of the uJiole of a Class may be said of any- thing contained in that Class, the Rule does not apply when something is said merely of a part of }». Class. (See the example "X is Y" in § 3 of the preceding Lesson.) * Lesson v.] quantity and quality. 8d § 2. You will have Heen that in some of the foregoing examples, the words "all," "every," or "any," which are used to denote the distribution of a Subject, and again, "some," wh''?h denotes its non-distrvibution, art; not ex- prefsed. They arc often understood, and left to be sup- plied in the re;id(^r's or hearer's mind. Thus, in the last example, "birds sing," evidently means "some birds;" and "man is mortal" would be understood to mean *^ every man." A Proposition thus expressed, is called ** Inde^ite ;'* it being left undetermined ["undefined"] by the form of expression, whetlior it is to be considered as Universal or as Particular. And mistakes as to this point will often given a plausible air to fallacies; such as that in the last lesson (§4) inspecting "Testimony." But it is plain, that every j)roposition must in reality be either Universal or Particular [that is, must have its Subject intended to be understood as distributed, or, as not distributed]; though we may not be told which of the two is moant. And this is called, in technical language, the distinction of Propositions according to their "Quantity;" namely, into Universal and Particular. "Every X is Y" and " some X is Y," are propositions differing from each other in their "quantity," and in nothing else. § 3. But the Predicate of a pro[)osition, you may ob- serve, has no such sign as "all" or "some," affixed to it, which denote, when affixed to the ^abject, the distribution or non-distribution of that term. And yet it is plain that each Term of a proposition — whether Subject or Predicate — -must always be meant to stand either for the whole, or for part, of what is signified by it ; — in other words, — must really be either distributed or undistributed. But this depends, in the case of the Predicate, not on the "quantity" of the proposition, but on what is called its " Quality;" that is, its being Affirmative or Negative. And the invariable rule (which will be explained presently) is, that the Predicate of a Negative-proposition is distributed and the Predicate of an Affirmative, undistributed. When I say "X is Y," the term "Y" is considered as standing iov part of the things to which it is applicable; I hi ANALYTICAL INTRODUCTION. [Part I. i; f;,tt in other words, ia "undiatributed." And it makes no dif- ference as to this point whether I say *^all X," or ''^ some X is Y." The Predicate is e(|nally undistributed in both cases; the only thing denoted by the signs ''all" or "some," being the distribution or non-distribution of the Subject. If, on the other hand, I say, "X is not Y," whether meaning, that ''iVo X is Y," or that ''so7ne X is not Y," in either caseV'jY," is distributed. § 4. The reason of this rule you will understand, by considering, that a term which may with truth be affirmed of some other, may be sucli as would also apply equally well, and in the same sense, to soniethiny else besides that other. Thus, it is tv\m that "all iron is a metal," although the tcjrm "metal" is equally applicable to gold, copper, &c., so that you could not say with truth that "all metal is iron," or that "iron, and that onlt/, is a metal." For the tei*m "iron" is of narrower extent than the term "metal;" which is affirmed of it. So that, in the above proposition, what we have been comparing, are the whole of the term "iron," and ])art of the term "metal;" which latter term, consequently, is undistributed. And this explanation applies to every affirmative pro- position. For though it may so happen that the Subject and the Predicate may be of equal extent [or ^^ equivalent;" or as some express it, "convertible"] so that the Predicate which is affirmed of that Subject could not have been affirmed of anything else, this is not irnjdied in the expres- sion of the proposition itself. In the assertions, for instance, that " every equilateral triangle is equiangular," and that "any two triangles which have all the sides of one equal to all the sides of the other, each to each, are of equal areas," it is not implied that "every equiangular triangle is equilateral," or that "any two triangles of equal areas, have their respective sides equal." This latter, indeed, is not true: the one preceding it is true : that is, it is true that "every equiangular triangle is equilateral," as well as that "every equilateral triangle is equiangular:" but these are two distinct propositions, and are separately proved in treatises on Geometry." If it happen to be my object to assert that the Predicate (( del lef Lesson v.] CONVERTIBLE TERMS. 35 as woW as the Sulitject of a coioain affirm ativ; proposition is to be uruU^rstood as distrihiited — and if 1 say, for instance, "all equilateral trian/^les, and no of/n'rn, are equiangular," — I am assertinf^, in reality, not 07ie pro- position merely, but tu)o. And this is the case whenever the ])ro])osition I state is understood (whether from the meaning of the words employed, or from the fjencral drift of the discourse) to imi)ly that the whole of the Predicate is meant to be affirmed of the subject. Thus, if I say of one number — suppose 100 — that it is the Square of another, as 10, then this is understood by every one, from his kmvdeihje of (he nnhire of nunthcrs, to imply, what are, in rejdity, tlie turn propositions, that "100 is the Square of 10," and also that "the Square of 10 is 100." Terms thus related to each other are called in technical language '"''convertible^^ [or "equivalent"] terms.* But then, you are to observe that when you. not only affirm one term of another, but also affirm (or imply) that these are '■^ convertible^^ terms, you are making not merely one assertion, but two. § 5. It appears, then, that in affirming that " X is Y," I assert merely that " Y," either the ivhole of it, or 2)art, (it is not declaimed which), is applicable to "X;" [or "comprehends," or "contains" X]. Consequently, if any part of a certain Predicate be applicable to the Subject, it must be affirmed, — and of course cannot be denied — of that Subject. To dem/, therefore, the Predicate of the Subject, must imply that no jm'^'i of the Predicate is applicable to that Subject; in short, that the whole Predicate is denied of that Subject. You may thus perceive that to assert that "X is not Y," is to sjiy that ?^o 2)(^rt of the term "Y" is applicable to "X;" (for if any part were applicable, <'Y" could be affirmed, and not denied of "X :") in other words, that the whole of *'Y" is denied of "X;" and that consequently "Y" is "distributed." When I say for instance, "All the men found on that island are sailors of the ship that was 111 ♦ In anj language which has a definite article— ^s "th«" in English,— this denotes that the terms are convertible. In Latin, which has no article, we ar» left to judge from the context. 36 ANALYTICAL INTRODUCTION. [Part I. wrockod thoro," this mifjlit be oqually true whother the wliole crow or only hoiik^ of th(nii wona savod on the ishiiul. To HJiy, tlioreforci, that "tho inoii found on that ishmd aro not .sailorH of th(3 sliip," kc, wouhl bo to deny that any part of that crow arc thoro; in short, it would be to say that tlio whole of that Predicate is t?mj)plicable to that subject. § 6. And this holds ^'ood efjually whether the negative pro[)osition be "universal" or "particular." For to say tliat some "X is not Y"" (or — which is the same in sense — that "All X is not Y") is to imply that there is no part of the term "Y" |no i)art of the chiss which "Y" stands for\ that is applicable to the whole without excep- tion, of the terra "X;" — in short, that tliore is some part of the term "X" to which " Y" is wholly inapplicable. Thus, if I say "some of the mon found on that island are not sailors of the ship that was wrecked there," or, in other words, "the men found on that island are Tiot, all of them, sailors of the ship," tfec, I imply that the term "sailors," kc, is wholly iu;ti)plicablo to some of the "men on the island;" though it might, perhaps, be applicable to others of them. Again if I say "some coin is made of silver," and "some coin is not made of silver" (or, in other words, that " all coin is not made of silver") in the former of these propositions I imply, that in some portion (at least) of the Class of " things made of silver," is found [or compre- hended] "some coin:" in the latter proposition I imply that there is "some coin" which is contained in no portion of the Class of "things made of silver;" or (in other words) which is excluded from the whole of that Class. So that the term "made of silver" is distributed in this latter proposition, aiid not, in the former. Hence may be understood the Rule above given, that in all Affirmative-propositions the Predicate is undistributed and in all Negative-propositions, is distributed. The " Subject" is, as we have seen above, distributed in a Universal proposition (whether affirmative or nega- tive) and not in a Particular. So that the distribution or non-distribution of the Subject depends on the " Quan- tity" of the proposition, and that of the Predicate, on the "Quality." I , Lesson vi.] terms of a syllogism. 37 LESSON VI. § 1. Tho noxt thing to bo loarut and ronKMnbored is tho nam(w of the tliroB Tenn.s that occur in a Syllogiam. For you will have perceived from tlu5 foregoing examples, that there are always three t(5rms ; wliich we have desig- nated by the Symlxjls X, Y, and Z. Each Hyllogism indeed has, in all, three Propositions ; and ev(!ry Pro- poHiti'" ■ ■ ■* Lesson viii.] habits op abstraction. 53 in to of of aly of any Conclusion consists in referring that of which something is to be affirmed or denied, to a class [or Predicable] of which that affirmation or denial can be made, our ability in Reasoning must depend on our power of abstracting correctly, clearly, and promptly from the subject in question, that which may furnish a " middle- term " suitable to the occasion. Ji 7} i] ■i 54 PART IT. COMPENDIUM. LESSON IX. 1^ § 1. We have gone through, in the way of a slight sketch, the Analysis of Reasoning. To analyse (as has been already explained) means to " take to pieces " so as to resolve anything into its elements [or component-parts.] Thus a Chemist is said to " analyse" any compound sub- stance that is before him, when he exhibits separately the simpler substances it is composed of, and resolves these again into their elements. And when, again, he combines these elements into their compounds, and those again into furthur compounds — thus reversing the former process, (which is called the "analytical,") he is said to be proceeding synthetically: the word "Synthesis" — ^which signifies "putting together," — being the opposite of "Analysis." Accordingly, it has been shown, in the foregoing Lessons, that every train of Argument being capable of being exhibited in a series of Syllogisms, a Syllogism contains three Propositions, and a Proposition two Terms. And it has been shown, how "Common-terms" (which are indispensable for reasoning) are obtained by means of Abstraction from Individual objects. This analytical method is the best suited for the first introduction of any study to a learner; because he there sees, from the very beginning, the practical application of whatever is taught. But the opposite method — the synthetical — is the more convenient for storing up in the mind all that is to be remembered. We shall therefore now go over a great part of the same ground in a reversed order, merely referring to such things as have been already taught, and adding such fur- ther rules, and explanation of additional technical-terms, as may be needed. I Lesson ix.] THE "DIALECTIC-ART." 65 § 2. The act of the mind in taking in the meaning of a Term, is called, in technical language, the act [or "operation"] of "Simple apprehension;" that is, ^^mere apprehension," [or "apprehension only."] When a pro- position is stated — which consists, as we have seen, of two terms, one of which is affirmed or denied of the other — ^the "operation" [or "act"] of the mind is technically called "Judgment." And the two terms are described in technical language, as "compared" together, and as "agreeing," or as "disagreeing," according as you affirm or deny, the one of the other. When from certain Judgments you proceed to another Judgment resulting from them, — that is^ when you infer [or deduce] a Proposition from certain other Propositions — this "operation" is called "Reasoning" or "Argument- ation," or (in the language of some writers) "Discourse." And these are all the mental operations that we are at present concerned with. Each of these operations is liable to a corresponding defect; namely, "Simple-apprehension" to indistinctness, "Judgment" to/alsity, and "Reasoning" to inconclusive" ness; [or fallaciousness.] And it is desirable to avail our- selves of any rules and cautions as to the employment of language, that may serve to guard against these defects, to the utmost degree that is possible : in other words, to guard, by the best rules we can frame, against Terms not conveying a distinct meaning; — against /a^se Propositions mistaken for true, — and against appare7it-arguments [or "Fallacies" or "Sophisms"] which are in reality incon- elusive, though likely to be mistaken for real [valid] arguments. And such a system of Rules,* based on a scientific view of the Reasoning-process, and of everything connected with it, is what the ancient Greeks, among whom it originated, called the "Dialectic-art;" from a word signi- fying to "discourse on," or "discuss" a subject. § 3. You are to observe, however, two important dis- tinctions in reference to the above-mentioned defects; ♦ You are to observe, that a Science properly consists of general tnUha tbJtX Are to l)« known: an Art, of practical nUa for souetldng tlxat la to be doM» *: ■ li ^1 56 COMPENDIUM. [Part II. 1st, you are to remember that which is, really, a Term, may be indistinctly apprehended by the person employing it, or by his hearer; and so also, a Proposition which is false, is not the less a real Proportion ; but, on the other hand, any exjM^ssion or statement which does not ::eally prvv anything is oiot, really, an argument at all, though it may be brought forward and passed off as such. 2ndly, it is to be remembered, that (as it is evident from what has been just said) no rules can be devised that will equally guard against all three of the above- mentioned defects. To arrive at a distinct apprehension of everything that may be expressed by any term whatever, and again, to ascertain the truth or falsity of every conceivable Pro- position, is manifestly beyond the reach of any system of rules. But, on the other hand, it is possible to exhibit any pretended Argument whatever in such a form as to be able to pro7iounce decisively on it validity or its fallaciousness. So that the last of three defects alluded to (though not the two former) may be directly and completely obviated by the application of suitable iniles. But the other two defects can be guarded against, (as will presently be shown,) only indirectly, and to a certain degree. In other words, rules may be framed that will enable us to decide what is, or is not, really a "Term," — really, a "Proposition," — or really an "Argument :" and to do this, is to guard completely against the defect of incon- dusiveness ; since nothing that is inconclusive is, really, an "Argument;" though that may be really a "Term" of which you do not distinctly apprehend the meaning; and that which is really a ^' Proposition" may be a false Proposition. § 4. When two terms are brought together (or "com- pared," as some express it) as Subject and Predicate of a Proposition, they are (as was above remarked) described in technical language, as "agreeing," or "disagreeing," according as the one is affirmed or denied, of the other. This "agreement," however, does not (you are to ob- serve) mean coincidence; [or that the two terms are »'« Lesson ix.] CONVERTIBLE TB^RMS. 57 " equivalent;"] for when I say "Every X is Y," or "Eveiy Sheep is a rurnnant-animal," this does not mean " X is equivalent to Y;" [or "X" and " Y" are terms of equal extent;] indeed, we know that " ruminant-animal" is in fact a term of greater extent than "sheep;" including several other species besides. We only mean to assert I that it is a Class [or Predicable] coTtipreheiiding under ity at least the term "Sheep;" but whether it does or does not comprehend anything else besides, the proposition before us does not declare. Hence it is that (as was formerly explained) the Pre- dicate of an 4^^^^^^^^'P^oposition is considered as undistributed : the Subject being compared with part at , least of the Predicate, and asserted to "agree" with it; but whether there be, or be not, any other part of the Predicate which does not agree with that subject, is not declared in the proposition itself. There are, it is to be observed, two apparent exceptions to this rule : 1st, the case of a Proposition which gives a Definitionoi anything : as when I say "a triangle is a three- sided figure;" which would not be a correct dejinitiovi; unless it were also true that "eveiy three-sided figure is a triangle ;" and 2ndly, by the case of an affirmative- Proposition, where both terms are singular, and denote, of course, one and the same Individual; as "Ishmael was the first-born of Abraham." In both these cases, the Subject and Predicate are, in each proposition, what are called "convertible" [or "equi- valent"] terms. But then, to assert or imply both that a certjain affirmative-proposition is true and also that its terms are equivalent, is to make (as was formerly remarked) not merely owe, but two assertions. Now if I am understood to mean not only that it is true that "a triangle is a three-sided figure," but also that this is the definition of a "triangle," then, I am understood as making two assertions; that not only "every triangle is a thi'ee-sided figure," but also that "every three-sided figure is a triangle." But this is understood not from the Pro- position itself, looking to the form of expression alone, but from what we know, or think, respecting the sense of the Terms themselves, or from what we suppose the speaker 1 58 COMPENDIUM. [Part II. to have intended by those Terms. For, all that is implied in the mere form of an affirmative-proposition, — as "X is Y" — ^is simply that some part at least of the term "Y" (whatever that symbol may stand for), is pronounced to agree with the term **X." § 5. And a like explanation will apply in the oth^i* Xjase also. If I understand from the sense of the terms ill isome affirmative-proposition, that the Subject and the Predicate are each a Singular-term (denoting, of course, Otie and the same individual), as "Ishmael was the first- '|K)m of Abraham," then I understand, as implied by the meaning of the words (though not, by the form of the Proposition) another proposition also ; namely, that " the first-bom of Abraham was Ishmael." In short, it is from my knowledge of the sense of the terms themselves that, I understand them to be ** convertible" [or equivalent J terms. For you may observe, that a Singuliar-term must from its own nature, correspond to a Gommion-term taken universally, [or "distributed"], inasmuch as it carmot hut stand for the whole (not merely some part) of that which it denotes. In such cases as the above, then, that which is expressed Wis one proposition, is so understood from the meaning of the words as in reality to imply two. And there is, there- fore, no real exception to the rule, that an Affirmative- proposition does not, 6y tJbeform of the eajj^ressiow, distribute its Predicate. § 6. That which pronounces the agreement or disagree^ ment of the two Terms of a Proposition [or which makesi it affirmative or negative] is called, as has been aoovo Staid, the "Copula." And this is always in sense, either ^''is" or "is not." For every Verb, except what is called ilie "Substantive-verb" to "be," contains something more than a bare assertion of the agreement or disagreement of two teiTiis. It always contains in it the Predicate (or part of the Predicate) also. Thus, the proposition "it rains" (which in Latin would be expressed by the single word "pluit") is resolved Sub. Cop. Pred. into "Rain — is — falling;" or in some such way. "Joha Subj. Cop. owes William a pound," is resolved into "Jolux — is— Lesson ix.] clearness of exfressiost. 50 Pred. owing [or indebted to] William a Pound." And so in all such cases. Sometimes, indeed, even the substantive-verb itself is both Copula and Predicate ; namely, where eocistence alone is affirmed or denied; as **God is;" "one of Jacob's sons is not";* in which cases "existing" is the Predicate. You are to observe, that the Copula has in itself no relation to time. If, therefore, any other tense besides the Present^ of the Substantive- verb, is used, it is to be understood as the same in sense with the Present^ as far as the assertion is concerned ; the difference of tense being regarded (as well as the person and number) merely as a matter of grammatical propriety : unless it be where the circumstance of time really does affect the sense of the proposition. And then this circumstance is to be regarded as part of one of the Terms; as, "this man was honest;" that is, "he is ohq formerly-honest.^* In such a case, an emphasis, with £« peculiar tone, is laid on the word *^was." An infinitive^ you are to observe, is not a Verb (since it can contain no affirmation or denial), but a verbal noun-substantive. And a Participle^ again, is a verbal adjective. A Participle, or any other Adjective, may be made a Predicate, but not (by itself) a subject of a proposition; as "this grass is green," "that grass is mown." An infinitive, though generally placed (in English) at the end of a Sv^ntence, is almost always (when it is by itself a Term) the Subject; as "I like to ride;" that is, Sub. Pred. "To ride, [or "riding"] is — a thing I like." And observe that there is, in English, an infinitive in " in^i" the same in sound with the Participle, but different in sense. When I say "Riding" [or " to ride"] "is plea- sant," and again "that man is riding," in the former sentence the word " riding" is a Substantive, and is the Subject ; in the latter it is an adjective [Participle] and is the Predicate. - I * Oen. xlil 13. eo COMPENDIUM. [Part II. One infinitive, however, is sometimes predicated of another infinitive: as, "seeing is believing;" "not to advance is to fall back;" "to be born is not to be per- fected." § 7. A term may consist (as was formerly explained) of one word, or of several. And care must be taken, when you are examining a proposition, not to mistake for one of its Terms a word which, though it might have been used as a Term, is, in that proposition, only a part of a Term. Thus, in one of the above examples, the word "pound" is not one of the Terms, but only a part of the Term "owing a pound to William." A description of some object will sometimes occupy a page or two, and yet be only the Predicate of a single Proposition. You are to observe, also, iihat one single sentence will often imply what may be regarded as several distinct Propositions ; each, indeed, implying the truth of the others, but having their terms different, according as we understand the drift (as it is called) or design of what is uttered: that is, according to what we understand the person to be speaking of (which is the subject), and what it is that he says [predicates] of it. 1 2 3 4 Thus "He — did not — design — your — death" — ^may be regarded as any one of at least four different proposi- tions. If (No. 1 . ), the word " He " be marked by emphasis in speaking, or by italics, it will be understood as the Predicate; and the drift of the 'sentence will be, that "whoever else may have designed your death, it was not He:" if the emphasis fall on No. 2, the Predicate will be "designing," [or by "design"], and the drift of the sentence will be, that " though he may have endangered your life, it was not by design :" and so with the rest. You should endeavour, therefore, so to express your- self, as to make it clearly understood not only what is the meaning of each word you employ, but also what is the general drift of the whole sentence; in short, what is the Subject of your Proposition, and what it is that you say of it. And as far as you can, you should make this clear by the structure of each sentence, without resorting to the expedient of italica or under-scoring ofteuer than is unavoidable. I y'i'/; Lesson x.] PROPOSITION. 61 There is frequently a great advantage towards such clearness, gained by the English word "it" in that sense in which it stands (not as the neuter pronoun, answering to "He" and "She," but) as the representative of the Subject of a Proposition, of whatever Gender or number ; so as to allow the subject itself to be placed last : as — Subj. Cop. Pred. Subj^ " It — is not — he — that had this design;" Or again — Subj. Cop. Pred. Sub|. " It — is not -— by design — that he did this," &c. m Hill LESSON X. § 1. A Proposition is, as has been said, an act of judg- ment expressed in words ; and is defined to be a " Sentence which asserts f^ or, in the language of some writers, an ** indicative Sentence :" " indicative," [or " asserting,"] meaning "that which affirms or denies something." It is this that distinguishes a Propositian from a Question^ or a Command, &c. Propositions considered merely as Sentences, are distin- guished into "Categorical" and " Hypothetical." The Categorical asserts simply, that the Predicate does, or does not, apply to the Subject: as "the world held an intelligent Maker:" "Man is not capable of rais- ing himself, unassisted, from the savage to the civilized state." The Hypothetical [called by some writers, "Com- pound"] makes its assertion under a Condition, or with an Alternative; as "if the World is not the work of chance, it must have had an intelligent Maker:" "Either man- kind are capable of rising into civilization unassisted, or the first beginning of civilization must have come from above." The former of these two last examples is of that kind called "Conditional-proposition;"* the ^^ condition" being denoted by "if," or some such word. The latter example is of the kind called "Disjunctive;" the alternative being denoted by "either" and "or." • Or, "hypothetical" according to those writers who use the word "com- pound" whenweTJItve used "hypothetical." 62 COMPENDIUM. [Part II. The division of Propositions into Categorical and Hypothetical, is, as has been said, a division of tliem con- sidered merely as Sentences; for a light distinction might be extended to other kinds of Sentences also. Thus "Are men capable of raising themselves to civilization]" "Go and study books of travels," are what might be called categorical sentences, though not prepositions. " If man is incapable of civilizing himself, whence came the first beginning of civilization]" might be considered as a conditional question; and "Either admit the conclusion, or refute the argument," is a disjunctive command. At present we shall treat only of Categoi.'ical Proposi- tions. § 2. It has been above explained, that Propositions (of thia Class, — the Categorical) are divided according to their "Quantity" into "Universal" and "Particular;" — that an " Indefinte-^ro^aition^' is in reality either the one or the other; though the form of expression does not declare which is meant: — and also that a ** Singular-pro- position is equivalent to "Universal," since its subject cannot but stand for the whole of what that Term denotes, when that whole is one single individual. You have also learnt that propositions are divided, according to their "Quality," into "affirmative" and "ne- gative." The division of them, again, into "true" and "false" is also called a division according to their "quality;" namely, the "quality of Matter;" (as it has relation to the subject-matter one is treating of;) while the other kind of quality (a proposition's being affirmative or negative) is "the quality of the expression." The "quality of the matter" is considered (in relation to our present inquiries) && accidental, and the "quality of the expression" as essential. For though the truth or falsity of a proposition — for instance, in Natural-history, is the most essential point in reference to Natural-history ^ and of a mathematical proposition in reference to Mathe- matics, and so in other cases, — this is merely accidental in reference to an inquiry (such as the present) only as to forms of expression. In reference to that,t\iQ essential difference is that between affirmation and negation. And here it should be remarked by the way, that as Lesson x.] CATEOORiCAL PROPOSITIONS. 63 on the one hfiikd^ ©very Proposition must be either true or false, fi<^ xiii the other hand, nothing else can be, strictly fe^eafeiiig, either true or false. In colloquial language, towever, "true" and "false" are often more loosely applied; as when men speak of the ^'true cause" of any- thing; meaning "the reul cause;" — the "true heir," that is, the rightful heir; — a ^'^ false prophet," — that is, a pre- tended prophet, CO* one who utt&rs falsehoods; — a "true" or " false" argument, meaning a valid [real], or an appa' rew^-argument — a man "true" or "false" to his friend; f. e., faithful, or unfaithful, » .»» Lesson xL] an argument defined. 71 square which ia not a square. The expression therefor© is merely a way of stating the Universal-proposition [E], "No virtuous man betrays his Country." So again, to say "A weary traveller in the deserts of Arabia must eagerly drink when he comes to a Spring," does not mean that he is compelled to drink, but that / cannot avoid believing that he will; — that there is no doubt in my mind. In these and many other such instances, the words "may," "must," "can," "impossible," ro- hable conclusion ; though the conclusiveness, — that is, the connection between the Premises and the Conclusion — is perfectly certain. * Seo aljove. Leason IX. § 4. Lesson xi.] an arqumei^t defined. 73 )t in 'remises Y a pro- bt is, the sion — is For instance, assuming that "every month has 30 days" (which is palpably false) then, from the minor- premise that *' April is a month," it follows (which happens to be true) that " April has 30 days:" and from the minor-premise that "February is a month," it follows that "February has 30 days;" which is false. In each case the conclusiveness of the Argument is the same; but in every case, when we have ascertained the falsity of one of the Premises, we know nothing (as far as that argument is concerned) of the truth or falsity of the Conclusion. § 3. When, however, we are satisfied of the falsity of some Conclusion, we may, of course, be sure that (at least) one of the Premises is false ; since if they had both been true, the Conclusion would have been true. And this — which is called the " indirect" mode of proof — is often employed (even in Mathematics) for establishing what we maintain : that is, we prove the falsity of some Proposition (in other words, the truth of its contradictory) by showing that if assumed, as a Premise, along with another Premise kno^ai to be true, it leads to a Conclu- sion manifestly false. For though from a false assumption, either falsehood or truth may follow, from a true assump- tion, truth only can follow. Let us now look to the case of a doubtful Premise. Suppose it admitted as certain that "a murderer deserves death," and as 'probable that " this man is a murderer," then, the Conclusion (that "he deserves death") is pro- bable in exactly the same degree. But though when one Premise is certain, and the other only probable, it is evident that the Conclusion will be exactly as prolaable as the doubtful premise, there is some liability to mistake, in cases where each Premise is merely, probable. For though almost every one would perceive that in this case the probability of the Conclusion must be less than that of either Premise, the precise degree in which its probability is diminished, is not always so readily apprehended. And yet this is a matter of exact and easy arithmetical calculation. I mean, that, given the probability of each Premise, we can readily calculate, and with perfect exact- ness, the probability of the Conclusion. I ii m If m ml m II r U V t 74 -1^, COMPENDIUM. [Part II. As for the probability of the Premises themselves that are put before us, that, of course, must depend on our knowledge of the subject-matter to which they relate. But supposing it agreed what the amount of probability is in each Premise, then we have only to state that probability in the form of a. fraction, and to multiply the two fractions together, the product of which will give the degi-ee of pro- bability of the Conclusion.* § 4. Let the probability, for instance, of each Premise, be supposed the same; and let it in each, be §; [that is, let each Premise be supposed to have two to one in its favour; that is, to be twice as likely to be true as to b© false;] then the probability of the Conclusion will be two- thirds of two thirds; that is, |; — rather less than one-half. For since twice two are four, and thrice three, nine, the fi-action expressitig the probability of the Conclusion will be four-ninths. For example, suppose the Syllogism to be "A man who has the plague will die of it" (probably); "this man has the plague" (probably); therefore (probably) "he will die of it." We are — suppose — not certain of either Premise; though we think each to be probable : we have judged — suppose — that of 9 persons with the symptoms this man exhibits, two-thirds, — ^that is, six, have the plague : and , again, that two-thirds of those who have the plague — that 18, four out of six — die of it: then, of 9 persons who have these symptoms, 4 may be expected to die of the plague. Aga.in " Every X is Y (|) ; Z is X (|) ; therefore Z is Y •fz=^) ; let the fractions written after each JPremise ex- press the degree of its probability : and the result will be that which is given as the probability of the Conclusion. For instance, "A Planet v/^ithout any atmosphere is un- inhabited: the moon is a planet without any atmosphere; therefore the moon is uninhabited :" supposing these Pro- positions to be those repiresented in the former example (of X, Y, and Z) then the probability that " the moon is Those who are at all familiar with Arithmetic will hardly need to be reminded that,— since a fraction is less than a unit, — what is called (not strictly, but figuratively) multi/piging anything by a fraction, means taking it less than onee ; so that for instance, 4 X § ^^^^ ^i & ^^^ multiplied (as is called) by two-thirds» mtftuut two-tfairdsofahalf; f. ^. or}. ■iilS. ■■.•^^■iu.Ai. i;\Uv.SrW:.;>^'i4;^wli>L- «„■..;.-;:■ the Lesson zi.] degrees of probability 75 uninhabited," will be two-thirds of three-fourths; or one- half, since § mliltiplied by three-fourths gives y»y= j.* rt In the example just given, you will observe, that the probability of each Premise has been supposed more than J ; that is, each has been assumed to be more likely to be true than not ; and yet there is, for one of these Conclu- sions, only an even chance ; and for the other less. The supposed patient is supposed to be rather less likely to die of the plague than not. And, of course, when there is a long train of reasoning, — ^the conclusion of each argument being made one of the Premises of a succeeding one, — then, if a number of merely-probable Premises are introduced, the degree of probability diminishes at each successive stage. And hence it may happen, in the case of a veiy long train of reasoning, that there may be but a slight proba- bility for the ultimate Conclusion, even though the Pre- mises successively introduced should be, some of them, quite certain, and the rest more probable than not. And hence, we often have to employ several distinct trains of argument, each tending separately to establish some degree of probability in the Conclusion. § 5. When you have two (or more) distinct arguments, each, separately, establishing as probable the same con- clusion, the mode of proceeding to compute the total pro- bability, is the reverse of that mentioned just above. For, there — in the case of two probable premises, — we consider what is the probability of their being both true; which is requisite, in order that the conclusion may be established by them. But, in the case of a conclusion twice (or offcener) * Some persons profess contempt for all such calculations, on the ground that we cannot be quite sure of the exact degree of probability of each Premise. And it is true, that we are, in most cases, exposed to this unavoidable course of uncertainty ; but this is no reason why we should not endeavour to guard against an ad^Uiov,al uncertainty, which can be avoided. It is some advantage to have no more c* oubt as to the degree of probability of the Conclusion, than we have in respect to the Premises. And in fact there are offices, kept by persons whose buisness it is, in which calculations of this nature are made, in the purchase of contingent-reversionat depending, sometimes, on a great variety of risks which can only be conjectu- lally estimated ; and in effecting Insurances, not only against ordinary risks (the calculations of which are to be drawn from statistical-tables), but also against every vuiety and degree o exfra-ordinary risks ; the exact amount of which no one can confidently pronounce upon. But the calculatiozu are based on the best estimate that can be formed. { 'i' ■■-.■.\ i I It ! 76 COMPENDIUM. [Part II. proved probable by separate arguments, if these distinct indications of truth do not all of them /ail, the conclusion is established. You consider, therefore, what is the pro- bability of both these indications of truth being combined in favour of any conclusion that is not true. Hence the mode of computation is, to state (as a frac- tion) the chances against the conclusion as proved by each argument; and to multiply these fractions together, to ascertain the chances against the conclusion as resting on both the arguments combined; and this fraction being subtracted from unity, the remainder will be the proba- bility ybr the conclusion. For instance, let the probability of a conclusion as established by a certain argument, be^ : (suppose that this man is the perpetrator of a certo,in murder, from stains of blood being found on his clothes :) and again of the same conclusion as established by another argument, | : (suppose from the testimony of some witness of somewhat doubtful character:) then, the chances against the conclu- sion in each case, respectively, will be f and |; which, multiplied together, give if or J against the conclusion. The probability, therefore, /or the conclusion as depending on these two arguments jointly (i. e. that he is guUty of the murder) will be |, or two to one.* As for the degree of pi-obability of each Premise, that, as we have said, must depend on the subject-matter before us; and it would be manifestly impossible to lay down any fixed rules for judging of this. But it would be absurd to complain of the want of rules for determining a point for which it is plain no precise rules can be given; or to dis- parage, for that reason, such rules as can be given for the determining of another point. Mathematical Science will enable us — given, one side of a triangle and the adjacent angles, — ^to ascertain the other sides; and this is acknow- ledged to be something worth learning, although mathe- matics will not enable us to answer the question which is sometimes proposed in jest, " How long is a rope?" Men are often misled in practice by not attending to these circumstances, plain as they are, when pointed out. -\.- • See Lesson XVIL, » 10. >■"?■■■-';■■■ ^ «*(it*« ■ •til. ijtinct usion e pro- Mned I frac- Y each er, to eating being proba- lon as at this stains of the ent, |: lewhat conclu- which, jlusion. )ending iiilty of }e, thciitf [• before wn any isurd to oint for r to dis- for the ace will idjacent icknow- L mathe- «rhich is r iding to ited out. Lesson xi.] principle op reasoning. § 6. It has been already explained that the Maxim [or Dictum] applicable to every Argument when stated in the clearest form, is, tliat whatever is predicated universally of any term may be predicated in like manner [affirmed or denied, as the case may be] of wliatever is compre- hended under that term ; and that this, consequently, is the " Universal principle of Reasoning." And you may observe, that this Dictum [or Maxim] may, in fact, l)e regarded as merely the most general statement of *'An Argument" — not this or that indivi-t dual argument; but any and every "Argument abstract- edly." ^ Fo^; instance, if you say " This man is contemptible be- cause he is a liar," you evidently mean to be understood, " Every liar is contemptible; this man is a liar; therefore he is contemptible." Now, if you so fai' generalise this Syllogism, as to omit all consideration of the very terms actually occurring in it, abstracting, and attending solely to the^brm of expression, you will have "Every X is Y; Z is X; th.erefore Z is Y;" and then if you proceed to make a still further abstraction, saying — instead of "Every X" — *^ any-term-distributed" and instead of ** Y" — "anything whatever affirmed of that term," and so on, you will have, in substance, the very " Dictum" we have been speaking of: which may be separated into three portions, corresponding to the three Propositions of a Syllogism; thus, — 1. Anything whatever (as "Y") affirmed of a wliole class (as "X"). , 2. under which class something else (as "Z") is com- prehended. 3. may be affirmed of that (namely " Z") which is so comprehended. These three portions, into which the Dictum has been separated, evidently answer to the Major-premise, Minor- premise, and Conclusion, of the Syllogism given above. And it is plain, that the like explanation will apply (if "denied" were put for "affirmed") to a Syllogism with a negative conclusion. So that the "Dictum" is in fact, as we have said, merely the most abstract and general form of stating the Act of Reasoning ^ universally. . .^ ,,, . > ii 78 COMPENDIUM. [Part II. § 7. Some persons have remarked of this "Dictum" (meaning it as a disparagement) that it is merely a some- what circuitous explanation of what is meant by a Class. It is in truth, just such an explanation of this as is need- ful to the student, and which must be kept before his mind in reasoning. For you are to recollect that not only every class [the Sign of which is, a " Common-term,"] compre- hends under it an indefinite number of individuals — and often of other Classes — differing in many respects from each other, but also most of those individuals and classes may be referred, each to an indefinite number of classes (as was formerly explained), according as we choose to abstract this point or that from each. Now to remind one, on each occasion, that so and so is referable to such and such a Class, and that the Class which happens to be before us comprehends such and such things, — this is precisely all that is ever accomplished hy Reasoning. For you may plainly perceive, on looking at any of the examples above, that when you assert both the Premises taken in conjunction, you have; virtually, implied the Conclusion. Else, indeed, it would not be impossible (as it is), for any one to deny the Conclusion, who admits both Premises. § 8. Hence, some have considered it as a disparagement to a Syllogism (which they imagine to be one kind of Argument) that you can gain no new truth from it ; the Conclusions it establishes being, in fact, known already by every one who has admitted the Premises. Since, however, a Syllogism is not f* certain distinct kind of argument, but any argument whatever, stated in a regular form, the complaint, such as it is, lies against Reasoning altogether. , . And it is undeniable, that no Tiew truths — in one sense of the word — (and that, perhaps, the strictest sense) can ever be established by Reasoning alone; which merely un- folds as it were, and developes, what was, in a manner, wrapped up and implied in our previous knowledge ; but which we are often as much unaware of, to all practical purposes, till brought before us, as if it had been wholly beyond our reach. :Vr ' . r^^" "4-»» ^-H^^c^ti^t}^] y>a- II. .»» Lenion xL] information and instruction. 79 New Truthi, — in the strictest sense of the vord— that is, such OS are not implied in anything that wa8 in our minds before, — can be gained only by the use of our senses, or from the reports of credible narrators, (fee. An able man may, by patient Reasoning, attain any amount of mathematical truths; because these are all im- plied in the Definitions. But no degree of labour and ability would give him the knowledge, by '^Reaamimg^* alone, of what has taken place in some foreign country; nor would Civable him to know, if he had never seen or heard of the experiments, what would become of a spoonful of salt or a spoonful of chalk if put into water, or what would be the appearance of a ray of light when passed through a prism. § 9. These two modes of arriving at any truth are per- ceived by all men as distinct. And they are recognised in the expressions in common use. The one is usually called "information'" the other "instmction.^^* We speak of trusting to the information (not the instruction,) of our senses. Ajiy one who brings news from any place, or who describes some expeiiments he has witnessed, or some spot he has visited, is said to aflford us information. A Mathematician again, a Grammarian — a Moralist — any one who enters into a useful discussion concerning human life, — any in short who satisfactorily pi^oves any- thing to us by reasoning, — is said to afford us instruction. And in conversing with any one who speaks judiciously, one sometimes says " Very true!" or " That is a very just remark: that never struck me before," &c. In these and such like expressions, we imply both that what he says is not superfluous, but valuable and important, and also that we are conscious of having ourselves possessed, in our own previous knowledge, the germ of what he Las developed, and the means of ascertaining the truth of what he has said ; so as to have a right to bear our testimony to it. But when any one gives us information about a foreign Country, &c., though we may fully believe him, and be interested by what he tells us, we never think of saying " Very true !" or " You are quite right." We readily per- ■:>':' * It is not meant that this is the only sense of these words. C' '?':'••!';-■ I« ^ui I COMPENDIUM. [Part II. ceive that in tliis case tlie knowledge imparted is new to us in quite ano1;her sense • ^.ndiis what no reasoning alone could have imparted; being not implied in anything we knew already. These two modes of attaining what are, in different senses, new truths (and which, of course, are often miosed together,) may be illustrated by two different modes in which a man may obtain an addition to his wealth. One man, suppose, has property to a, certain value, heqiieathed to him; another discovers on his estate a mine of equal value. Each of these is enriched to the same degree. But the former of them acquires what he had, before, no right to; the latter merely comes to the knowledge and use of that which wes before, legally, his property; though, till discovered, it brought him no advantage. Any mode of attaiaing knowledge, distinct from Rea- soning, is, of course, foreign from the present inquiry . LESSON XII. § 1. The Dictum [or Maxim] above explained as the Univ^ei'sal-principle of Reasoning, will apply to a Syllo- gism in such a form as that of the examples given. "Every (or No) X is Y*; Z (whether some Z or every Z) is X; therefore — some, or every — Z is Y;" or "No Z is Y;" or *' Som*^ Z isi not Y;" as the case may be. And in that form every valid argument may be exhibited. But there are other Syllogisms in other forms, to which the "Dictum' cannot le immediately/ applied (though they may be reduced into the above form), and which yet a/re real Syllogisms, inasmuch as their conclusiveness is manifest from the form of expression, independently of the meanuig of the Terms. For instance, "No Savages have the use of metals; the ancient Germans had the use of metals; therefore they were not savages," is a valid Syllogism, though the Dictum cannot be applied to it as here started. But it may readily be reduced into the form to which the Dictum ♦ See Lesson IX., S 7. fiaJjA/.,i, ' l-» .V--. Lesson xii.] terms of the conclusion ■» does apply; by illatively converting the Major-premise, into "men who have the use of metals are not Savages." But the argument as it originally stood was a regular Syllogism; and so are some others also in a different form; although the Dictum does not immediately apply to them. Accordingly, certain rules [or "Canons"] have been framed which do apply directly to aU categorical Syllo- gisms, whether they are or are not in that form to which the Dictum is immediately applicable. 1st Canon. Two terms which agree with one and the same third, may be pronounced to agree With each other: and — 2nd Canon. Two terms whereof one agrees snd the other disagrees with one and the same third, may be pronounced to' disagree with each other. The technical sense of the words "agree" and "disagree" hias been explained in a former Lesson. The two terms wliich are each compared with the same thii'd, are the Terms [or "Extremes"] of the Conclusion; viz.: the Major-term and Minor-term: and that third Term with which they are separately compared in the two Premises, is the Middle-term. On the former of these two Canons rests the proof of affirmative-conclusions; on the latter, of negative. § 2. To take first a Syllogism in the form originally given: "Every X is Y; 2 is X; therefore Z is Y;" or again, "No X is Y; Z is X; therefore Z is not Y;" in these examples, " Y" and "2/" are, in the two Premises respectively, compared with "X:" in the former example they are assumed to "agree" with it; and thence in the Conclusion, they are pronounced (according to the 1st Canon) to "agree" with each other; in the latter example, "Y" is assumed to "disagree" with "X," and "Z"to ''agree" with it; whence in the Conclusion they are pro- nounced (according to the 2nd Canon) to "disagree" with each other. Again, to take a Syllogism in the other form, such as that in this Lesson, "No Savages," &c., or, "No Y is X; Z is X; therefore Z is not Y;" you will perceive that the 2nd Canon will apply equally well to this as to the preceding example. ^D of a stllooism. 87 s., It is evident that all the possible collocations of the Middle must be four ; since it must be either the Subject of the Major-premise and the predicate of the Minor ; or the Predicate of each ; or the Subject of each ; or the Predicate of the M^jor and Subject of the Minor. On looking to the examples originally given, you will see that a Syllogism in that form [" Every X is Y ; Z is X; therefore Z is Y"] has the Middle-term made the Sithject of the Major-premise, and the Predicate of the Minor. Tliis is called the First Figure ; and it is to Syllogisms in this figure alone that the "Dictum" above-mentioned will at once apply. § 9. If you look to the fonn afterwards exemplified: (§ 1 of this Lesson) as "No savages, &c." or ''No Y is X ; Z is X ; therefore Z is not Y," you will see that the Middle is the Predicate of each Premise. This is called the Second Figure. And in this, evidently none but nega- tive Conclusions can be proved ; since one of the Premises must be negative, in order that the Middle-term may be (by being the Predicate of a Negative) distributed. Again, the Middle-term may be the Subject of each Pre- mise. And this is called the Third Figure. Thus "Some X is Y ; every X is Z ; therefore some Z is Y ;" is a cor- rect Syllogism in the Third Figure, being conformable to the first Canmi. And the Syllogism here given as an example may be easily reduced to the First Figure, by simply converting the Major-premise, and taking it for the Minor ; [transjJosiTig the Premises ; ] which will enable you to infer the simple- converse of the Conclusion : as " Every X is Z ; some Y is X j therefore some Y is Z :" and this implies that " some Z is Y ;" since (as was explained formerly) the simple conversion of I is illative. For instance, " some painful things are salutary ; every thing painful is an object of dread : therefore some things which are objects of dread are salutary ;" this, though a valid Syllogism as it stands, may be reduced, in the man- ner abov9 stated, to the First Figure. In this, or in other ways, any Syllogism in the Third Figure may be easily ''reduced" (as the teclmical phraso is) to the First Figure. : ' ■ n / V 88 COMPENDIUM. •V [Part It In this Third Figure you will find that none but Pa/r- tioular Conclusions can be drawn. To infer a Universal wouH always, you will find, involve an " illicit process of the Minor-term." For if the Premises are both Universal, (which as we have already seen (J 6) they must alwiays be, to warrant a Universal Conclusion,) then, supposing them to be A, A, there will have been,— in this Third Figure — no term distributed except the Middle; (affirma- tives not distributing the Predicate;) and consequently no term can be distributed in the Conclusion ; which must therefore be I. And if the Premises be E and A, there will have been (besides the middle) only one term, — the Predicate of E, distributed ; and consequently only one term can be dis- tributed in the Conclusion; and that one must be the Predicate of O ; since the Universal [E] would have both terms distributed. § 10. The Third Figure might be called the ** exceptive" or the " refutatory " Figure ; (or, agreeably to the expres- sion of the Greek writers, the " enstatic ;") as being a very natural form of expressing arguments which go to establish the contradictory of some Universal Proposition that any one may have maintained, or that may be generally believed. For instance, if any one were speaking of " metals " as being, universally, "conductors of heat," you might adduce " Platina" as an exception Or should any one contend that "no agent incapable of distinguishing moral good and evil (as for instance a madman) can be deterred from any act by apprehension of punishment," you might refute this, by adducing the case of a brute, — ^for instance, a dog — deterred from sheep-biting by fear of punishment. And such arguments would fall very naturally into the Third Figure. It Is, especially, the most natural form in which to ex- press an argument — such as we often employ for the above purpos(3 — in which the Middle-term is a Singular-term. ; as when, for instance, you prove, by the example of a cer- tain individual,* the contradictory of a proposition (which would seem to most persons a very probable conjecture) • See the Note on a former Lesson, on the case of Laura Bridgenian. LesBon xiii.] figure op syllogism. 89 that a deaf and dumb person, bom blind, cannot be taught language. ' * The Second Figure may be called the ^^exchisive" Figure; being a very natural form for arguments ui?ed in any inquiry in which we go on excluding^ one by one, certain suppositions, or certain classes of things, from that whose description we are seeking to ascertain. Thus, certain symptoms, suppose, exclude, ^' /Small Fox;" that is, prove this not to be the patient's disorder; other symptoms, suppose, exclude "Scarlatina" &c., and so one may proceed, by gradually narrowing the range of possible suppositions. These three Figures are the only ones in wliich any ar^ment would, designedly, be stated. For, as to what is called the Fourth Figure (in which the Middle-term is made the Pi^dicate of the Major-premise and the Subject of the Miiior) though a Syllogism so stated would be un- deniably valid if conformable to the rules (as " very Y is X; no X is Z; therefore no Z is Y"), this form is only a clumsy and inverted way of stating what would naturally be expressed in the First Figure; as, in this example, might be done by transposing the Premises, and simply converting the Conclusion. it Mil i >1 ii LESSON XIII. § 1 . Besides C ategorical-ar guments^ which we have been treating of. Reasoning is often expressed in a Hypothe- tical form. And though such arguments may be rediiced into categorical form, this4s not necessary, except for the purpose of pointing out the sameness in all cases of the Reasoning-process. For you may exhibit in a hypotheti- cal form a perfect " Syllogism" as above defined. A Hypothetical (or as some writers call it, a "com- pound") Proposition, consists of "two or more Categorical propositions, united by a Conjunction, in such a manner as to make them one proposition." And the difierent kinds of hypothetical-proposition are named after their respective Conjunctions; namely, "Conditioi:ial" and \i f III ■A^.,^, 90 COMPENDIUM. [Part II. "Disjunctive."* For instance, "if A is B, then X is Y," is a Conditional-Proposition ;t "either A is B, or X is Y" is Disjunctive. : .,.i\ And each of these is a real Proposition, i. e. asserts some- thing; and consequently is either true or false; which (as was formerly explained) is peculiar to Propositions ; and each is also one Proposition, though consisting of several parts [or "members"] each of which if taken separately would be itself a proposition; but the Conjunction (which is called the Copula) makes the whole one Proposition. § 2. For instance, "the world is eternal," is a proposi- tion; "records earlier than the Mosaic exist," is another proposition; and "i/the world be eternal, records earlier thau the Mosaic must exist," is a third proposition distinct from each of the others, and which may be true, though they be both false ; since it does not assert the trtUh of either of them, but only the conneodon between them. Again, should any one say "if the Northern-lights be shining, some great revolution of an empire is going on," this would be, properly speaking, a false Proposition, even should it turn out that each of the "members" stated aa a categorical proposition is true; supposing it admitted that they have no connexion with each other. Observe, however, that no false cor elusion can be de- duced from a false Conditional-proposition, when it so happens that both its "members" (stated as categorical- propositions) are true. In the case of a Disjunctive-proposition, on the other hand, it is implied, that one at least of its "members" (stated as a categorical-proposition) must be true, and that if not, the whole proposition must be false. As, "this man was either at Oxford or at Cambridge" would not be true, if he were not at Oxford, and not at Cambridge. And it is usually meant to be understood that onli/ one of the members can be true; for if this were not the meaning in such an example as the foregoing, it would have been more coiTecfc to say "this man was either at Oxford, or Cambridge, or both" * See Lesson X. t Tliose writers who use the word compound-pToposltioxi instead of hypotht' ticai, empl»y "hypothetical" to signify "conditionaL" .-, l;T..-i,:,l,. Lesson xiii.] hypothetical-propositions. 91 § 3. A Hypothetical-8y^/o^i«w, ia one in which the rea- soning itself turns on the fff/pothesis; not, every syllogism that has in it a hypothetical premise; for the "hypothesis" may be a poHion of one of the Terms, and the syllogism may be merely categorical. For instance, " Real miracles are evidence of a divine commission ; if the works of Jesus were acknowledged miraculous by the unbelieving Jews, they must have been real miracles ; therefore the works of Jesus (if they were acknowledged, ?i- sequence." (Consequence) For instance " If- (Consequent) (Antecedent) ^this man is a murderer (Consequent) he deserves death." " The English are well o ff (Consequence) (Antecedent) if they know their own advantages." The natural order is to place the "Antecedent" first ; but this (as you will see from the example above) is not essential. § 4. The meaning, then, of a Conditional proposition, is, that "the Antecedent being assumed to be true, the Con- sequent is to be granted as true also." And this may be considered in two points of view : 1st, allowing that the Antecedent is true, the Consequent must be true ; 2ndly, supposing the Antecedent were true, the Consequent wovM be true. ^!^"^.o. IMAGE EVALUATION TEST TARGET (MT-3) A 4f. 1.0 1.1 11.25 ■^ 1^ III 2.2 ^ 14.0 U IIII1I.6 71 c^ /: '^:> >^ '^ 7 Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 iV 92 COMPENDIUM. TPart n. Hence, there are two kinds of Conditional-syllogism ; Ist, if the Antecedent be (in the minor-premise) grsLnted to be true, the Consequent may ( in the Conclusion ) be inferred : 2ndly, if the Consequent be not true — that is, if its Contradictory be assumed in the minor-premise — ^the Antecedent cannot be true \ that is, its Contradictory may, in the Conclusion, be inferred: since if the Antecedent had been true, the Consequent (which we have assumed to be false) would have been true also. , A Syllogism of the former kind, is called *^ Constructive^* of the latter kind " Destructive" :j^,^i: For instance, if "A is B, X is Y:" let this be the major- premise; then, if you add, "but A is B ; therefore X is Y," this forms a Constructive-syllogism ; if you say *' X is not Y; therefore A is not B;" this is a Destructive-syllogism. Thus "if this river has tides, the sea into which it flows must have tides;" then if I add "this river has tides," it follows in Conclusion, that " the sea into which it flows has tides ;" which is a Constructive-syllogism. If I add " the sea into which it flows has no tides," it follows that "this river has no tides," 'Pm'':n'i^y^i'^,\,m'^iJ'ifx,- ■ ■ ;j.-: § 5. And here observe, by the way, that in hypotheti- cal-arguments we are not concerned with the distinction between affirmative a/nd negative Conclusions. For, of the two members of a Conditional-Proposition, either, or both, may be ajfirmative, or may be negative ; so that we may establish the truth " constructively" of either an affirma- tive or a negative Consequent ; or may ("destructively") establish the falsity — that is, infer the Contradictory — of either an affirmative or negative Antecedent. ^ • a For instance, " if no miracles had been displayed by the first preachers of the Gospel, they could not have obtained a hearing ; but they did obtain a hearing ; therefore some miracles must have been displayer* by them ;" is a Destructive-conditional-Syllogism. The Consequent, as has been said, depends on the Antecedent ; so that, if the Antecedent be true, the Conse- quent will be true also ; but as the Antecedent does not depend on the Consequent, nothing is proved by denying the Antecedent, or again, by assuming the taruth of the Consequent. . Suppose it granted, that " if A is B, X is Y," Lesson ziii.] conditional-proposition. though it may indeed su happen that X is Y, only on thai condition, — ^that is, that if X is Y, A is B, — this is not implied by the original assertion; so that (meretly assum- ing that original assertion), to add that "A is not B," or again, to say " X is Y," proves nothing. - For instance, "if tMs man has committed theft, he de- serves punishment," does not authorize me to proceed either to say "he has not committed theft; therefore he does not deserve punishment;" or again, "he deserves punishment; therefore he has committed theft." For it is (in this case) evident that a man may deserve punish- ment for some oiiher offence. § 6. And you may observe, that the fallacy of affi/rming 'the Consequent and thence inferring the truth of the Ante- cedent, answers to the fallacy (in Categoricals) of undis- irihuted-middle or to that of negative-prerrmes ; as may be seen from the above example. For to say, "every one who has committed theft deserves punishment; and this man deserves punishment," would evidently be a case of undistributed Middle. And again, if instead of saying "if this man has a fever he is not fit to travel; and he is not fit to travel; therefore he has a fever," you say "no one who has a fever is fit to travel," &c., tiLere will be the fallacy of two negative-premises. v > ??^ f v si^tv^ The fallacy again of denying tue Antecedent, and thence inferring the denial of the Consequent, would correspond (in Categoricals) either to an "illicit-process of the Major- term,*' or to the Fallacy of *'two negative-premises," or that of introducing palpably "more than three terms." For instance, suppose instead of saying " If this man has committed theft," &c. you say, " Every one who has com- mitted theft deserves* punishment; this man has not committed theft," (fee. this would be an illicit-process of the Major. Or again, suppose, instead of saying, ".If this man has a fever, he is not fit to travel ; but he has not a fever ; therefore he is fit to travel," you say, "No one who has a fever is fit to travel ; this man has not a fever," &c., this would be to employ "two negative-premises." Again, "If this army is not brave it will not be victorous; it is brave; therefore it will be victorious;" would, if expressed cate- gorically, have palpably more than three terms. If 11 \ v I: n COMPENDIUM. [Part II. . ,: -■* § 7. It is plain, from what has been above said, that a Conditional-proposition may be illatively converted, hy tak- ing the Contradictory of the Consequsnt /or cm Antecedent and (of course) the. Contradictory of the Antecedent for a Consequent. "If A is B, X is Y," implies that '*if X is not y , A is not B." " If all wages be i«gulated by the price of food, an English labourer will have higher wages than an American;" this manifestly implies, that, "if an Eng- lish labourer has not higher wages than an American, aU wages are not regulated by the price of food. ^f This corresponds to the conversion of the categorical- proposition A, "by negation;" ["contraposition;"] every Conditional-proposition corresponding in fact to a Uni- versal-affirmative-Categorical; the Antecedent answering to the Suhject; and the Consequent, to the Predicate. It is evident, that if you thus convert the Major-premise [the hypothetical-premise] of any Conditional-syllogism, you change the Syllogism from ^^Constritctive" to ^^Des- tructive" or vice versS, from Destructive to Constructive. The Proposition "if A is B, X is Y" on,y be conpidered as amounting to this ; "The case [or supposition] of A being B, is a case of X being Y." And then to say (as in the •Minor-premise and the Conclusion, of a constructive-con- ditional syllogism) "A is B; and therefore X is Y," is equivalent to saying "the present [or the existing] case is a case of A being B ; therefore this is a case of X being Y." Or again, "if the Stoics are right, pain is no evil; but pain is an evil; therefore the Stoics are not right," (which is a destructive-conditional syllogism,) may be reduced to a Categorical, thus : "To say that pain is no evil ^is not true; to -say that the Stoics are right ^is ^to say that pain is no evil; therefore to say that the Stoics are right is not true." This Syllogism is in the First Figure. The argument might be exhibited 'n the Third Figure, thus: "that poin is no evil is not true; but that is maintained by the Stoics ; therefore something maintained by the Stoics is not true." In some such way (taking care always to preserve the same sense) any argument may be exhibited in various dif- ferent /orww of expression, (the choice of which is merely a matter of convenience,) so a^ to point out and impress on Lesson xiii.] conditional-pboposition. 1 1 i : 95 ihe mind that the reasoning-process itself is always essen- tially one and the same, aii'l may ultimately be referred to the " Dictum" fbrmeriy mentioned, i^/i 4-v ., ^ § 8. In a disjunctive proposition, as has been already observed, it is implied, that at least some one o/the ** mem- bers" mtist he true. If therefore all except one be (in the Minor-premise) denied, the truth of the remaining one may bo infeiTed. ■ ■ For instance, "either the Gospel was an invention of impostora, or it was a dream of fanatics, or a real reve- lation; it was neither of the two former; therefore it was a real revelation." But if there be more than two members, and you deny (in the Minor-premise) one or more of them, but not cUl except onCf then you can only draw a disjunctive Conclusion : as, " thiseventoccurred either in Spring, Summer, Autumn, or Winter ; it did not occur in Summer or in Winter ; therefore it occurred either in Spring or in Autumn." , In a disjunctive-proposition it is (as has been said above) usually understood that the members are exclusive ; t. e. that ovdy one of them can be true ; and you may, on that supposition, infer from the trvJlh of one of them (assumed in die Minor) the Contradictory of the other, or others. As ** either A is B, or C is D, or X is Y: but A is B ; therefore C is not D, nor is X Y." § 9. A Disjunctive-syllogism may readily be reduced to a ConditioncUy by merely altering the form of the Major premise; namely, by taking as an Antecedent the Contra- dictory of one or more of the members; everything else I'emaining as before. Thus, in the example lately given, you might say " If this did not occur in Summer, nor in Winter, it must have occurred either in Spring or in Autumn;" &C. - -'--'x ■?«^---.ii^^v .■..^^1■^}^;■;:\:S^if -/; Ci^»mii>^; .H».^ . ' A Disjunctive-proposition, you are to observe, is, (as well as a Conditional, ) always affirmative. For, either kind of Hypothetical proposition always affirms the connexion of the members of it, [categorical-propositions contained in it,] whether these be ajQfinnative or negative propositions. Andihe contradictionof a Hypothetical-propositionmust therefore consist in denying thia connexion; which is done, not in a Hypothetical^ but in a Categorical- proposition* 96 CX>MPENDIUli. [Part II. When it is asserted, tHat "if A is B, X is Y" you would contradict this by saying " it does not /oUmo that if A is B, X must be Y ;" or by some such expression. Or when it is asserted that " either A is B, or X is Y, " you might contradict this, by saying *Ht is possible that neither A is B, nor X Y f or you might contradict a Disjunctive-propo- sition by two or more Categorical propositions ; namely, by asserting separately the Contradictory of each member; as " either some Z is Y, or else some W is not X," might be contradicted by " no Z is Y, and every W is X." LESSON XIV, § 1. It will often happen, that you will have occasion to employ that complex kind of Conditional-s^llcgism (con- sisting of two or more such syllogisms combined) whicJt^is commonly called a ^^ Dilemma." When you have before you as admitted tn.^hs two {or more) Conditional-propositions, with differeit Antece- dents, but each with the same Consequent, and these Antecedents are such that you cannot be sure of the truth of any one of them separately, but are sure that one or other must be true, you will then naturally be led to state both of the Conditional-propositions first ; and next, to assert disjunctively the Ajitecedents ; and thus to infer the common Consequent. As " if every A is B, X is Y; and if some A is not B, X is Y; but either every A is B, or some A is not B ; therefore X is Y." , F This kind of argument was urged by the opponents of Don Carlos, the pretender to the Spanish Throne ; which he claimed as heir-male, against his niece the queen, by virtue of the Salic law exclading females ; which was established (contrary to the ancient Spanish usage) by a former king of Spain, and was repealed by King Ferdi- nand. They say, " if a king of Spain has a right to alter the law of fiuccession Carlos has no claim ; and if no king of Spain has that right, Carlos has no claim ; but a king of Spain either has or has not, such, right; therefore (on either supposition) Carlos has no olaiin." , Lesson xiv.] DILEMMA. 97 of Lcli by ras § 2. Wlien several Conditional-propositions have dif- ferent Consequents as well as different Antecedents, then we can only disjunctively/ infer those Consequents : that is, we can only infer that (supposing some one or other of the Antecedents true) one or other of the Consequents must be true. As " if A is B, X is Y; and if C is D, P is Q ; but either A is B, or C is D ; therefore either X is Y, or P is Q." Thus " if the obedience due from Subjects to Rulers extends to religious woi-ship, the ancient Christians are to be censured for refusing to worship the heathen idols; if the obedience, &c., does not so extend, no man ought to suffer civil penalties on account of his religion ; but the obedience, &c., either does so extend, or it does not; therefore either the ancient Christians are to be cen- sured, &c., or else no man ought to suffer civil penalties on account of his religion." So also, "if a man is capable of rising, unassisted, from a savage to a civilized state, some instances may be pro- duced of a race of savages having thus civilized them- selves; and if Man is not capable of this, then, the first rudiments of civilization must have originally come from a superhuman instructor; but either Man is thus capable, or not ; therefore either some such instance can be pro- duced, or the first rudiments," &c. § 3. And when there are several Antecedents each with a different Consequent, then, we may have a Destructive- dilemma : that is, we may, in the Minor-premise disjun- tively deny the Consequents, and in the Conclusion dis- junctively deny the Antecedents. Or again, you may have a Dilemma partly Constructive and partly Destmotivu; that is, in the Minor-premise (which in a Dilemma is always a disjunctive-proposition) the members — suppose for instance there are two, — may be, one of them, the assertion of the Antecedent of one of the Conditional- propositions, and the other, the contradictory of the Con- sequent of the other Conditional. Suppose we say, "if X is not Y, A is not B; and if P is not Q, C is not D; but either A is B, or C is D; there- fore either X is Y, or P is Q;" this would be a Destruc- tive-Dilemma; and you may see that it corresponds ex- actly with the example given a little above, only that we E 'i^ ! 98 COMPENDIUM. [Part II. have, here, converted both of the Conditional-propositions. (See § 7 of the preceding Lesson). If we had converted one only, and not the other, of the Conditionals (as *'if A is B, X is Y; and if P is not Q, C is not D ;" ko.), then the Dilemma would have been partly Constructive, and partly Destructive. For, as has been formerly explained, the Difference between a Constructive and Destinictive Syllogism consists merely in the form of expression, and it is very easy to reduce either form into the other. |; y It may be worth while to observe, that it is very com- mon to state the Jfmor-premise of a Dilemma first ; in order to show the more clearly that the several Categorical propositions which are, each, doubtful, when taken sepa- rately, may be com"jined into a Disjunctive-proposition that admits of no doubt. And this Minor-premise being disjunctive, some have hence been led to suppose that a Dilemma is a kind of disjunctive argument ; though it .8 really, as we have shown, a Conditional. . i .,.; ..i The name of "i>ilemma," again, has led some ,to sup- pose that it must consist of two members only; though it is evident that there may be any number. § 4. When there is a long Series of arguments, the Conclusion of each being made one of the Premises of the next, till you arrive at your ultimate Conclusion, it is of course a tedious process to exhibit the whole in the form of a series of Syllogisms. This process may, in many cases, be considerably abridged, without departing from the strict syllogistic form: [that is, such a form as shows the conclusiveness of the reasoning, from the expression a?owe, independently of the meaning of the Terms, and equally well when arbitrary Symbols are used to stand for the Terms]. What is called a "Sorites" (from a Greek word signify- ing a heap, or pile) is such an abridged form of stating a train of arguments. When you state a series of proposi- tions in which the Predicate of the first is made the Sub- ject (distributed) of the next, and the Predicate of that, again, in like manner, the Subject of the next, and so on, to any length, you may then predicate in the Conclusion, the Fredicate) of the last Premise of the Subject of the first. .. ., Lesson xiv.] SORITES. 99 y- I '" Tlius "A (either "some" or "every") is B; every B is C; every C is D ; every D is E; 100 OOMPENDICH. [Part II. its Jfmor-premise, the first of them ; and the Conclusion of this first syllogism will be a proposition which is (in the Sorites) not expressed but understood ; and which will be the Minor-premise of the next Syllogism. And of this next syllogism the Major-premise will be the third that is expressed in the Sorites ; and so on. For instance (1st), "every B is C ; A is B;" ["therefore A is C"] ; (2ndly), "every C is D j" ["A is ; therefore A is D'% &c. The portions enclosed in brackets are those which in ; the Sorites are understood. The only J/inor-premise expressed in the Sorites is the first proposition of the Series; all the succeeding Minor- premises being understood. And hence it is that (as has been above said) this firs is the only ono of all the Premises that may allowably b a Particular: because, in the first Figure, though th Minor may be either Universal or Particular, the Majo (as you see from what was formerly said of the "Dictum") must always be Universal ; and all the premises in th Sorites, except the first, are J/a/or-premises. In this way may also be explained what was above said, that the last of the premises of a Sorites is the only om that can allowably be a Negative; since if any of th others were negative, the result would be that one of thi Syllogisms of the Series would have a negative Mino; premise; which in the first Figure (as you will see b again referring to the " Dictum") is inadi^issible. ' § 7. A Series of Conditional-&y\\ogi%m^ (which corr spend, as has been shown, to Categorical-syllogisms in th| first Figure) may in like manner be abridged into a Soriti by making the Consequent of the first proposition tlij Antecedent of the next ; and so on : and then drawing t Conclusion by either assciting the first Antecedent, ai thence (constructively), inferring the last Consequent, else, denying the last of the Consequents, and (destruj tively) inferring the Contradictory of the first Antecedei As "if A is B, C is D; and if C is D, E is F; and if is F, G is H," Lesson xv.] DIFFERENCE. 106 Species. As, ' ' What is a pen f answer, an * ' Instrument ;" [a kind or species of Instiniment ;] " What is a circled' "A curvilinear-plane-figure:" so also "a Magnet" would be said to be a " Species [or kind] of* Iron ore," <^c. When you are asked ''What kind of [or "what sort of] instrument is a pen]" you would answer. One designed for writing ;" this being what characterizes it, and distin- guishes it from other instruments; " What kind of animal is Man?" the answer will be " Rational;" as distinguish- ing the Species from other animals; "What kind of plane- curvilinear-figure is a circle?" answer "One whose circum- ference is everywhei'e equidistant from the Centre;" which circumstance distinguishes it from an Ellipse: ka. Such a Predicable then is technically called the ^^ Dif- ference;'^ [or by the Latin name "Differentia;"] in pop- ular language, frequently, the "Characteristic," or the "distinguishing point." And tlio '''Difference" together with the "Genus," are technically spoken of as ^^consti- txUing ["making-up"] the " Species." Any quality [or "attribute"] which invariably and peculiarly belongs to a certain Species, but which yet is not that which we fix on as characterizing the Species, is technically called a '•'- Property [or " Proprium"] of that Species. Thus "risibility" [or the faculty of laugh- ter] is reckoned a " Property" of Man: one of the " Pro- perties" of a Circle is, that any angle drawn in a semi- circle is a right-angle: &c. The power of "attracting iron" might be taken as the "dif- ference [or "characteristic"] of a Magnet; and its "Polarity" as a " Property:" or again, this latter might be taken as its Difference, and the other reckoned among its Properties. For it is evidently a mere question of convenience, which in any such case we fix on as the Characteristic of the Species M'e are contemplating. And either the one arrange- ment, or the other, may be the more suitable, according to the kind of pursuit we may be engaged in. An Agriculturist, for instance, (see Lesson VIIT. § 5), would not characterize each kind of plants in the same way as a Botanist, or again, as a Florist ; no more would a Builder and a Geologist, and a Chemist, characterize in the same way the several kinds of stones. 106 SUPPLEMENT. [Part ill. § 3. Any Predicable which belongs to some (and not to other) individuals of the same Species, [or which *'may be present or absent, the Species remaining the same,"] is called an ^^ Accident." ^ And these are of two kirids. A " Separable-accident" is one which may be remove jrom the Individual; [or, which miy be absent or present, in that which we regai'd as one and the same individual;] as, for instance (in an example formerly given), the "Sun ' is regarded as the same indivi- dual thing, whether "rising," or "setting" or in any other situation relatively to the spot we are in: "rising," there- fore, or, "setting" are separable accidents of the Sun. So also, to be in this or that dress or posture, would be a separable-accident of an individual man; but to be a native of France, or of England, or to be of a ceitain tharacter, would be " inseparable-accidents." It is by inseparable accidents that we commonly distin- guish one Individual from another of the same Species, and to enumerate such accidents is called "giving De- 8criptio7i." (See below, § 10.) Of course it is only from individuals that any "Accident" can be "inseparpble;" for anything that is inseparable from a Species, [or, which forms a part of the signification of a Term by which we denote a certain Species,] is not an Accident, but a Property. § 4. Some writers enumerate among Properties siich Pre- dicates as are peculiar but not universal; that is, which do not apply each to every individual of a certain species, but are peculiar to that species, as Man alone can be "vir- tuous," — can be a "philosopher," &c., which are attributes not belonging to man. But these are more correctly reck- oned Accidents, though Accidents peculiar to the Species. Some again speak of " Properties" which are universal but not peculiar ; as "to breathe air" belongs to the whole human species, but not to that species alone. Such a Predicable however is not, strictly speaking, a Property of the Species "Man," but a property of a higher [more com- prehehsive] Species, "land-animal;" which stands in the relation of ^' Genus" to the species "Man." And it would be called accordingly, in the language of some writers, a "generic-property of Man." A Proper+y, strictly so --V Lesson iv.] DIVISION. 107 called, of any Species under our consideration, would be called its "s/)eci/fc-propei'ty." Predicables then have been usually divided into these five heads: *' Genus, Species, Dillsrence, Property, and Accident." You are to remember, that as every Predicable is so called iVi relation to the Terms of which it can be (affirmatively) predicated, so, each Common-term is to be regarded as belonging to this or that Head of Predicables, according to the Term to which it is in each instance applied, or which may be applied to it. Thus the term " Iron-ore" is a Species in respect of the term "Minerai," and a Genus in respect of the term " Magnet ;" and so in other instances. §5. When we "enumerate c^z^JiJmc^/?/" [or "separately"] the several things that are signified by one Common-term, — as the several Species included under some Genus — we are said to ^^ divide'' that Common-term. Thus, "natural- productions" are divided into "Animal, Vegetable, and Mineral ;" and each of these again may be subdivided into several "members;" and so on. Perhaps the word ^^distinguish" if it had been originally adopted, would have been preferable to ^' divide;' (which, however, has been so long in geno-al use in this sense, that it could not now be changed;) because ^^ Division" being (in this sense) a metaphorical word, the ^'Division'* we are now speaking of is liable to be confounded with "Division" in the other (which is ilie original and proper) sense of the word. "Division," in its primary sense, means separating from each other (either av^tually, or in enumeration) the parts of which some really-existing single object consists : as when you divide "an animal" (that is, any single animal) into its several members; or again, in'^o its "bones, nmscles, nerves, blood-vessels," &c. And so, with any single Vegetable, &c. Now each of these 2mrts into which you thus "physically" (as it is called) divide "an animal," is strictly and pro- perly a "part," and is realli/ less than the whole; for you could not say of a bone, for instance, or of a limb, that it is "an i!Lnimal." In the very same sense, we divide any Group ["Class"] of ohjects, by separating (actually or mentally) those 108 SUPPLEMENT. lif^m! objects from each other; as, when all the Cattle on a farm are divided into cows, horses, sheep, &c., or again, when the horses are divided, that is, placed separate from each other. Each horse is, here, actually less than "all the horses;" and again, all the horses, less than "all the Cattle." But wo commonly designate each Group [or Class] by a term that is applicable not merely to the whole Class col- lectively, but to each one of the objects thus placed to- gether: as, for instance, the term "Metal" may be applied not only to all the Metal that exists, but to any kind of Metal, and to any portion of each kind; and so also " Iron" may be applied not only to all the Iron existing, but to any individual piece of Iron. And hence men have been led to employ the word "divide" metaphorically, (as has been said above,) in reference to the term itself which denotes a Class; as, when we speak of dividing "Metal" — that is the Genus "Metal" — into Gold, Silver, Iron, &c., or "Animal" — that is, the Genus "Animal" — into Beast, Bird, Fish, &c. Now when you thus — in the secondary sense of the word — "divide" a Genus, — that is, the term denoting a Genus, — each of the parts [or "members"] is metaphorically called a " part," and is, in anothei* sense, more than the whole [the Geaus] that is thus divided. For you may say of a Beast or Bird that it is an "Animal;" and the term "Beast" implies not only the term "Animal" but something more besides; namely, whatever "Difference" characterizes " Beast" and separates it from " Bird," " Fish," &c. And so also any Singular-term [denoting one individual] implies not only the whole of what is understood by the Species it belongs to, but also more; namely, whatever distinguishes that single object from others of the same Species: as "London" implies all that is denoted by the term " City" and also its distinct existence as an individual city. § 6. The "parts" ["members"] in that figurative sense with which we are now occupied ^ are each of them less than the whole, in another sense; that is, oiless comprehen- sive signification. Thus the Singular-term "Bomulas" embracing only an individual king, is less extensive than the Species "King;" and. that, again, less extensive than th 3 Genus " Magistrate," &c. ■■i.--* > Lesson x.v.] DIVISION. 100 ':'.' -• An " /wdividuar* thon is socallec] from its being incapable of bei.'if/ (in this figurative sensa) divided. :> And though tlie two senses of the word "Division" are easily distinguishable when explained, it is so commonly employed in each sense, that through inattention, confu- sion often ensues. We speak as familiarly of the "division" of "Man" (meaning Mankind) into the several races of " Europeans, Tartars, Hindoos, Negroes," Sic, as of the "division" of the Earth into "Europe, Asia, Africa," etc., though "the Earth" [or "the World"] is a singular term, and deriotes what we call 07ie Iniioidual. And it is plain, wo coald not say of Europe, for instanca, or of Asia, that it is a " World." But we can predicate " Man " of every individual European, Hindoo, &LQ. And here observe, that there is a common colloquial in- correctness (increasing the liability to confusion) in the use of the word "division" in ea^h of these cases, to denote one of the '■^pai'ta" into which the whole is (iivided. Thus you will sometimes hear a person speak of Europe as one "division" if the Earth : or of such and such a "division" of an Army : meaning ^yortion." And so again a person will sometimes speak of "animiils that belong to the feline division of the Carnivora " [flesh eating animals] meaning that portion of the Class " Carnivora." § 7. Division, in the sense in which we are here speak- ing of it, (the figurative,) is evidently the reverse process to "Generalization." (See Lssson VII. § 4.) For as, in generalizing, you proceed by laying aside the differences between several things, p nd abstracting that which is com- mon to them, so as to denote them, — all and each, — by one Common-term, so, in dividing, you proceed by adding on the differences^ so as to distinguish each by a separate term. When you take any Common-term to be divided and sub- divided, for any purpose you have in hand, — as, the Term "Animal" in a work on zoology — that term is called your ^^Summum [highest] genus, ^^ the several Species into which you proceed to divide it, and which are afterwards divided each into other Species, are called, each of them, a " Sub- altern" Species or Genus; being, each, a Species i!n relation 110 SUPPLEMENT. [Pai-t III. to that which can be predicated of ifc, and a Genus in re- lation to the Species of which it can be predicated. Thus "Iron-ore" (in the example lately giv^en) is a Sub- altern Species, or Genus in relation to "Mineral" and to "Magnet" respectively. Any Species that is '■^ 7iot made a Genus of any lower Species," in the division you ^^appen to be engaged in, — or, in other words, which is not regarded as any further divisible except into individuals, — is asually called (by the Latin name) "m/?wiGr/ Species;" that is, the ^Howest Species." " Proximum Genus" is a technical name often used to denote the '^ Genus-next-above" [or " nearest,"] the Species you may be speaking of; as "Iron-ore" would be the "nearest" [proximum] Genus, of Magnet; and " Mineral" would be its more remote Genus ; that is, the Genus of its Genus. § 8. It is usual, when a long and complex course of Division is to be stated, to draw it out, for the sake of clearness and brevity, in a form like that of a genealogical "Tree." And by carefully examining any specimen of such a "Tree" (going over it repeatedly, and comparing each portion of it with the explanations above given) you will be able perfectly to fix in your mind the technical terms we have been explaining. Take for instance as a "Summum-Genus ' the mathema- tical term. "Plane-superficial-figure." :■ I I I Mixed Figure Rectilinear Figure Curvilinear Figure (of Rect. and Curv.) Triangle Quadrilateral, / :fV t if liCSSOn XT.] THEE OP EXPRESSION. ;i" .1 J-, ,,•(■ '.^ .jji^i . i./f':- >. I 00 09 «- & e as much subdivision as the occasion may require : and not a mere catalogue of the "lowest-Species,"omittingiVi,'3?*m<36Zi«V//i--\.;-«' - . *. _. J ..-*^;ii...>,i. . V.-ihli^til-'^ilfei&i ■ttllM.ikjZi' Lesson xv.] RULES FOR DEFINING. 115 ideas speak of, but,— the Terni itself, regarded as a *^>)l(/n,'^ tkc, aH was forinoi-ly expluiiiod. And in many cases, acconlingly, tlio "Nominal" and the " Real" Doliiiition do coincido. But by a "i\'om//m/-doti- nition, is moant (strictly spcnkin*^), one which expresses exactly what the Name itself conveys to evertj-one who understands that name : and nothlmj beyond this. And any Definition may be called (in a greater or less degree) a iteaWefinition which explains anything — more or less, — heyoiid what is necessarily implied in the Name itself. Thus, any one who gives suc^» an account of some one of the " metals" for instance, or of the " Sun," as modern researches would enable him to give, would be advancing beyond a mere Nominal-definition; since, in this latter, — the mere explanation of the words "iron" or "sun" — we and our ancestors 500 years ago, would coincide; since both they and we use those words in the same sense; thoiigh they knew much less than we do of the nature of those things. In the case of strictly-scie^iii/ic-terms, the Nominal and the Real-definition may be regarded as coinciding. Thus^ the mathematical-definition of a Circle, may bo considered as strictly "Nominal," inasmuch as it denotes precisely the same as the word "Circle," and nothing beyond; every name being (in Mathematics) regarded as merely the "de- finition abridged." And again, it may be regarded as so far a "i?ea^-definition," that it conveys all that can belong to the thing spoken of, since there can bo no property of a Circle that is not in fact implied in the dejinitlon of a Circle: or, which is the same thing, in the name, "Circle." It is therefore as much of a real-definition as can conceiv- ably be given of a Circle. And so with other scientific-terms. In respect of these, in short, the meaning of the name, and the nature of the thing, are one and the 8a7ne. And accordingly, in Mathematics, the definitions are the Princiiiles from which our reasonitigs set out. On the other hand, since a "diamond," or a "planet," or a "sheep," &c., have each of them (that is, each indivi- dual of any such Species) a real, actual existence in nature, independently of our thoughts, any of these may possess attributes not implied in the meaning we attach to the 1 .11 I '^ iMM 116 SUPPLEMENT. [Part III. name; and which arc to be discovered by observations and experiments. Any explanation, however, of the nature of any object beyond what is implied in the signification of its name, is not usually called a "Definition; but the word " Description" is often used to denote such an explanation. § 13. What we are concerned with at present is " Nominal-definition ;" it being important with a view to Reaaoniiig, to ascertain the exact sense in which each Term is employed, and especially to guard against any ambiguity in the Middle-term of an Argument. The rules [or cautions] commonly laid down in various treatises for framing a Definition, are very obvious: namely, i. That a Definition should be ^'adequate;" i. e., com- prehending neither more, nor less, than the term to be defined. For instance, if in a definition of " Money" you should specify its being " made of metal," that would be too narrow, as excluding the shells used as money in some pares of Africa : if again you would define it as an "article of value given in exchange for something else," that would bo too widCf as it would include things exchanged by barter ; as when a shoemaker who wants cdals, makes an exchange with a collier who wants shoes.* And observe, that such a defect in a Definition cannot be remedied by making an arbitrary exception; (such as was alluded to above, § 10;) as if for instance and it is an instance which actually occuri'ed) a person should give such a Definition of " Capital" as should include (which he did not mean to do) "Land;" and should then propose to remedy this by defining "Capital" any "property of such and such a description except Land^ ii. The other caution usually given, is, that a Defini- tion should be clearer than the Term defined : clearer, that is, to the persovis you are speaking to : since that may be obscure to one man which is intelligible to another. And this rule evidently includes (what some give as a third rule) a caution against excessive prolixity, excessive brevity, and ambiguous language. '^ See Lesson I, on Money Matters. rt* f 117 PAIIT lY. FALLACIES. LKS80N XVr. § 1. Although siitulry kiuda of Fanacioa h.avo heon from tiriio to time noticed in tlio forgoing LosHon«, it will bo worth while to make some furth(n'ol)servations thereon. By a " Fallacy" is commonly meant ** any deceptive argument or ai)paront argument, whereby a man is him- self convinced — or endeavours to convince others — of something which is not really proved." Fallacies have been usually divided into two Classes ; those in the form, and those in the matter : though the diflference has not been in general clearly explained. The clearest wtiy of proceeding will be to consider a " Fallacy-in-fotm" as one in which the Conclusion does not really follow from the Premises ; and a " Fallacy-in- matter" as one where the Conclusion does follow from the Premises, though there will be still something faulty in the procedure. In this latter case (where the Conclusion does follow) one may either object to the Premises as being " unduly- assumed," or to the Conclusion as irrelevant; that is, different, in some way, from what ought to have been proved — -namely, from what was originally maintained, — from what had been undertaken to be established, — from what the particular occasion requires ; &c. These that have been mentioned (as the ** Fallacies-in- form," and " in matter") must evidently include every possible Fallacy ; since whatever objection can be brought against any argument, or apparent argument, must be an objection either against the Conclusion, or against the Premises, or against the connexion between the premises and conclusion ; that is, against the conclusiveness of the apparent argument. § 2. " Fallacies-in-form," [in which the Conclusion does not really follow from the Premises] are such as we have ■■I 118 FALLACIES. fl>art IV. r"^': t:.^ already given examples of, as violations of the rules above- explained : such as "undistributed-middle," — "illicit-pro- cess," tkc. Among others was noticed the fault of an " equivocal Middle-term," taken in one sense in the one premise, and in a diflerent sense in the other. And since this Fallacy turns on the meaning of tvords, and not on the mere form in which the argument is expressed, some may be disposed to rank it rather under the Head of " Fallacies-in-matter." The most convenient course, however, will be to keep to the division already laid down; and, accordingly, to reckon the Fallacy of "equivocal-middle" along with all the others in which the conclusion does notfoUoiv from the Premises. And, in truth, the technical rules do apply to this — the "Fallacy of equivocation" — as soon as it is ascertained that the Middle-term is employed in two different senses, and consequently is, in reality, not one, but two terms. But of course the rules of Syllogism do not, alone, enable us to ascertain the meaning or meanings of any Term. That must be judged of from our knowledge of the subject-matter, — from the context, [or general drift of the discourse] — and often from what we know or believe concerning the writer or speaker. And the same may be said, in many cases, in respect of not only the signification, but also the distribution or non- distribution, of a Term ; on which depend the fallacies of "undistributed-middle" and "illicit-process." For when a Proposition is expressed indefinitely (as " Man invents arts ;" " Man is mortal ;") we are left t.^ judge from the subject-matter, &c., whether it is to be understood as Universal or as Particular. And again, the sign "all," (which in an Affirmative-pro- position, denotes Universality) in a Negative-proposition, generally, though not invariably, indicates a Pai'ticular ; that is, usually, though not always, the negation is under- stood as a negation of universality. For instance, of these two propositions, " all they that trust in Him shall not be confounded," and " we shall not all sleep," the one would be understood as Universal, and the other, as Particular. Observe also that the sign "all" is sometimes under- Btood as meaning ^^dXl-coUectively f^ sometimes "every-one, ,.i-.\- yj-^-'^^iri (J- !<^ Tr.?! Lesson xvL] EQUIVOCATION. 119 separately ." As " all the apples on that tree are enough to fill a bushel ;" i.e., all together; and " they are a/' ripe;" i. e., every wie. If this ambiguity be overlooked, two propositions, both true, may appear to be Contradictories. For instance, "All these apples are worth twenty shillings ;" and " Some of these apples are not worth twenty shillings." The right contradictory would be "All these apples together are not worth twenty shillings." There is an ambiguity answering to this, in the word " some," which ocasionally means " some definite one," and occasionally, ^^ either onQ or else another." For in- stance, if I say " some food is vegetable," I mean that '' there actually exists some kind of vegetable food ;" and this being true, its contradictory, "no food is vegetable," must be false. But if I say "some food is necessary to life," the apparent co'" tradictory, "no food is necessary to life," is, in a certain sense, true ; for there is no one definite article of food of which it can be said that it is necessary to life. But some article of food or other is necessary ; which is the meaning of the original proposition ; and the real contradictory to it will therefore be, "all food is not neces- sary to life ;" i. e., " life may be supported without any food at all." [See § 12 of this Lesson.] § 3. You are to observe that we cannot always decide absolutely as to which Class we should pronounce some particular fallacy to fall under, those in "form" or those in "matter:" because it will often happen, when an argument is stated (which is usually the case) as an Enthymeme, that the suppressed premise may be either one which is false, but which tvoidd, if granted, r^ake the Syllogism complete : or else one which is t7-ue, but which would not complete a regular Syllogism.. Now, on the former supposition, the Fallacy would be in the ''7natter;" on the other supposition, it would be in the ^^forni." For instance, in this Enthymeme, "The Country is dis- tressed ; therefore it is misgoverned," we cannot decide absolutely whether the premise meant to be understood, is, " every Country that is distressed is misgoverned ;" whicn would make the syllogism correct, but would not be admitted as true; or, every Country that is misgoverned ■:*f "l"*':^-" ■^^^t:^'^^-'''^'C^ 120 tW^^^r^ ' FALLACIES. [Part IV. is distressed ; which woukl leave the Middle-term undis- tributed. And again, when both Promises are expressed, it will often happen (as in an example formerly given) that we have the alternative of either denying the truth of one of the premises, — supposing the Middle-term used in the same sense in both — or denvinsr the conclusiveness of the armi- ment, supposing the Middle-term used in each premise m such a sense as to make that j)remise true. If by ^^ contrary to experienced^ you mean two different things, in the two premises, respectively, then, each is, by itself, true, but they prove nothing: if you mean by it the same in both premises, respectively, then, one of them is untrue. § 4. But observe, that when you mean to charge any argument with the fault of " equivocal-middle," it is not enough to say that the Middle-term is a word or phrase which admits of more than one meaning; (for there are few that do not;) but you must show, that, in order for each premise to be admitted, the Term in question must be understood in one sense (pointing out lohat that sense is) in one of the premises, and, in another sense, in the other. And if any one speaks contemptuously of "over-exact- ness" in fixing the precise sense in vdiich some term is used, — of attending to minute and subtle distinctions, &c., you may reply that these mi^iute distinctions are exactly those which call for careful attention; since it is on/;y through the neglect of these that Fallacies ever escape detection. For a very glaring and palpable equivocation could never mislead any one. To argue that "feathers dispel darkness, because they are Ught" or that " this man is agreeable, because he is riding, and riding is agreeable," is an equivo- cation which could never be employed but in jest. And yet, however slight in any case may be the distinction between the two senses of a Middle-term in the two pre- mises, the apparent-argument will be equally inconclu- sive ; though its fallaciousness will be more likely to escape notice. Even so, it is for want of attention to minute points that houses are robbed, or set on fire. Burglars do not in general come and batter-down the front door; but climb in at some window whose fastenings have been neglected. '•pw^ Lesson xvi.] EQUIVOCATION. 121 sscape And an incendiary, or a careless servant, does not kindle a tar-barrel in the middle of a room, but leaves a lighted turf, or a candle-sn .ff, in the thatch, or in a heap of shavings. In many cises, it is a good maxim, to " take care of little things, and great ones will take care of themselves." § 5. Of the Fallacies of " undistributed-middle " and of "illicit-process," ». ' Lesson xvi.] ANALOGY. 123 the te (in » from elves. But instances of this kind are far less common than those in which the same name is applied to two things, not from their being themselves similar, but from their having similar relations to certain other things. And this is what is called "Analogy." Thus, the sweetness of a "sound" and of a "taste" can have no resemblance; but the word is applied to both, by analogy, because as a "sweet" taste gratifies the palate, so does a "sweet" sound the ear. Thus also we speak in the "secondary" [or "transferred," or "analogical"] sense of the "hands" of a Clock, — the "legs" of a Table, — the "foot" of a Mountain, — the "mouth" of a River, &c.; which words in their "primary" ["proper," or original] sense, denote the "hands" of a man, — the "legs, foot, and mouth" of animals; from the similar relations in which they stand to other things respectively, in refe- rence to use, position, action, &o. The words pertaining to Mhid may in general be traced up, as borrowed, (which no doubt they all were, originally) by Analogy, from those pertaining to Matter: though in many cases the primary sense has become obsolete. Thus "edify,"* in its primary sense of "buildup,"! is disused, and the origin of it often forgotten; although the substantive "edifice" remains in common use in a corresponding sense. When, however, we speak of " weighing" the reasons on both sides, — of "seeing" or "feeling" the force cf an argument,— "imprinting" anything on the memory, &c., we are aware of these words being used analogically. It is in an analogical sense that " Division," " Part/' and several other technical terms, have been employed in these I I a ''I at to Lesson xvi.] FALLACY-IN-MATTER. 133 whether a brute or a madman — can never be deterred from any act by apprehension of punishment," (as for instance a dog, from sheep-biting, by fear of being beaten,) you prove that "the beating of one dog does not operate as an example to other dogs, !' 136 DIFFERENT KINDS OP ARGUMENT^. [I*art V. occasion, the Conclusion maintained — we are naturally led to inquire concerning the diflferent kinds of Arguments one often finds alluded to in books, or in conversation. These are in general very indistinctly described, and confusedly enumerated. We hear persons speaking of " Syllogistic Reasoning," and such as is not "Syllogistic;" — of "Categorical, or Hypothetical Arguments," — or "Demonstrative, and Pro- bable, [or Moral] Reasoning ;"^ of " Direct and Indirect Arguments;"— of "A priori Arguments," "Arguments from Testimony," — from "Analogy," — from "Example"— by " Parity-of-Reasoning," &c., without any distinct account being given of these and other modes of procedure. In reality, to enumerate thus confusedly the several kinds of Argument, is to commit the fault formerly noticed in reference to "cross-divisions;" there being, in this instance, no less than four different divisions ; which ought not to be bleDf''?d together. Fimc. The division of Arguments into irregular and syllogistic, and of Syllogisms again, into Categorical and Hypothetical, &c., is a division, strictly speaking, not of Arguments themselves, but of the forms of stating an argument. For it is manifest (as above explained) that one individual argument may be stated in a Hypothetical or in a Categorical form, and in the first Figure, or in the second, &c. Secondly. The division of Arguments into probable and demonstrative is evidently according to the subject-matter: and is strictly, not a division of Arguments, considered as arguments, but rather, of the Propositions they consist of, in respect of the "matter" of those propositions. § 4. Thirdly. Arguments are divided into ^^direct" and *'indii'ect" according as your object is to establish either the truth of the Conclusion, or the falsity [the " Contra- dictory"] of one of the premises. For when we arrive by sound reasoning, at a false Conclusion, it is plain that one at least of the Premises must be false. In short, every valid argument may be stated in the form of a Conditional Proposition; *^If the Premises are true, the Conclusion is true;" then, supposing you admit the Premises to be true, you must admit the truth of the Leoion xvii.1 two classes of arguments. 137 )i the les are ladmit of the Conchision; (which corresponds to a Constructive Condi- tional-syllogism;) and hence also, supposing you find the Conclusion false, you must admit that the Premises, or one of them, cannot but be false ; since if they were both true, the Conclusion would be true : and this corresponds to a Destructive Conditional-syllogism. Now the above is evidently a Division, not strictly speaking, of Arguments^ but of the purposes for which any Argument may be designed : namely, either to prove its Conclusion, or to disprove one its Premises. For the same individual Argument may answer both purposes in different persons. For instance, "Whatever is maintained by the Stoics (or by such and such a philoso- pher, sect, party, &c.) must be admitted; that pain is no evil (or such and such a doctrine, whatever it may be, in each instance) is so maintar.ied: therefore this must be admitted :" now a zealous partizan would be so fully convinced of the Premises that he will assent to the Con- clusion : others may be so revolted by the Conclusion, that they will thereupon reject the Major-premise. The Argument therefore will, to the one, be "ilirect," and to the other ''indirect." § 5. Fourthly. When we speak of arguing from a Cause to an Effect, or of arguing from Testimony to the truth of what is attested, or again, from a known case to a>' unknown similar case, &c., these kinds of arguments are distinguished fi'om each other " according to the relation existing between the Premises and the Conclusion, in respect of the subject-matter of each." This then, and this alone, is properly a division of Arguments, as such. When we say, for instance, that in arguing from the "fall of rain" to the consequent "wetness of the roads," the Premise is a Cause, and the Conclusion drawn, an Effect, it is evident we are not speaking of the more syllogistic connexion of the Premise and Conclusion ; (which, as was formerly explained, is always the same ;) nor again are we speaking of the subject-matter of those Propositions (as in the second Head) considered, — each by itself — merely aa Propositions, independently of the Argument, for "Cause," and "Effect" are relative words; and the Premise is called ";1|1J \i*.^Sifmm*i^mfti ■■r^r^*^i^■ TV 138 DIFFERENT KINDS OF ARGUMENTS. [Part V. a Cause ©/"that Effect which is inferred in the Conclusion. So that it is the relation, in respect of matter, of the Premise to the Conclusion, that we are speaking of. And so also in respect of Arguments from Testimony, and the other kinds that have been alluded to. § 6. Arguments, then, may be divided, first, into two classes : First, such as might have been used to account for the Conclusion, supposing it had been already granted; and secondly, those which could not. Or, in other words, first, Arguments from Cause to Effect ; and, secondly, all other kinds. For instance, if I infer from a "fall of rain" that "the roads must be wet," I am using an Argument of the former Class [an "A-priori- Argument"]; since if it were known, and remarked by any one, that the roads are wet, I should account for that fact by informing him that it had rained. Or again, if a person were knoum to have committed a murder, and it were inquired how he came to perpetrate such a crime, then, any one would be said to account for it, [to show why he did it,*] by saying that he was a man of ferocious and revengeful character; or that he was known to bear malice against the deceased; or to have an interest in his death, ct the »any re- ises; as led the Lcreased d their lid thus 3 would If the earth should yield two bushels of com, or two tons of iron or lei«d, for one that it now yields, these articles would be much cheaper ; wliile a bushel of com would be as useful in feeding us, as now; and so with most other c.i'ticles. But if the supply of gold or silver were thus doubled, the chief use of these being for coin, and the utility of coin depending on its vahie, the only importi-nt change would be that a sovoreign or a shilling vrould bo tvrice as large as now ; and therefore twice aa cumbro'.is. So that no advantage won Id rocult. It is manifest that in a train of E-ensoning, it will often happen that Geyerai of the different kinds of argument we have spoken of will be combined. Thus we may per- haps have < o prove by several Sramples, the existence of a certain "CauBo;" end from that cc/ase to infer a certain "Effect;" and that efieet again misj be employed as a "Sign" to infer a certain " Condition,". &c. In this, and the prsc3ding Lessons, ijcvers,! interesting subjects haTO been veiy eiightlj uoushed on, which may be found more fully treated ot^ and ths^ vie^/s now taken more developed, in treatiises on those jeveral subjects.* If you proceed, in following up this course of study, to peruse such treaoises, you will have been prepared, it is hoped, to find that pemsal the easier and the more inter- esting, from what hcuS been explained in these Lessons : and you will be the better able to understand what is valuable, in other works on such subjects, and to detect anythiiig that may be erroneous. * In the EUnenta of Rhetoric, Part L, the subjects of tl''s last Lesson are more fuUy treated of. . . ,-, ■ f i ■, ,,1. ., 'jr • X UW4 I- ^H* ^:-.*f ■i/ • ' f .. 'f ,r.* \ ^> 'I ;■ n # / f flfi *, « -^ - / ' * , r: * ^ < , . «:i< '**•) .*N N f ! ; %' * ■, s* 'W* ^> »■ ' t-^r -•■it'- ... .»■•. ■?-;;i' 149 INDEX. [To be made by the Student] Lesson. § Page. h A i •■>, •- i.ii ' i M ii ! K » " ' : - "ai^ivg " «aiagtiiL.iL,(i i iMMLMB 150 \ INDEX. Lesson. § Pag©- .. 7 ■::■,;, ,--t./!<%^iJi,| ^ ■"■ ■■*,■',■ V;.f. ,t e. ■ ■■it'.:,' •■.,.^ A ::f-,I ->J: INDEX. i -' ■■■ ■*" Lesson. § 151 Page. 152 5 , : INDEX. ..» Lesson. § Page. ♦ , •,-!(■ \ x>'> ■ INDEX; > i:i/i Lesson, § lit: Page. »,'',■->!■ ' i S*,; 104 • - \ ' \'\ '■'■' ;'. *- ■ ;'!■■■ ,' .'X-'v' • ■ - ",■■'■ i/-^ \ -■** '^*,'- .A" ' ■ " I - * • \ '.. :' "-if I , .1,1' ;, ', , ■'! INDEX. Ii«sson. § Page, ... V i-> 56. ■■%. '^'■ :h:-y^ i ^ Lesson. § Page. » , •►■. > mmmmm f1 ; ^r ^ IH nn>iz. Lesson, f Pagei I,!"/'' -♦-:•;- ; nfW3|». .!>r;.i^ .ooaaeCC v^"^ leaioiL { Page. ■%.' IM^ 'i^f "i totmia Lmmo. I Pigt. -4-'(t--. X :t" HiE^ *J. % V. 'f'. t * ■ \: LesfiOD. § Pige. -,',f^;',-( 1 ■*^'; ^:.*:V ifioo. f Page. ;ii",,;v „H- '■»•::■-■■ 1'-'' _ ■ ( '■ '■.:>>■ fc';i-r._ ,^s^ -.• I ■.*«?T V ■^>^-