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THE 
 
 ELEMEJNTS OF LOGIC 
 
 CAPACITY OF YOUNGER STUDENTS. 
 
 DESIGNED FOR ACADEMIES AND THE HIGHEK 
 CLASSES OF COMMON SCHOOLS. 
 
 By CHARLES K. TRUE, D.D. 
 
 Nihil difficile amantL—OiOBRa 
 
 NEW YORK : HUNT & EATON 
 CINCINNATI : CRANSTON & CURTS 
 
 UNIVERSITY i 
 

 Entered according to Act of Congress, in the year 1860. 
 
 Bt CARLTON & PORTER, 
 
 in the Clerk's Office of the District Court of the United States foi 
 the Southern District of New- York. 
 
'^^ Of THE 
 
 UNIVERSITY 
 
 Of 
 
 PREFACE. 
 
 Logic, as a science, is simple and 
 limited. Most modern treatises upon the 
 subject have erred, by extending it be- 
 yond its proper department, on the one 
 hand, and by excluding it from its legiti- 
 mate province on the other. By some it 
 has been made to occupy the ground of 
 mental science or of rhetoric ; by others it 
 has been denominated, " amj art of reason- 
 ing," as if there were any sound reasoning 
 which is not logical, while others have 
 claimed for it the unlimited sphere of 
 teaching " the right use of reason." These 
 errors have been exposed by Archbishop 
 
1: PREFACE. 
 
 Whately, and the true nature and ap- 
 propriate office of logic have been ex- 
 plained and vindicated. His learned and 
 able treatise has obtained favor in the 
 universities of Great Britain and the 
 United StatCi^, and will go far, undoubt- 
 edly, to revive and extend a neglected, 
 but invaluable science. The principles of 
 that work, which are none other than 
 those of Aristotle, have been adopted as 
 the basis of the present volume. 
 
 The treatise now presented to the 
 public is designed for a department 
 hitherto unoccupied. 
 
 A science, so rudimentary in its prin- 
 ciples, and so extensive in its applications, 
 ought to be studied with the common 
 elements of learning. Nor, when prop- 
 erly explained, will it be found any more 
 difficult to the younger student than 
 grammar or arithmetic. It will not task 
 
PREFACE. 
 
 the powers beyond what is desirable in 
 salutary discipline, while its tendency to 
 promote a habit of • thinking will be 
 greater than that of any other science. 
 Indeed, logic must be studied early, and 
 rendered perfectly familiar, in order to be 
 of much practical utility in the business 
 of life. It is so long postponed in existing 
 systems of education, and, after all, so 
 superficially studied, that there is scarcely 
 one educated man in a thousand who pro- 
 fesses to be master of logic. 
 
 This work, though simple in its arrange- 
 ment, embraces all that is essential to 
 logic, while everything which does not 
 strictly and necessarily come within the 
 appropriate province of the science has 
 been excluded. Collateral matter and 
 discumve explanations have been avoided, 
 as rather calculated to embarrass and con- 
 fuse the youthful mind. The principles 
 
6 PREFACE. 
 
 and rules of the science have l»een stated 
 distinctly, and illustrated by a variety of 
 examples. If any •further explanation is 
 necessary the enlightened teacher can 
 easily supply it. The great points will 
 thus stand out prominently to view, and 
 all that is added by way of comment will 
 be associated with them in the . mind. 
 The attention of the learner wiU not be 
 distracted by many particulars, nor the 
 memory encumbered with unessential 
 matter. 
 Boston, August 14, 1840. 
 
Of THE 
 
 UNIVERSITY 
 
 Of 
 
 PREFACE TO THE REVISED EDITION. 
 
 The first edition of this book has been 
 used chiefly in academies of a high grade 
 and as a manual in some colleges. The 
 improvements in this edition will make it 
 still more acceptable to advanced students, 
 while it will be no less adapted to the 
 object for which it was originally de- 
 signed, namely, to follow immediately 
 after grammar in all schools where the 
 higher branches are commenced. Will 
 teachers of grammar schools now give 
 this book a trial, and make known to 
 the public the results of the experiment ? 
 Consider : Will it not be of the greatest 
 
b t»REFACE TO THE REVISED EDITION. 
 
 advantage to form the habit in early 
 life of analyzing one's process of thought 
 in reasoning, and especially observing 
 whether the reason given for an opinion 
 is a general reason. For example: It is 
 of itself no proof, that you are not at 
 the scene of a murder, because you are 
 here. Indeed! what other proof is neces- 
 sary? Clearly this general prmdple — 
 that no being but God can be in two 
 places at the same time. Without this 
 as a major premise, your alibi as a minor 
 premise answers no purpose. To be sure 
 this principle is implied in the minor 
 premise, and it happens to be a sound 
 one ; but how often in practical life do 
 we imply in our statements a general 
 Drinciple which is not sound; but its 
 unsoundness escapes us, because we are 
 not in the habit of considering it dis- 
 tinctively. It would be easy enough 
 
PBEFAOE TO THE EE VISED EDITION. 9 
 
 to give illustration of this from any 
 political or religious newspaper that 
 comes to hand. I insist, therefore, that 
 a science so pertinent to every-day 
 practical life should not be excluded 
 from elementary studies, but should be 
 taught in every grammar school. 
 
 The most important improvements in 
 this edition are the Analytical Outline, 
 the Chapter on Distinctions of Reason- 
 ing, and the Essay on the Philosophy of 
 Induction. 
 
 New Yokk, October, 1860. 
 
CONTENTS. 
 
 tMm 
 
 Analytical Outlinb 13 
 
 PART I.— ON TERMS. 
 
 SacTioii 
 
 I. Different Kinds of Terms 23 
 
 II. Opposition of Terms 26 
 
 HI. Species and Genus 28 
 
 IV. Division *. 30 
 
 V. Definition 31 
 
 PART II.— PROPOSITIONS. 
 
 I. Parts of a Proposition 36 
 
 11. Distinction of Propositions 37 
 
 III. Further Distinctions 41 
 
 IV. Distribution of Terms of Propositions 43 
 
 V. Opposition 46 
 
 VL Conversion 52 
 
 PART in.— ARGUMENTS. 
 
 Definition of Arguments 511 
 
 1. Syllogisms 58 
 
 n. Rules of Syllogism * 61 
 
 in. Irregular Syllogisms 71 
 
 rv. Hypothetical Syllogism. — Dilemma 77 
 
 V. Distinctions of Reasoning 83 
 
12 CONTENTS. 
 
 PART IT.— FALLACIES. 
 
 PAas 
 
 DisnNCTiON OP Fallacies 95 
 
 L Logical Fallacies 98 
 
 U. MATERLA.L FALLACIES 102 
 
 SUPPLEMENT. 
 
 L Moods and Figures op Syllogisms. 107 
 
 II. Reduction 114 
 
 Questions in Review 120 
 
 APPENDIX. 
 
 I. Dissertation on Induction 121 
 
 FL Miscellaneous Examples for Practice 152 
 
 Supposed Exceptions to Rules 168 
 
ELEMENTS OF LOGIC, 
 
 INTKODUCTION. 
 
 ANALYTICAL OUTLINE. 
 
 1. IjOGio is the science of inference; it teaches 
 how one judgment may be inferred from other 
 judgments. To reason is to infer, hence it is 
 usually called tEe science of reasoning. 
 
 2. It assumes that every mind conceives in- 
 tuitively some ideas or judgments which are 
 at once primary and certain ; otherwise we could 
 have no foundation for inference ; and to infer 
 one idea or judgment from others would give # 
 no certainty. 
 
 These ideas are called first truths. They are 
 given by the senses, the consciousness, and the 
 reason, and are innumerable. I exist There 
 is an external world. This hodnj is sclid^ ex- 
 
14 ELEMENTS OF LOGIC. 
 
 tended^ rounds red, warm, or cold, are first 
 truths. 
 
 3. At first these ideas are particular, but 
 afterward the mind unites those which are the 
 same in some respect into classes by simple ad- 
 dition. This is called genq^j^lization. To ex 
 press this we no longer say, This hody^ a/nd 
 that hody, and yonder hody^ etc., but hod/y. 
 Red hody would be a lower class made up of 
 this red thing, that red thing, etc. 
 
 4. It is evident, furthermore, that in order to 
 reason the mind must have some general ideas, 
 or judgments, that are conceived intuitively, 
 and not formed by mere addition or generali-' 
 zation ; for if you make a class by adding all 
 the individuals, you gain nothing by drawing 
 one or more out again. These general ideas are 
 called first principles, or axioms, and are the 
 offspring of the reason. Some of the earliest 
 are these : Every hody is in space. No event 
 happens without a cause. lAJce material causes 
 produce like effects. 
 
 5. It is the province of psychology to explain 
 under what circumstances these primary ideas 
 are given by the senses, the consciousness, and 
 the reason; but logic assumes their existence 
 
ANALYTICAL OUTLINE. 16 
 
 as the indispensable basis of inference, and its 
 appropriate office is to explain in what way 
 we infer one judgment from another. 
 
 6. The process of reasoning when completed 
 is found to be simply this : Something is jpredi- 
 ca^ed^ that is^ affirmed or denied of a class / an 
 individual is affirmed to belong to this class, 
 and then, of course, the same thing can he af 
 f/rmed or denied of thai vndividual. 
 
 In whatever form a sound argument is ex- 
 pressed, it may always be shown to involve this 
 process, and every unsound argument deviates 
 from it. In reasoning we always proceed from 
 generals to particulars, and never from particu- 
 lars to generals, for this is impossible, as it would 
 be to draw out what was never put in. A gene- 
 ral principle, to be sure, may be inferred from one 
 still more general ; but in relation to that more 
 general principle it is only a particular ; it is a 
 class in a class of classes — a species under a 
 genus. For example, the general law of ter- 
 restrial gravity is an inference, not from par- 
 ticular instances of bodies falling to the earth, 
 but from a more general law, which these par- 
 ticulars indicate. This is an instance of in- 
 duction. 
 
16 ELEMENTS OF LOGIC. 
 
 7. As induction has been supposed to be a 
 mode of reasoning opposite to deduction, let 
 us take a simple and common case. I infer that 
 heat to such a degree as will cause the mercury 
 in the thermometer to rise to the point marked 
 two hundred and twelve degrees on Fahrenheit's 
 thermometer will always ca/me water to hoil ^ 
 in other words, it is proved by induction to 
 be a law of nature that two himdred and 
 twel/oe degrees Fahrenheit will cause water to 
 hail. 
 
 Now this conclusion is not drawn from any 
 number of instances of the boiling of water, but 
 from a few instances combined with the prin- 
 ciple that like cause will produce like effects; 
 for if this principle were not true, then forty 
 thousand instances of water boiling by such a 
 degree of heat would not prove that another 
 case would happen, no more than finding forty 
 thousand clovers bearing three leaves only 
 would prove that clover always has only three 
 leaves ; or finding forty different varieties of 
 cloven-footed animals marked with horns would 
 prove that swine must have horns. But now I 
 know that like causes will produce like effects, 
 and I know also by observation that two hund- 
 
ANALYTICAL OUTLINE. 17 
 
 red and twelve degrees Fahrenheit did once, 
 or twice, or thrice cause water to boil, and I 
 therefore infer that it will always cause water 
 to boil. Admit the premises and the conclusion 
 is unavoidable ; and to do this is simply to 
 affirm something of a class, then to refer an in- 
 dividual to that class, and then to affirm the 
 same thing of that individual. 
 
 l^ow the first premise is a general principle, 
 which is intuitively true. The only question is 
 about the second premise, namely, whether two 
 hundred and twelve degrees Fahrenheit was the 
 cause of boiling in the instances observed. 
 
 You may now prove this by another argu- 
 ment made up of another intuitive principle, 
 and an observed fact, or perhaps by two argu- 
 ments, thus : no event hapjpens without a cause / 
 the boiling of water is an event, therefore it 
 happened not without cause ; in other words, it 
 happened by some cause. What cause? 
 
 It is a presumption of reason that those 
 thvnqs which immediately and invariably pre- 
 cede a certain event a/re its caMse^ or include its 
 cause. 
 
 Now observation and experiment have shown 
 when two hundred and twelve degrees Fahren- 
 
18 ELEMENTS IF LOGIC. 
 
 heit was present water invariably and imme« 
 diately boiled ; and when it was absent, the 
 other circumstance remaining just as before, it 
 did not boil. Hence it is concluded that it was 
 the cause of the boiling in these cases. 
 
 Thus the second premise of the main argu- 
 ment being proved, the first conclusion is estab- 
 lished, namely, that two hundred and twelve 
 degrees Fahrenheit is always the cause of water 
 boiling. 
 
 Every case of induction proper proceeds 
 upon the same grounds and in the same way. 
 It is, therefore, evident induction is no excep- 
 tion to the rule that inference is always from 
 generals to particulars, and not from particulars 
 to generals. 
 
 8. Reasoning by analogy proceeds in the 
 same way ; the difference is only in the char- 
 acter of the first premise, which is, that simila/r 
 causes are likely to produce similar effects^ m 
 that things which agree in certain attributes oi 
 relations are liJcely to agree in certain other at- 
 ti'ibutes or relations. Thus we reason by analo- 
 gy that Jupiter is likely to be inhabited as well 
 as the earth, and that retribution may be ex- 
 pected in a future life as well as in this. 
 
ANALYTICAL OUTLINE. 19 
 
 %9. Reasoning a jpriori and a posteriori are 
 not different modes of reasoning, but arguments 
 differing in the character of one of the premises : 
 in the one we reason from antecedents, and 
 in the other from consequents. From the idea 
 of perfection, as an antecedent in the human 
 mind, Des Cartes argued a priori for the exist- 
 ence of a Perfect Being ; and Paley, from the 
 marks of contrivance in the world as an effect, 
 proved a posteriori an intelligent Creator. 
 
 10. It will be seen that the value of any con- 
 clusion depends upon the degree of certainty 
 which belongs to the premise*. If they are cer- 
 tain the conclusion is certain ; if they are prob- 
 able the conclusion is only probable This is 
 the only distinction between mathematical and 
 moral or practical reasoning ; nor does this al- 
 ways exist, for some moral arguments may claim 
 premises that are absolutely certain. 
 
 11. It remains only to observe that the syl- 
 logism is merely a certain convenient mode of 
 stating an argument ; and that is the most per- 
 fect syllogism which is framed so as to make 
 the true process of inference the most apparent. 
 The above instance of induction would be stated 
 as a syllogism, thus: 
 
20 ELEMENTS OF LOGIC. 
 
 like canses will ever produce like effects. « 
 
 Two hundred and twelve degrees Fahrenheit is lik« 
 the canse that produced boiling of water; 
 Therefore, it will ever produce the like effect 
 
 Or thus: 
 
 Whatever caused the boiling of water once will always 
 cause it. 
 
 Heat 212" Fahrenheit caused the boiling of water 
 once; 
 
 Therefore, it will always cause it. 
 
 12. Analyzing a syllogism, for example: 
 
 All men are mortal. 
 Mohammed w<is a man ; 
 Therefore, Mohammed was mortal : 
 
 we find that it is made up of three propositions ; 
 that each proposition contains two terms and a 
 copula, expressing an agreement or disagreement 
 of the terms. Each term denotes an idea, as aU 
 men^ mortal, Mohammed; each proposition ex- 
 presses a judgment as to the relation of two terms 
 to each other, and the last of these propositions 
 is an inference from the other two judgments. 
 The three operations of mind concerned in rea- 
 
ANALYTICAL OUTLINE. 21 
 
 Boning are therefore simple apprehension, judg- 
 ment, and inference. 
 
 13. Language serves to express these mental 
 operations, but the mind has ideas, judgments, 
 and inferences before it has language, inasmuch 
 as a sign must of necessity be subsequent to the 
 thing signified. 
 
 14. From this analysis it appears that logic 
 enters into the vital processes of the mind, and 
 conducts it from the known to the unknown. 
 A demonstration is essentially a discovery : the 
 propositions in a book of geometry are involved 
 in the axioms and definitions on the first page, 
 but to draw them out is as much a discovery to 
 the mathematician as the continent of America 
 was to Columbus. 
 
SYNTHESIS OF LOGIC; 
 
 PART I. 
 
 OI^ TEEMS. 
 
 1. The first part of Logic treats of Tekms. 
 
 A Term is one or more words expressing a 
 thing, or what is thought of a thing ; as, 
 
 Chrass is green. Grass is a term, and green is 
 a term. 
 
 The Sim shmes hrightly. The sun is a term, 
 and shines brighth/ is a term. 
 
 SECTION I. 
 
 DIFFEEENT KINDS OF TERMS. 
 
 2. A Singular Term expresses only one indi- 
 vidual; as, 
 
 Boston^ Connecticut River, this rock, the discoverer of 
 America. 
 
 * Younger students corAnience here. 
 
24 ELEMENTS OF LOGIC 
 
 3. A Common Term is one whicli is not con- 
 lined to a single object, as Gity^ which may 
 apply to Boston and to all other cities. 
 
 Rock, River, Conqueror, Mariner. 
 Strong, Happy, Wise, Great, Balmy, Dark. 
 
 4. A Relative Teem expresses an object 
 that is related to another object ; as, Husband^ 
 which is related to wife. Pa/rent^ which im- 
 plies offspring. 
 
 Rider, Rnler, Brother, Servant, Magistrate. 
 
 6. An Absolute Term expresses a thing con- 
 sidered by itself, without reference to any other 
 thing; as, 
 
 River, Mountain, Power, Wisdom. 
 
 6. A Positive Term expresses a thing as 
 actually existing; as. 
 
 Sight, Seeing, Speech, A man speaking. 
 
 7. A Privative Term is one which expresses 
 the absence of an attribute from a thing capable 
 of it; as, a blind man^ which denotes the ab- 
 sence of the power to see. 
 
 A lame stag, A leafless oak, A dead plant. 
 
DIFFERENT KINDS OF TERMS. 26 
 
 8. A Negative Term denotes the absence 
 of an attribute from a subject, which is not 
 capable of it at all ; as, 
 
 A dumb statue, Lifeless marble, Silent dews. 
 
 9. An Abstract Term is one which ex 
 presses a quality, without reference to any 
 subject in which it may be found ; as. 
 
 Roundness, Hardness, Wisdom, Justice, Folly. 
 
 10. A Concrete Term expresses both the 
 attribute and the object to which it belongs ; 
 as, wrong^ which expresses both an action and 
 its quality ; i^ler^ which indicates an agent and 
 his office. 
 
 Philosopher, Governor, Wise, Energetic, Hard. 
 
 11. An Indefinite Term is one which does 
 not define or mark out an object, and has the 
 particle not attached to it, expressed or under- 
 stood; as, not a mem, which may imply any 
 other being. 
 
 Not Brutus, Incorporeal, Unfinished, Unwise 
 
26 ELEMENTS OF LOGIC. 
 
 12. A Definite Term is one which does de- 
 fine or mark out an object and has not the 
 particle not attached to it ; as, 
 
 Man, Brutus, Finished, Complete, Established. 
 
 EXAMPLES. 
 
 1. Man is a rational being. 
 
 2. Cicero was a great orator. 
 
 3. This town is pleasantly situated. 
 
 4. Mothers have much solicitude. 
 
 5. Strength is acquired by exercise. 
 
 6. Far-sightedness is peculiar to seamen. 
 T. A dumb man is a pitiful object. 
 
 8. The silent tomb, the lifeless statue. 
 
 9. Wisdom is more precious than rubies. 
 
 10. Just and good are the laws of God. 
 
 11. The society is organized. 
 
 12. The plan is incomplete. 
 
 SECTION n. 
 
 OPPOSITION OF TERMS. 
 
 13. Consistent Teems are those which may 
 at the same time be affirmed of the same thing; 
 as, dry and cold. 
 
OPPOSITION OF TERMS. 27 
 
 14. Opposite Terms cannot at the same time 
 be affirmed of the same thing; as, black and 
 white. 
 
 The opposition of terms is fourfold. 
 
 15. Relative Opposition is that w^hich is be- 
 tween relative terms, that cannot at the same 
 time be applied to the same subject; as, father 
 and son, 
 
 16. CoNTEABY Opposition is that between 
 absolute terms, that expel one another from a 
 subject capable of either ; as, wise and foolish. 
 
 IT. Privative Opposition is that between a 
 positive and privative term ; as, seeing and 
 hlind. 
 
 18. Contradictory Opposition is that be- 
 tween a definite and indefinite term ; as Cesa/r 
 and not Cesa/r. 
 
 EXAMPLES. 
 
 1. Good and small. 
 2 Master and servant. 
 
 3. Ruler and subject. 
 
 4. Material and immaterial. 
 
 5. Lovely and hateful. 
 
 6. Hearing and deaf. 
 
28 ELEMENTS OF LOGIC. 
 
 SECTION III. 
 
 SPECIES AND GENUS. 
 
 This subject involves no mystery, as lormerly 
 under a false philosophy. 
 
 19. Species is a term that denotes a class, in- 
 cluding several individuals ; as, Beast, which in- 
 cludes the horse, cow, lion, deer, etc. 
 
 20. Genus is a term that denotes a class, that 
 includes several species ; as Animal, which in- 
 cludes beast, bird, fish, man, insect. 
 
 A genus which cannot be comprehended 
 under a higher genus is called highest geniis^ 
 and a species which includes no lower species 
 is called lowest species, 
 
 21. The Essential Difference denotes an 
 essential part of a species that distinguishes it 
 from other species ; as rational, which is the 
 essential difference of the species man, because 
 it is the essential part of man that distinguishes 
 him from beast, bird, etc. 
 
 22. A Property is something necessarily 
 joined to the essential difference ; as jpower of 
 laughing, which is the property of man as a 
 rational being. 
 
SPECIES AND GENUS. 29 
 
 23. An Accident is something that may be, 
 or may not be joined to the essential difference, 
 as tall or shorty li/vrng in London^ horn in 
 Paris, 
 
 EXAMPLES 
 
 1. This tree is a Pine, with very thick 
 boughs. 
 
 2. This is a small magnet, having the power 
 of attraction, and it turns upon a pivot in a 
 direction north and south. 
 
 3. This vessel is a ship, having three masts, 
 full rigged, and very long. 
 
 4. A republic is a government in which the 
 people have sway and choose their own rulers. 
 
 5. This seminary of learning is a college. 
 
 6. A lame animal, a blind stag. 
 
 7. General terms are names of classes. 
 
 8. A bird with blue feathers and broad 
 wings 
 
 9. Mercury is the planet nearest the Hun. 
 
 10. A circle is a figure whose circumference 
 is in every part equally distant from the 
 center. 
 
 11. A whale is the largest of fish, and is 
 often seen in our waters. 
 
80 ELEMENTS OF LOGIC. 
 
 12. A plant is an organized being, destitute 
 of sensation. 
 
 SECTION IV. 
 
 DIVISIOIT. 
 
 24. Division is the distinct enumeration of 
 the several things signified by a term ; as, 
 
 New England is divided into Maine, New Hampshire, 
 Vermont, Massachusetts, Rhode Island, and Connecticut. 
 
 Bark signifies the rind of a tree, a small ship, and the 
 cry of a dog. 
 
 25. EuLE OF Division. The several parts must 
 not he contained m one another, and all to* 
 gether must he exactly equal to the thmg 
 divided. 
 
 EXAMPLES.* 
 
 1. The year is divided into Summer, 
 Autumn, Winter, and Spring. 
 
 2. Metals are divided into gold, copper, and 
 iron. 
 
 3. The Human race is divided into Ameri- 
 cans, Africans, Asiatics, Chinese, and Europeans. 
 
 ♦ Examples, it will be seen, are given for cr -ticiBm. 
 
DEFINITION. 91 
 
 4. King signifies a ruler and also a man's 
 Aamc. 
 
 6. Mercury is the name of a heathen deity, 
 a planet, a plant, and quicksilver. 
 
 6. The globe consists of land and water. 
 
 7. Form signifies shape and ceremony. 
 
 8. Trump is a trumpet and a winning card. 
 
 9. Orchard is an inclosure for apple-trees 
 and fruit-trees. 
 
 10. A solid body has length and breadth. 
 
 11. A tree consists of trunk, branches, and 
 leaves. 
 
 SECTION Y. 
 
 DEFINITION. 
 
 26. A Definition is an expression explaining a 
 term, so as to distinguish or separate it from 
 everything else. 
 
 27. A Nominal Definition distinguishes the 
 meaning of a term by an equivalent term, 
 wliich is better known ; as, 
 
 Decalogue — ^the Ten Oommandments. 
 
 When all the equivalent terms are given it is 
 one kind of division. 
 
82 ELEMENTS OF LOGIC. 
 
 28. A PnrsioAL Definition lays down the 
 real parts of the essence ; as, 
 
 Injustice is the intentional violation of another's rights. 
 A plant has leaves, stalks, roots. 
 
 This last is another kind of division. 
 
 29. A Logical Definition assigns the Genus 
 and the Essential Difference of the thing de- 
 fined; as, 
 
 Man is a rational animal. 
 
 30. Accidental Definition, or Description, 
 assigns the accidents or properties of the thing 
 defined ; as, 
 
 Man is an animal that uses fire to dress his food. 
 Columbus was a native of Genoa. 
 
 31. It will be observed that more than one 
 of these kinds of definition will coincide in 
 matters strictly scientific. 
 
 32. Rule of Definition. A Definition mvM 
 be adequate^ that is^ not too extensive nor too 
 narrow^ for the thing defim^ed; plainer^ and 
 contained in a suitable number of proper^ not 
 f-gurative terms. 
 
 33. The chief concern of Logic with defini 
 
DEFINITIONS. 88 
 
 tions is, that words be not used in differmi 
 senses in argument. 
 
 EXAMPLES. 
 
 1. Pleiades — the seven stars. 
 
 2. A king is the ruler of a people. 
 
 3. A square is a figure having four sides and 
 four right angles. 
 
 4. Surprise is a state of mind produced by 
 some unexpected occurrence. 
 
 6. A circle is a figure whose circumference 
 is in every point equally distant from the 
 center. 
 
 6. Species is a term for a class. 
 
 7. Wine is the juice of the grape. 
 
 8. Whiteness is the color arising from the 
 prevalence of brightness. 
 
 9. A plant is an organized being destitute of 
 sensation. 
 
 10. Logic is the science of infeience. 
 
 11. Man is a risible animal. 
 
 12. Mercury is the planet nearest the Sun. 
 
 13. A Church is a congregation of faithful 
 men, in which the word of God is preached, 
 and the ordinances duly administered. 
 
84 ELEMENTS OF LOGIC 
 
 14:. Punishment is pain inflicted for a crime, 
 in order to correct the offender. 
 
 15. Courage is boldness and endurance in 
 time of peril. 
 
 16. Sin is voluntary transgression of a known 
 law. 
 
 17. Sin is any transgression of God's law. 
 
PART !!• 
 
 OF PEOPOSITIONS. 
 
 The second part of Logic treats of Propo 
 Bitions. 
 
 SECTIOK I. 
 
 1. A Proposition is a judgment expressed 
 in words, or a sentence, whereof one part 
 is affirmed or denied of the other ; as, 
 
 Man is an animal. 
 
 Moses and Thomas are not Statesmen. 
 
 All animals are mortal. 
 
 2. The Subject of a proposition is that part, 
 of which something is affirmed or denied ; as, 
 in the last example all animals is the subject. 
 
 3. The Predicate of a proposition is that 
 which is affirmed or denied of the subject; as, 
 in the same example, mortal is the predicate. 
 
B6 ELEMENTS OF LOGIC. 
 
 4. The Copula is the verb by which the 
 two terms are connected. It is the present tense 
 of the verb to he, with or without the particle not. 
 
 5. Sometimes one part of a proposition is 
 contained in another; as, the wind blows, I 
 think,* which imply, / am thinking, the wind is 
 Mowing. 
 
 6. The subject of a proposition usually 
 stands first, and the predicate last; but this 
 order is sometimes inverted, as. 
 
 In the West are extensive Prairies. 
 
 EXAMPLES. 
 
 1. Matter is divisible. 
 
 2. Man is not infallible. 
 
 3. Christopher Columbus was the discoverer 
 
 of America. 
 
 4. A wise man rules his own spirit. 
 
 6. George Washington was a brave but pru- 
 dent general. 
 
 6. The world exhibits marks of a great con- 
 
 vulsion. 
 
 7. I see — he feels — ^you w^alk — they run. 
 
 8. All tyrants deserve death. 
 
 9. Blessed are the pure in heart. 
 
DISTINCTION OF PROPOSITIONS. 37 
 
 SECTION II. 
 
 DISTIKOTION OF PROPOSITIONS. 
 
 7. Pbopositions are distinguished into af- 
 firmative and negative, which is a distinction 
 with respect to Quality. 
 
 8. An Affirmative Proposition is one in 
 which the predicate is declared to agree with 
 the subject; as, 
 
 Man is a fallible oreatnre. 
 
 9. A. Negative Proposition is one m whicli 
 the predicate is declared to disagree with the 
 subject; as, 
 
 The world is not eternal ; no miser is happy. 
 
 10. Propositions are also distinguished into 
 iJniversal and Particular, which is a distinc- 
 tion in respect to Quantity. 
 
 11. A Universal Proposition is one in which 
 the predicate is asserted of the whole of the 
 subject. 
 
 The signs of universality are all^ every, no, 
 neither, and the like, which are expressed or 
 
38 ELEMENTS OF LOGIC. 
 
 understood ; also, proper names, as John, Lon- 
 don ; and common names with a singular or 
 a definite sign ; as, That hoy^ five hoohs, 
 
 No discontented man is happy. 
 Those stars revolve about the sun. 
 
 Exceptions. In negative propositions the 
 idiom of the English language makes all and 
 eoery particular or singular terms; as, all tJie 
 sailors were not drowned^ does not mean that all 
 the sailors escaped drowning, but that some of 
 them only escaped drowning ; or, it denies 
 drowning of the totality as a collective unit. 
 
 To state a universality here you must say: 
 None of the sailors were drowned^ or simply, 
 The sailors were not drowned, 
 
 12. A Particular Proposition is one in 
 which the predicate is asserted of an indefinite 
 part of the subject. 
 
 The signs of particularity are some^ many, 
 few^ several, and the like ; as, 
 
 Some culprits were not punished. 
 
 13. A Universal Affirmative Proposition 
 is one in which the predicate is said to agree 
 
DISTINCTION OF PROPOSITIONS. S9 
 
 with the whole of the subject ; as, in the above 
 example — All men are mortal. This is not only 
 a universal proposition, but a universal affirma- 
 tive proposition. 
 
 All tyrants deserve death. 
 
 14. A Universal Negative Proposition is 
 one in which the predicate is said to disagree 
 with the whole of the subject; as, no disoon 
 tented man is happy j which is not only a uni- 
 versal proposition, but a universal negative 
 proposition. 
 
 No sins are excusable. 
 
 15. A Particular Affirmative Proposition 
 is one in which the predicate is asserted to 
 agree with only some part of the subject; as, sorihe 
 islands are fertile* which is not only a par- 
 ticular proposition, but a particular affirmative 
 proposition. 
 
 Several men were drowned. 
 
 16. A Particular Negative Propodiiion is 
 one in which the predicate is asserted to dis- 
 agree with only some part of the subject ; as, some 
 culprits were not pimished; which is not only 
 
4:0 ELEMENTS OF LOGIC. 
 
 a particular proposition, but a particular nega 
 tive proposition. 
 
 17. A, E, I, O are symbols employed to re- 
 present these propositions : thus, 
 
 A stands for universal affirmative. 
 
 E stands for universal negative. 
 
 I stands for particular affirmative. 
 
 O stands for particular negative. 
 
 EXAMPLES. 
 
 1. These sailors were not drowned. 
 
 2. Paris is a gay city. 
 
 3. Some animals are sagacious. 
 
 4. Men are unaccountable beings. 
 
 5. Every effect must have an adequate 
 
 cause. 
 
 6. Few men become suddenly rich. 
 
 7. Many criminals are not brought to pun- 
 
 ishment. 
 
 8. Planets are bodies moving in orbits about 
 
 the sun. 
 
 9. Islands are surrounded by water. 
 
 10. The Christian religion is attested by 
 
 miracles. 
 
 11. Every sinner will be punished. 
 
DISTINCTIONS OF PROPOSITIONS. 41 
 
 12. That man was the inventor of lightning 
 
 rods. 
 
 13. Not all his foes could alarm him. 
 
 14. No flower is always in bloom, 
 
 15. All laws are not useful. 
 
 16. Every soldier was not killed. 
 
 SECTION III. 
 
 FURTHER DISTINCTIONS OF PROPOSITIONS. 
 
 18. Propositions are distinguished into Cate- 
 gorical and Hypothetical. 
 
 19. The Categorical asserts simply that the 
 predicate agrees or disagrees with the sub- 
 ject; as, 
 
 Truth is invaluable. 
 
 The eye is a natural telescope. 
 
 20. The Hypothetical asserts with a con- 
 lition, or with an alternative ; as, 
 
 If it storms, the ship will not saiL 
 It is summer or winter. 
 
 21. Hypothetical Propositions are divided 
 into Conditional and Disjunctive. 
 
42 ELEMENTS OP LOGIC. 
 
 22. A Conditional Proposition is one whose 
 parts are limited by the particle if^ or some 
 word expressing a condition ; as, 
 
 If there be no fire, there will be no heat. 
 Cesar deserved death, if he was a tyrant. 
 
 23. A Conditional Proposition contains two, 
 and only two, Categorical Propositions, whereof 
 one follows from the other. 
 
 If the Bible is true, it ought to be studied. 
 
 The first is called the antecedent, and that 
 which results from it is called the consequent. 
 
 24. A DisjuNcnvE Proposition asserts that 
 a subject agrees with one of two or more pred- 
 icates, or a predicate with one of two or more 
 subjects; as, 
 
 It is either day or night. 
 
 Prosperity or adversity wiU be yonr lot. 
 
 25. A Disjunctive may easily be converted 
 j.nto a Conditional ; thus, 
 
 It is either day or night. 
 K it is not day, it is night. 
 
TERMS OF PROPOSITIONS. 48 
 
 EXAMPLES. 
 
 1 . Man is free, or he is not responsible. 
 
 2. This proposition is either true or false. 
 
 3. The earth must move, if the sun be fixed. 
 
 4. If the harvest is large, corn will be cheap. 
 6. If there be no providence, prayer avails not. 
 
 6. If the boat goes, the letter will probably 
 
 reach him before morning. 
 
 7. Wisdom is the principal thing, if Solomon 
 
 is right. 
 
 8. Either the sun or the moon will be eclipsed 
 
 that day. 
 
 9. If logic is useful, it deserves to be studied. 
 10. If Cromwell was an Englishman, he was 
 
 a usurper. 
 
 SECTION lY. 
 
 DISTRIBUTION OF THE TERMa OF PROPOSI- 
 TIONS. 
 
 26. A Term is said to be distributed when it 
 is taken universally or in its utmost extent, so 
 as to stand for everything to which it is capable 
 of being applied, that is, for each of its signifi- 
 cates ; and undistributed when it stands for an 
 
4:4 ELEMENTS OF LOGIC. 
 
 indefinite portion only of the things signified 
 by it, that is, for an indefinite part of a class. 
 In the following example the subject is dis- 
 tributed and the predicate undistributed. 
 
 All birds are animals. 
 
 In the following the predicate is distributed 
 and the subject undistributed. 
 
 Some birds are not web-footed. 
 
 It is evident that the whole class of web- 
 footed are separated by the not from some 
 
 birds. 
 
 RULE I. 
 
 27. Subjects are distributed in all uni/versal 
 a/ad no jpa/rticula/r propositions. 
 
 All men are mortal. 
 Great Britain rules the ocean. 
 Wicked men are not wise. 
 The fixed stars twinkle, 
 No miser is a happy man. 
 
 RULE n. 
 
 28. Predicates are distributed in all ntigattve 
 and no affirmative propositions. 
 
 No virtue is an evil. 
 
 Some rich men are not good men. 
 
TERMS OF PROPOSITIONS. 46 
 
 A distributes the subject, O the predicate, I 
 neither, and E both. 
 
 N. B. — A defini'-e portion of a class is a small 
 class, and the term which expresses it is dis- 
 tributed. 
 
 Most men are poor. 
 These men are rich. 
 
 Eule II has some Exceptions in what logi- 
 cians call tmnatmral jyroposiUonSj such as, 
 
 All triangles are all figures bounded by three straight 
 lines. 
 Some stars are all the planets. 
 Some stars are not some planets. 
 
 But these being noted by the form of ex- 
 pression will make no difficulty. 
 
 I do not see with Sir William Hamilton suffi- 
 cient reason, in such exceptions, to revolutionize 
 ihe established forms of logic. 
 
 EXAMPLES. 
 
 1. Many ships were lost in the gale. 
 
 2. The storm did not last long. 
 
 3. Most Americans can read. 
 
 4. All the laws were not enforced. 
 
46 ELEMENTS OF LOGIC. 
 
 5. Everything in the political world looks 
 
 dark. 
 
 6. "No good man can hate his brother. 
 
 7. Every sin is a violation of the divine law. 
 
 8. All visible things had a beginning. 
 
 9. Some difficult things are not evils. 
 
 10. Charity never faileth. 
 
 11. Charity- suffereth long and is kind. 
 
 12. Five men were shipwrecked, 
 
 SECTION Y. 
 
 OPPOSITION OF PROPOSITIONS. 
 
 29. Two propositions are said to be opposed, 
 which, having the same subject and predicate, 
 yet differ in quantity, or quality, or both ; as, 
 
 A. All islands are fertile, 
 I. Some islands are fertile 
 
 ., >• m quantity, 
 lie, ) ^ 
 
 A. All islands are fertile, ) . 
 
 > m cinahty. 
 E. No island is fertile, J ^ ^ 
 
 A. All islands are fertile, , . , .. 
 
 Y in both. 
 O. Some islands are not fertile, 
 
 E. No island is fertile, r . , , 
 
 Y m both. 
 I, Some isl ands are fertile, 
 
 iile, ) 
 bUe, ) 
 
OPPOSITION OF PROPOSITIONS. 47 
 
 30. With any given subject and predicate, 
 four distinct propositions may be stated, namely, 
 A, E, I, and O, any two of which may be said 
 to be opposed ; as. 
 
 Or, 
 
 A. Every disease is contagious. 
 E. No disease is contagious. 
 
 I. Some diseases are contagious. 
 O. Some diseases are not contagious. 
 
 31. There are four different kinds of opposi- 
 tion. 
 
 32. Contrary Opposition is when a uni- 
 versal affirmative is opposed to a universal 
 negative; as, 
 
 A. All human inventions are perfect. 
 E. No human invention is perfect. 
 
 33. SuBCONTRARY OPPOSITION IS wlieu the 
 particular affirmative is opposed to the particu- 
 lar negative ; as, 
 
 I. Some human inventions are perfect. 
 0. Some human inventions are not perfect. 
 
 34. Subaltern Opposition is when a univers- 
 al affirmative is opposed to a particular affirm- 
 
48 ELEMENTS OF LOGIC. 
 
 ative, or a universal negative to a particular 
 negative; as, 
 
 A. Every human invention is perfect 
 I. Some human inventions are perfect. 
 
 Or, 
 
 E. No human invention is perfect. 
 
 0. Some human inventions are not perfect. 
 
 35. OoNTRADioTORY OpposnioN is wheu the 
 universal affirmative and the particular negative 
 are opposed, or the universal negative and the 
 particular affirmative; as, 
 
 Or, 
 
 A. Every human invention is perfect. 
 
 O. Some human inventions are not perfect, 
 
 E. No human invention is perfect. 
 L Some human inventions are perfect. 
 
 36. Four conditions are requisite to consti- 
 tute a contradiction, namely, to speak of the 
 same thing : (1.) In the same sense ; (2.) In the 
 same respect; (3.) With regard to the same 
 third thing; and, (4.) At the same time. If any 
 of these be wanting, is and is not may 
 agree. As, 
 
OPPOSITION OF PROPOSITIONS. 49 
 
 1. An opinion is and is not faith* It is an 
 inoperative and unacceptable belief; it is not 
 an effectual and saving faith. 2. Troilus is 
 wnd is not red-haired. He is with respect to 
 Lis head ; he is not with respect to his beard 
 3. Socrates is and is not long-haired^ he is in 
 comparison with Scipio ; he is ot in compari- 
 son with Xenophon. 4. Solomo\ was and was 
 not a good man. He was in his youth ; he was 
 not in his middle age. 
 
 THE RULES OF OPPOSITION, 
 RULE L 
 
 37. Coin-RADioTORY Propositions are always 
 the one true and the other false ; as, 
 
 A. All men are mortal. 
 
 0. Some men are not mortaL 
 
 E. No tyrant deserves death, 
 
 1, Some tyrants deserve death. 
 
 RULE n. 
 
 38. Contrary Fropositionb may be both 
 
 false, but never both true ; as, 
 4 
 
60 ELEMENTS OP LOGIO. 
 
 A. Every, disease is contagions. 
 E. No disease is contagions. 
 
 BULE nL 
 
 39. SuBooNTRABiES are never both false, but 
 tliey may be both true. 
 
 I. Some jminsements are innocent. 
 0. Some amnsements are not innocent. 
 
 RULE IV. 
 
 40. Subalterns are sometimes both true, 
 sometimes both false, and sometimes one is true 
 and the other false ; as, 
 
 A. Every defensive war is jnst, 
 L Some defensive wars are just. 
 E. No crime is an evil. 
 
 0. Some crimes are not an evil. 
 
 A. Every measure of government is wise. 
 
 1. Some measures of government are wise. 
 
 A^- Contraries' 
 
 Diagram showing the N. 
 
 I \ 
 relation of the four judg- © %-^^ 
 
 ments-.AEIO. S X S 
 
 x^- — s 
 
 Subcontraries- 
 
OPPOSITION OF PROPOSITIONS. 61 
 
 EXAMPLES. 
 
 1. Some horses are unruly. 
 Some horses are not unruly. 
 
 2. No intolerant men are good men. 
 Some intolerant men are good mea 
 
 3. All pleasures are hurtful. 
 Some pleasures are not hurtful. 
 
 4:. All hopes are consoling. 
 Some hopes are consoling. 
 
 5. No virtuous man is ungrateful. 
 Some virtuous men are ungrateful 
 
 6. All islands are fertile. 
 Some islands are fertile. 
 
 T. All animals are mortal. 
 All animals are not mortal. 
 
 8. Every patriot is a Christian. 
 Some patriots are not Christians. 
 
 9. Some diseases are contagious. 
 All diseases are contagious. 
 
 iO. All laws are not useful. 
 Some laws are not useful. 
 
62 ELEMENTS OF LOGIC. 
 
 SECTION VI. 
 
 CONVERSION OF PROPOSITIONS. 
 
 41. A proposition is said to be converted, 
 when its terms are transposed and the truth 
 preserved ; as, 
 
 Some painters are poets. 
 Some poets are painters. 
 
 42. The proposition to be converted is called 
 the Original, that into which it is converted 
 the Converse ; as. 
 
 Original. No reptile is a quadruped. 
 Converse. No quadruped is a reptile. 
 
 43. Simple Conversion is where the subject 
 and predicate simply change places ; as, 
 
 Some boasters are cowards. 
 Some cowards are boasters. 
 
 44. Particular Conversion is where, in 
 transposition, the converse requires a particular 
 term to preserve the truth of the original ; as, 
 
 All swallows are birds. 
 Some birds are swallowa. 
 
CONVERSION OF PROPOSITIONS. 58 
 
 45. Rule. In all cases the converse muat he 
 timly implied hy the original^ and no tenn 
 must he distributed in the converse that was not 
 distributed in the original. Hence, 
 
 A. All men are mortal ; 
 All mortals are men, 
 
 is not proper conversion, for A distributes the 
 subject only, (28) but mortal is the predicate, 
 therefore its distribution in the converse, 
 namely, all mortals^ is unwarranted. 
 
 46. The converse of a universal affirmative 
 proposition is a particular affirmative ; or, more 
 briefly, A is converted into I. 
 
 A. All men are mortal. 
 I. Some mortals are men, 
 
 47. The converse of a universal negative is a 
 universal negative — E into E ; as, 
 
 E. No deer is an elephant. 
 E. No elephant is a deer. 
 
 48. Particular affirmative propositions are 
 converted only into the same — I into I; as, 
 
 I. Some infidels are learned men. 
 I. Some learned men are infidels. 
 
54 ELEMENTS OF LOGIC. 
 
 49. A particular negative is inconverti- 
 ble; as, 
 
 0. Some birds are not swallowrs. 
 
 You cannot say, 
 
 0. Some swallows are not birds; 
 
 Or, 
 
 E. No swallows are birds ; 
 
 For these are negative propositions, and dis- 
 tribute the predicate, (28) which is hirds; but, 
 in the original, hirds^ is not distributed. (27.) 
 
 Some logicians teach that the particular 
 negative may be converted by considering the 
 particle not attached to the predicate, by which 
 the proposition is taken as an affirmative. 
 
 Some statesmen are not wise^ may be stated . 
 
 Some statesmen are not- wise. 
 This you may convert simply: 
 
 Some not-wise, that is, unwise, are statesmen. 
 
 In like manner a universal affirmative may 
 
 be simply converted by changing its quah'ty; 
 
 thus, 
 
 All good reasoners are candid men, 
 
 may be converted into 
 
 None but candid men are good reasonera 
 
CONV'jflRSION OF PROPOSITIONS. 65 
 
 This is called conversion bj contraposition. 
 
 50. Exceptions. Universal affirmatives may 
 
 be converted simply when the predicate by 
 
 some word notifies its distribution, contrary to 
 
 rule, sec. iv, 28, and when it is understood to be 
 
 exactly equal to the subject, as in definitions, 
 
 etc. 
 
 All men are [aU] rational animals. 
 
 So some particular negative proposition ma^ 
 be converted simply when the predicate notifies 
 its non-distribution. See exceptions to Kule II, 
 Sec. iv, 28. 
 
 Some elms are not some trees. 
 
 EXAMPLES. 
 
 1. All Britons are freemen. 
 
 2. Some Britons are freemen. 
 
 3. No unhappy man is a perfect Christian. 
 
 4. Some fish are not salmon. 
 
 5. Some orators are not statesmen. 
 
 6. No offensive wars are righteous ente^ 
 
 prises. 
 
 7. Every learned man is a thankful man. 
 
 8. Some great geniuses are ignorant meiL 
 
 9. Some parrots are not talkers. 
 
66 ELEMENTS OF LOGIC. 
 
 10. Every true Christian is a patriot. 
 
 11. Some angels are sinners. 
 
 12. Some amusements are hurtful. 
 
 13. All birds have feathers and wings. 
 
 14. All equiangular triangles are equilateral 
 
 15. Some stars are all the planets. 
 
 16. Some stars are not some planets. 
 
 17. A few men are not all the voters. 
 
 18. Some birds are not like some birds. 
 
PART III. 
 
 OF AEGTJMENT. 
 
 1. The third part of Logic treats of Argxt 
 ment, or reasoning expressed in words. 
 
 2. An Argument is an expression in which, 
 from something laid down and granted as true, 
 something else beyond this mnst be admitted to 
 be true, as following necessarily from the other. 
 That which is laid down is called the Premises, 
 that which results therefrom is called the Con- 
 clusion. 
 
 3. Every valid argument must conform to 
 the Logical axiom, that being the only prin- 
 ciple on which all reasoning proceeds, namely: 
 
 Whatever is universally affirmed or denied of a 
 class, may be affirmed or denied, in like manner^ 
 of everything comprehended in that class. 
 
 Or, as stated by Aristotle, and hence called 
 Aristotle's dictum : 
 
68 ELEMENTS OF LOGIC. 
 
 Whatever is predicated of a term disi/i'lhuted 
 ma/y he predicated in lihe manner of every- 
 thing contaimed in it. As, 
 
 All tyrants deserve death ; 
 
 Oesar was a tyrant; 
 
 Therefore Oesar deserved death. 
 
 No man enslaved by appetite can be happy ; 
 The sensualist is enslaved by appetite ; 
 Therefore, no sensualist can be happy. 
 
 SECTION I. 
 
 OF SYLLOGISM. 
 
 4. An argument stated at full length and in 
 its regular form is a Syllogism. The above 
 examples are syllogisms. 
 
 5. Every regular syllogism contains three, 
 
 and only three terms, called the Minor term, 
 
 Major term, and Middle term. 
 
 •* 
 All tyrants deserve death, 
 8 2 
 
 Cesar was a tyrant^ 
 
 1 8 
 
 Therefore, Gesa/r deserved death 
 
OF SYLLOGISM. 59 
 
 6. The subject of the conclusion is the minor 
 l,erm ; the predicate of the conclusion is the 
 
 .major term ; and the other term with which 
 these are compared is the middle terra ; as, 
 
 All tyrants deserve death ; 
 
 MlddU. 
 Cesar was a tyrant ; 
 
 Minor. Major. 
 
 Therefore Cesar deserved death. 
 
 The predicate of the conclusion is called the 
 major term on account of its being naturally 
 more extensive than the subject. By the 
 rule it is undistributed in affirmative proposi- 
 tions, that is, it has applications beyond the 
 subject. Part II, Sec. iv, 28. 
 
 In the example, deserving death is applicable 
 to many besides Cesar. 
 
 7. Every regular syllogism contains three, 
 and only three propositions, called the Major 
 premise, the Minor premise, and the Conclu- 
 sion. 
 
 8. The Major Premise is that in which the 
 major term is compared with the middle term 
 
 Major Premise. All tyrants deserve death; 
 Cesar was a tyrant; 
 Therefore, Cesar deserved death. ^ 
 
60 ELEMENTS OF LOGIC. 
 
 9. The Minor Premise is that in which the 
 minor term is compared with the middle 
 term; as, 
 
 All tyrants ('eserve death ; 
 Minor Premise. Cesar was a tyrant ; 
 
 Therefore, Cesar deserved death. 
 
 10. The Conclusion is that in which the 
 major and the minor terms are compared to- 
 gether. 
 
 All tyrants deserve death ; 
 Cesar was a tyrant ; 
 Conchision. Therefore, Cesar deserved death. 
 
 11. In every regular syllogism the major 
 premise is placed first, the minor next, and the 
 3on elusion last. 
 
 EXAMPLES. 
 
 1. All the faithful are dear to God ; 
 Some that are afflicted are faithful ; 
 Therefore, some that are afflicted are dear 
 
 to God. 
 
 2. No work that exhibits marks of design 
 
 can be the effect of chance ; 
 The world exhibits marks of design, 
 Therefore, the world cannot be the effect 
 
 of chance. 
 
THE RULES OF SYLLOGISM. 61 
 
 3. That which improves the mind is useful ; 
 Study improves the mind ; 
 Therefore, study is useful. 
 
 4. No literary production is perfect. 
 This treatise is a literary production ; 
 Therefore, this treatise is not perfect. 
 
 5. Every vegetable is combustible ; 
 Every tree is a vegetable ; 
 Therefore, every tree is combustible. 
 
 SECTION II. 
 
 THE RULES OF SYLLOGISM. 
 
 12. The validity of all arguments may be 
 tested by the logical axiom (3) ; and no syllo- 
 gism is valid which does not conform to it. 
 
 13. It cannot, however, always be directly 
 and conveniently applied; as, for example, in 
 the following valid syllogism : 
 
 No virtues are evils ; 
 
 All virtues are difficult ; therefore, 
 
 Some difficult things are not evils. 
 
 Tliis syllogism may be altered by converting 
 the minor premise, and then it will plainly 
 appear to conform to the logical axiom; thus. 
 
62 ELEMENTS OF LOGIC. 
 
 No virtues are evils ; 
 
 Some diflScult things are virtues ; therefore, 
 
 Some difficult things are not evils. 
 
 14. But to avoid the inconvenience of alter- 
 ing a syllogism, in order to apply the logical 
 axiom, logicians have adopted the following 
 canons and rules by which to test the validity 
 of syllogisms. 
 
 15. Canon I. If two terms agree with one 
 and the sa/me thirds they agree with each other. 
 
 16. Canon II. If one term agrees and the 
 other disagrees with one a/nd the same thirds 
 these two disagree with each other. 
 
 This agreement must be understood to be 
 that kind of class relation explained by the 
 logical axiom, and required by Aristotle's 
 dictum, otherwise the canons will mislead. 
 
 Silver is a mineral ; 
 Platina is a mineral ; 
 
 Will not prove that platina is silver, though 
 these terms agree with the term mineral. 
 
 All studies which tend to increase national and private 
 wealth are useful; 
 
 The studies at Oxford do not tend to increase national 
 and private wealth; 
 
 Therefore, the studies at Oxford are not useful. 
 
THE RULES OF SYLLOGISM. 63 
 
 This might at first seem to be founded on 
 canon II, but it is a fallacy, as is easily seen in 
 a cafee precisely parallel. 
 
 All cultivated plants grow • 
 
 The wild rose-bush is not cultivated; 
 
 Therefore, the wild rose-bush does not grow. 
 
 John Jones is sentenced to die ; 
 
 The first private in the ranks is John Jones ; 
 
 Therefore, the first private in the ranks is sentenced to die. 
 
 Here the first canon is observed, but the 
 logical axiom is not complied with unless you 
 consider proper names as distributed and stand- 
 ing for a class of one. See Part II, Sec. ii, 11 ; 
 and Sec. iv, 28. Strictly this is rather a case 
 of identification than of inference. 
 
 To avoid error, we must add to the two 
 canons the following five rules or cautions: 
 
 RULE I. 
 
 17. Every syllogism must have three^ and 
 only three terrm^ am,d three^ ami only three^ 
 propositions. 
 
 Ambiguous terms are to be considered as 
 two terms. 
 
64 ELEMENTS OF LOGIC. 
 
 The following example has, in reality, foui 
 terms : 
 
 Repentance is a good thing ; 
 Wicked men abound in repentance ; 
 Therefore, wicked men abound in a good thing. 
 
 If the word repentcmce be regarded as having 
 the same meaning in both premises, then one 
 proposition or the other is false. 
 
 Ambiguous terms are fruitful sources of error 
 in argument. 
 
 Sometimes an argument will appear to 
 have too many terms when a little alteration, 
 not affecting the sense, will show but three; 
 thus: 
 
 No irrational agent could produce a work which manifests 
 
 design ; 
 The universe is a work which manifests design ; 
 Therefore, no irrational agent could have here produced 
 
 the universe ; 
 
 This seems to have five terms, but the first pre- 
 mise is properly: 
 
 A work that manifests design could not be produced bj 
 an irrational agent. 
 
THE BULES OF SYLLOGISM. 65 
 
 RULE n. 
 
 18. The middle term must he distributed once 
 at least in the premises. 
 The following example violates the rule : 
 
 Granite is a mineral ; 
 Lead is a mineral ; 
 Therefore, lead is granite. 
 
 The middle term mineral is undistributed; 
 hence, granite is compared to mineral in a 
 part of its extension, and lead is compared to 
 it in another part of its extension ; therefore, 
 neither of the canons of logic are complied 
 with, for the two extremes are not compared 
 to one and the same third. 
 
 The following seems to violate the rule: 
 
 True patriots are disinterested ; 
 Few men are disinterested ; 
 Therefore, few men are true patriots. 
 
 But by putting the minor premise in another 
 form, and transposing the premises, it would 
 stand thus: 
 
 Disinterested men are ftw ; 
 
 True patriots are disinterested; 
 
 Therefore, true patriots are few. 
 5 
 
66 ELEMENTS OF LOGIC. 
 
 BULE m. 
 
 19. No tenn must he distributed m the con- 
 cUision^ which was not disPnbuted in one of tJu 
 premises. 
 
 The following violates the rule: 
 
 Some diseases are contagious ; 
 
 No rheumatic fevers are contagious ; 
 
 Therefore, rheumatic fevers are not diseases. 
 
 Here you employ the term diseases in the 
 whole of its extent in the conclusion, while you 
 employ it in only a part of its extent in the 
 premise. 
 
 RULE IV. 
 
 20. Two negaime or two jpartiaula/r premises 
 prove nothing. As, 
 
 Slate is not a metal. 
 Mint is not a metal. 
 
 Here two terms disagree with a third. This 
 is not according to the canons, which requires 
 either that both should agree with the third, or 
 one agree and the other disagree. 
 
 Some bad men are eloquent orators ; 
 Some good men are eloquent orators ; 
 Therefore, some good men are bad men. 
 
THE RULES OF SYLLOGISM. 67 
 
 Here you have the middle term undis- 
 tributed, which is contrary to Rule 2, and 
 therefore, not according to the canons. 
 
 Some bad men are eloquent orators ; 
 Some good men are not eloquent orators ; 
 Therefore, some good men are not bad men. 
 
 This is contrary to Eule 3. 
 
 The following syllogism with negative 
 premises may be made regular by considering 
 one of them an affirmative: 
 
 No man is happy who is not secure ; 
 Ko tyrant is secure ; 
 Therefore, no tyrant is happy. 
 
 No man who is insecure is happy ; 
 Every tyrant is insecure; 
 Therefore, no tyrant is happy. 
 
 RULE V. 
 
 21. If either premise he negative or particu- 
 lar, so also is the conclusion. As, 
 
 No virtuous man is a rebel ; 
 X and Y are virtuous men ; 
 Therefore, X and Y are not rebels. 
 
^8 BLEMENTS OP LOGIC. 
 
 Here one term '5 said to disagree >^ith a 
 middle and the other to agree, hence thej dis- 
 agree with each other, and the conclusion 
 must be negative. 
 
 All who study diligently deserve reward ; 
 Some scholars study diligently ; 
 Therefore, some scholars deserve reward. 
 
 Here is a particular premise, and you cannot 
 draw anything but a particular conclusion, for 
 a universal conclusion Would be contrary to 
 Rule 3, and against the canons. 
 
 The following in form violates the first part 
 of this rule, but it might be stated so as to be 
 regular. 
 
 None but candid men are good reasoners. 
 
 Few infidels are candid ; 
 
 Therefore, few infidels are good reasoners. 
 
 It may be changed thus : 
 
 All good reasoners are candid; 
 
 Most infidels are not candid ; 
 
 Therefore, most infidels are not good reasoners. 
 
 Or thus : 
 
 Those wh6 are uncandid are not good reasoners; 
 
 Most infidels are uncandid; 
 
 Therefore, most infidels are not good reasoners. 
 
THE RULES OP SYLLOGISM. 69 
 
 EXAMPLES. 
 
 L. Ko one is free who is enslaved by his ap- 
 petites ; 
 A sensualist is enslaved by his appetites ; 
 Therefore, a sensualist is not free. 
 
 2. All gold is precious ; 
 This mineral is precious; 
 Therefore, this mineral is gold. 
 
 3. All wise legislators adapt their laws to the 
 
 genius of the people ; 
 Solon adapted his laws to the genius of the 
 
 people ; 
 Tlierefore, Solon was a wise legislator. 
 
 4. All pious men desire the freedom of their 
 
 country ; 
 Thomas Paine desired the freedom of his 
 
 country ; 
 Therefore, Thomas Paine was a pious man. 
 
 5. Warm countries alone produce wine; 
 Spain is a warm country ; 
 Therefore, Spain produces wine. 
 
 6. Some poisons are vegetables ; 
 No poisons are useful drugs ; 
 Therefore, some useful drugs are not vege 
 
 tables. 
 
70 ELEMENTS OF LOGIC. 
 
 7. They who subvert the foundations of mo- 
 
 rality ought not to be respected ; 
 
 Atheists subvert the foundations of mo- 
 rality ; 
 
 Therefore, Atheists ought not to be re- 
 spected. 
 
 8. All vegetables grow; 
 This animal grows; 
 
 Therefore, this animal is a vegetable. 
 
 9. Most men are poor ; 
 Most men are intelligent ; 
 
 Therefore, some intelligent men are poor. 
 
 10. Light is contrary to darkness ; 
 Feathers are light ; 
 
 Therefore, feathers are contrary to dark- 
 ness. 
 
 11. An enslaved people is not happy ; 
 
 The English are not an enslaved people ; 
 Therefore, the English are happy. 
 
 12. None but whites are civilized; 
 
 The Ancient Germans were whites ; 
 Therefore, they were civilized. 
 
 13. None but whites are civilized ; 
 The Hindoos are not whites ; 
 Therefore, they are not civilized. 
 
IRREGULAR SYLLOGISMS. 71 
 
 14. None but civilized people are white; 
 The Gauls were white; 
 Therefore, the Gauls were civilized. 
 
 SECTION III. 
 
 IRREGULAR SYLLOGISMS. 
 
 22. The Enthymeme is a defective syllo^ 
 ism, having one premise suppressed; as, 
 
 Christianity teaches the way to future happiness ; 
 Therefore, it should be diligently sought. 
 
 Here the major premise is suppressed. Sup- 
 ply it, and the syllogism is complete ; thus. 
 
 Whatever teaches the way to future happiness should 
 be diligently sought ; 
 Christianity teaches the way to future happiness ; 
 Therefore, Christianity should be diligently sought. 
 
 Every man is mortal ; 
 Therefore, every king is mortal. 
 
 Here the minor premise is omitted. (9.) 
 Frequently the conclusion •is stated first ; 
 thus. 
 
 Enthusiasm should be avoided. 
 Because it leads astray from reason. 
 
72 ELEMENTS OF LOGIC. 
 
 23. A regular syllogism may be changed 
 into an Enthymeme by simply suppressing one 
 of the premises, or by stating the conclusion 
 first, and joining thereto one of the premises by 
 the conjunction for^ aSy or hecause. As, 
 
 Whatever enables us to overcome difficulties is nseM ; 
 Perseverance enables us to overcome difficulties; 
 Therefore, perseverance is useftd. 
 
 This may be changed to Enthymeme, thus : 
 
 Whatever enables us to overcome difficulties is useful ; 
 Therefore, perseverance is usefuL 
 
 Or thus : 
 
 Perseverance enables us to overcome difficulties; 
 Therefore, perseverance is usefuL 
 
 Or thus : 
 
 Perseverance is useful, for it enables us to overcome 
 difficulties. 
 
 Or thus : 
 
 Perseverance is useful ; for, 
 
 Whatever enables us to overcome difficulties is useful 
 
 24. To reduce an Enthymeme to a syllogism, 
 observe first what is the conclusion or point 
 
TRREGULAB SYLLOGISMS. 78 
 
 established. This contains the minor and major 
 terms, (10) and the remaining term must be the 
 middle term. Having these, the syllogism maj 
 be easily constructed according to the rules 
 (Sec. I.) by supplying the implied premise. 
 
 In the last example, persevera/nce is useful^ is 
 the conclusion. Consequently the remaining 
 term, enables us to wercome difficulties^ is the 
 middle term. (6.) Persemrcmce enables us to 
 overcome difficulties is implied, and makes the 
 minor premise. (9.) 
 
 25. The Sorites is a continued argument, 
 consisting of a series of propositions arranged 
 in such a manner that the predicate of each 
 forms the subject of the following proposition, 
 except the concluding, which takes the subject 
 of the first proposition ; as. 
 
 There can be no enjoymeni of property withoTit gov- 
 ernment ; 
 
 No government without laws enforced; 
 
 No laws enforced without a magistrate ; 
 
 No magistrate without obedience ; 
 
 And no obedience where every one acts as he pleases ; 
 therefore, 
 
 There can be no enjoyment of property where every 
 )ne acts as he pleases. 
 
74 ELEMENTS OF LOGIC. 
 
 26. Every Sorites contains as many syllo- 
 gisms as there are propositions intervening 
 between the first and the last proposition. 
 
 The English are a brave people; 
 A brave people are free ; 
 A free people are happy ; 
 Therefore, the EngUsh are happy. 
 
 This may be broken up into two syllogisms, thus 
 
 « 
 A brave people are free ; 
 The English are a brave people ; 
 Therefore, the English are free. 
 
 A free people are happy ; 
 The English are a free people ; 
 Therefore, the English are happy. 
 
 27. The Epiohieema is a compound argu- 
 ment, of which one or both the premises are 
 separately proved before the conclusion is 
 drawn. As, 
 
 Unjust laws endanger the stability of government, f(n 
 they create discontent among the people; 
 
 Laws restraining freedom of conscience are unjnst, fo7 
 they require the people to abandon their dea/reat c&neems; 
 
 Therefore, laws restraining freedom of conscience en- 
 danger the stability of government. 
 
IRREGULAR SYLLOGISMS. 76 
 
 28. Irregular syllogisms are the most com- 
 oionly employed in discourses of every kind : 
 for the regular form of syllogism would not 
 often consist with elegance of style, nor is it 
 often requisite to produce conviction. 
 
 EXAMPLES. 
 
 1. The mind is a thinking substance ; 
 A thinking substance is a spirit ; 
 
 A spirit has no composition of parts ; 
 That which has no composition of parts 
 
 is indissoluble ; 
 That which is indissoluble is immortal ; 
 Therefore, the mind is immortal. 
 
 2. He is a good man, therefore he is happy. 
 
 3. He is a miserable man, because he is 
 '' vicious. 
 
 4. Whatever tends to subvert government 
 
 should be deprecated ; 
 Therefore, civil dissensions should be dep- 
 recated. 
 
 5. Every man is an animal ; 
 
 Every animal is a living creature ; 
 Every living creature is a substance ; 
 Therefore, every man is a substance. 
 
76 ELEMENTS OF LOGIC. 
 
 6. A religion attested by miracles is from God, 
 
 for none but God can suspend the laws 
 of nature, and God would not permit 
 them to be suspended but for his glory. 
 
 The Christian religion was attested by 
 miracles, for the friends and the enemies 
 of Christianity have agreed in declaring 
 it was; 
 
 Therefore, the Christian religion is from 
 God. 
 
 7. No opinion that tends to immorality should 
 
 be embraced. 
 Atheistical sentiments tend to immo- 
 rality ; 
 Therefore, atheistical sentiments should 
 not be embraced. 
 
 8. It is lawful for one man to kill anothei* 
 
 who lies in wait to kill him, for the laws 
 
 of nature and the customs of mankind 
 
 sanction it ; 
 Clodius lay in wait to kill Milo, for his 
 
 equipage, arms, guards, movements, 
 
 etc., prove it ; 
 Therefore, it was lawful for Milo to kill 
 
 Clodius. 
 
HYPOTHETICAL SYLLOaiSMS. 77 
 
 9. With some of them God was not well 
 pleased, for they were overthrown in the 
 wilderness. 
 
 10. He that is of God heareth my words; 
 
 ye therefore hear them not, because yo 
 are not of God. 
 
 11. Men are free agents, for they are account- 
 
 able beings. 
 
 12. Skepticism is an enemy to man, since it is 
 
 an enemy to truth. 
 
 • 
 
 SECTION lY. 
 
 HYPOTHETICAL SYLLOGISMS DILEMMA. 
 
 Hypothetical Syllogisms are of tWo kinds: 
 Conditional and Disjunctive. 
 
 29. A Conditional Syllogism is one in which 
 the major premise is a conditional proposition ; 
 as. 
 
 If there is a God, this world is governed by a provi 
 dence; 
 Bik there is a God ; 
 Therefore, this world is governed by a providence. 
 
 30. The clause containing the condition is 
 called the Antecedent, that containing the as- 
 sertion is called the Consequent. 
 
78 ELEME-NTS OP LOGIC. 
 
 81. Rule. If the cmtecedent he granted so is 
 
 the consequent^ if the consequent le denied so is 
 
 • 
 
 the antecedent I hut not vice versa; that is, the 
 antecedent heing denied proves nothing^ cmd the 
 consequent hemg granted, proves nothing j as, 
 
 If Samuel is a father he has authority; 
 But Samuel is a father ; 
 Therefore, he has authority. 
 
 If Samuel is a father he has authority ; 
 But he has not authority ; 
 Therefore he is not a father. 
 
 But vice versa, the argument is not valid. 
 
 If Samuel is a father he has authority ; 
 Bbt Samuel is not a father ; 
 Therefore, he has not authority. 
 
 But lie might have authority from some other 
 relation or office. Again, 
 
 If Samuel is a father he has authority ; 
 But he has authority ; 
 Therefore, he is a father. 
 
 32. Conditional Syllogisms may be reduced to 
 regular syllogisms, by considering the anteced- 
 ent tbe subject, and the consequent the pr<».dicate 
 of an universal affirmative propositio 
 
HYPOTHETICAL SYLLOGISMS. 79 
 
 If the Atheists are right the world exists withoQt a 
 oause ; 
 But the Atheists are not right ; 
 Therefore, the world does not exist without a cause. 
 
 Reduced thus, when it appears a fallacy : 
 
 The case of the Atheists being right is the case of the 
 world existing without a cause ; 
 
 But the present case is not the case of the Atheist being 
 right; 
 
 Therefore, the present case is not the case of the world 
 existing without a cause. (See Rule 3, Sec. ii.) 
 
 33. A DisJUNcrrivE Syllogism is one whose 
 major premise is a disjunctive proposition. 
 
 The earth either moves in a circle or an ellipse. 
 But the earth does not move in a circle ; 
 Therefore, it moves in an ellipse. 
 
 It is either spring, summer, autumn, oi winter' 
 But it is not summer, autumn, or winter ; 
 Therefore, it is spring. 
 
 34. Disjunctive syllogisms are easily con- 
 vertible into conditional, and so brought under 
 the foregoing rules ; as, 
 
80 ELEMENTS OP LOGIC. 
 
 if the earth does not move hi a ch*cle it moves in an 
 ellipse ; 
 But it does not move in a circle ; 
 Therefore, it moves in an ellipse. 
 
 35. The Dilemma is a complex conditional 
 syllogism, of which the major premise contains 
 two or more conditional propositions, and the 
 minor a disjunctive proposition ; as, 
 
 If A is B, is D, and if E is F, G is H; 
 But either A is B or E is F ; 
 Therefore, is D or G is H. 
 
 If ^schines joined in the public rejoicings he is iucon- 
 sistent ; if he did not he is unpatriotic ; 
 
 But ^schines either did or did not join in the public 
 rejoicings ; 
 
 Therefore, he is either inconsistent or unpatriotic. 
 
 The advantage of the Dilemma is this : that 
 you may not be able to affirm or deny any 
 proposition, but you may always state it dis- 
 junctively. Demosthenes might not be able to 
 prove that .^chines did join in the public re- 
 joicing, or that he did not join ; but certainly 
 he did or he did not. 
 
 This Dilemma may easily be reduced to two 
 
OF 
 
 DILEMMA. 81 
 
 or more conditional syllogisms and these to 
 regular syllogisms. 
 
 36. Thus all hypothetical syllogisms as weU 
 as all otlier arguments may be reduced to regu- 
 lar syllogisms, and so subjected to the test of 
 the logical axiom. But it is more convenient 
 in ordinary practice to try them by their own 
 rules. 
 
 EXAMPLES. 
 
 1. If this man has a fever, he is sick ; ^S^ 
 But he is sick ; 
 
 Therefore, he has a fever. 
 
 2. The world was created by chance, or by 
 
 an intelligent agent ; 
 But it was not created by chance ; 
 Therefore, it was created by an intelli 
 
 gent agent. 
 
 3. If Louis Phihppe is a good king France is 
 
 likely to prosper ; 
 But Louis Philippe is a good king ; 
 Therefore, France is likely to prosper. 
 
 4:. If C be not the center of the circle some 
 
 other point must be ; 
 
 But no other point can be the center ; 
 
 Therefore, C is the center of the circle. 
 6 
 
82 ELEMENTS OF LOGIC. 
 
 6. If this man were wise he would not speak 
 irreverently of the Scriptures in jest; 
 if he were good, he would not do so in 
 earnest ; 
 But he does it either in jest or in earnest ; 
 Therefore, he is either not wise or he is 
 not good. 
 
 6. If logic is useless it deserves to be neg 
 
 lected ; 
 
 But logic is not useless ; 
 
 Therefore, it does not deserve to be neg- 
 lected. 
 
 7. Either money or produce will be scarce 
 
 in the market; 
 But produce will not be scarce ; 
 Therefore, money will be scarce. 
 
 8. If W. were a general he would have 
 
 power ; 
 But W. is not a general ; 
 Therefore, he has not powei. 
 
 9. If W. be a general he must be obeyed ; 
 But W. must be obeyed ; 
 Therefore, he is a geueraL 
 
DISTINCTIONS OF REASONING. 83 
 
 SECTION Y. 
 
 DISTINOTIONS OF KEASONING. 
 
 1. The divisions of reasoning into Deduction 
 and Induction, Mathematical and Moral, De- 
 monstrative and Probable, by Analogy, A 
 priori, A posteriori, A fortiori, Reductio ad ab- 
 surdum, and Reductio ad impossibile, are only 
 different ways of laying down premises, the 
 process of reasoning being always the same, 
 namely, deductive — from generals to particulars. 
 
 The degree of certainty in the conclusion, 
 when the process of inference is correct, 
 depends upon the degree of certainty in the 
 premises. 
 
 2. In Pure Mathematical REAsoiaww, the 
 principles and judgments beipg always self-evi- 
 dent, the conclusions are absolutely certain ; in 
 Mixed Mathematics self-evident axioms and 
 judgments are mixed with matters of fact 
 and measurements of instruments, to which 
 some uncertainty is attached; consequently 
 the same uncertainty attaches to the conclu- 
 sion. 
 
84 ELEMENTS OF LOGIC. 
 
 EXAMPLE. 
 
 If a straight line meet another straight U7ie^ 
 the sum of the adjacent angles will he equal to 
 two right amgles. 
 
 Suppose the straight line DC E p 
 
 meets the straight line A B 
 at the point C; then will the 
 angles A D and D C B to- ^ B 
 gether be equal to the two right angles ACE 
 and E C B. 
 
 Axiom. — A whole is equal to the sum of all its parts. 
 
 A D is a whole of which A E and E D are its 
 parts. 
 
 Therefore, A D is equal to all its parts, namely, 
 A E and E D. 
 
 Axiom. — If equals be added to equals the sum is equal ; 
 BOB added to ^ D, and D B added to A E 
 plus E D are equals added to equals. 
 Therefore, the sum is equal. 
 
 Now, as A C E is one of the right angles in 
 question, you have only to prove that the other 
 two angles E C D and D C B equal the othei 
 right angle E C B. 
 
DISTINCTIONS OF REASONING. 85 
 
 The sum of all the parts is equal to the whole. 
 
 E D plus D B are all the parts of the angle E B 
 
 Therefore, they are equal to the whole E B. 
 
 Thus you have proved that DOB added to 
 A C D is equal to A C E added to E C B. 
 
 This is a case of pure mathematics, because I 
 have supposed D C a straight line meeting 
 another A B ; but if I take a rod and make a 
 line between two points on a field, I do not know 
 that it is in reality a perfectly straight line. 
 Hence, there is a mixture of practical uncer- 
 tainty, with the absolute certainty of the 
 axioms employed in any ^calculation about it ; 
 hence, such calculation is called mixed mathe- 
 matics. 
 
 3. Induction is a course of argument by 
 which, from the principles of causation, joined 
 with particular phenomena, we infer the gen- 
 eral law of those phenomena. 
 
 Some of the principles of causality are the fol- 
 lowing : No events no phenorrienon happens 
 t'nthout a cause. Like material causes jproduce 
 like effects. No cause can operate where it is 
 not. 
 
 From the principles we directly infer the pos- 
 tulate : The immediate and invariable contecedent 
 
86 fiLEME^TTS OF LOGIC. 
 
 of any ^phenomenon may he presumed to he its 
 cause or contain its cause. 
 
 Jn respect to spiritual agencies tlie principles 
 of causation are the same, except in relation to 
 the will, whose distinguishing characteristic is 
 freedom. Of this alone we cannot predicate 
 that like causes will produce like eflPects. We 
 cannot certainly know how it will behave under 
 any circumstances. 
 
 It should be observed, that it may be beyond 
 human power to perceive, w^hen any physical 
 change takes place, what the real cause is; 
 but we know that it must be found where the 
 event takes place, and that the invariable and 
 immediate antecedent of the event must con- 
 tain it. 
 
 To discover the cause, therefore, of any phe- 
 nomenon, we must observe under what circum- 
 stances that phenomenon happens and notice its 
 invariable antecedent. 
 
 Having done this we are prepared to make 
 the proper inference, and the whole process ca# 
 be put into a syllogism with the particular 
 cause, as discovered in one or two cases, for a 
 minor premise, and a principle of causation for 
 a major premise. The principles of causality 
 
DISTINCTIONS OF REASONING. 87 
 
 are intuitively true, like the axioms of mathe- 
 matics ; hence, induction has the same certainty 
 as mixed mathematics. 
 
 EXAMPLE. 
 
 The law of magnetic attraction, or that the 
 magnet will always attract iron, is proved thus : 
 
 A material cause will always produce the same effect. 
 
 Or, more particularly, 
 
 "Whatever is the cause of the attracting of iron in one 
 or two cases will always attract iron ; 
 A magnet is the cause of attracting iron in one or twc 
 
 Therefore, it will always attract iron. 
 
 ITow how do we know that it was the 
 magnet and not something else that caused the 
 iron to move ? 
 
 We must make several experiments, and 
 apply the following rule : 
 
 BITLE FOR OBSERVATION. 
 
 If a phenomenon he preceded hy anything^ so 
 that when that thing is present in different dr- 
 efimsta/nces that phenomenon takes place, but 
 
88 ELEMENTS OF LOGIC. 
 
 does not take jplace when that thing is absent 
 though the circumstances remain the saine^ tJien 
 that thing is the cause of the ^phenomenon or 
 contains the cause, 
 
 . This rule will show, on making a few experi 
 ments, that the magnet is the cause of the at- 
 traction of iron. 
 
 Some things will not admit of the latter part 
 of the rule being applied, as matter, gravita- 
 tion, electricity, etc., can never be absent from 
 any event in this world. 
 
 This rule in its two parts may be symbolically 
 exhibited thus: 
 
 Part I.— A BO. A D E. 
 a b c. a d e. 
 
 Let a represent a phenomenon, and A some- 
 thing supposed to be its cause. In one case A 
 has the circumstances or adjuncts B C, in the 
 other case different circumstances, D E. Now 
 a appearing with A in different circumstances 
 shows the latter to be its cause. 
 
 Part II.—N0W, if we have ABO. B Q 
 
 a b c. be, 
 this will show the absence of a when A is 
 absent, though the circumstances which at- 
 tended A remain the same. 
 
DISTINCTIONS OF REASONING. 89 
 
 Sometimes the particular cause is obtained "by 
 testimony or revelation, and you have only to 
 supply the major premise. Thus, we know God 
 predicted contingent events in the prediction 
 concerning the sins of Judas and Peter, and 
 from this we prove his absolute foreknowledge. 
 
 In this case the arguments would stand thus ; 
 
 Whoever can predict contingent events foreknows aU 
 things. 
 God has predicted contingent events ; 
 Therefore, God foreknows all things. 
 
 To prove the minor premise we may say — 
 
 Human transgressions are contingeut events ; 
 God has predicted human transgressions in the case of 
 Judas and Peter ; 
 Therefore, God has predicted contingent events. 
 
 By induction the psychologist discovers dis- 
 tinctions between the powers of the mind ; for 
 example, that sensation and perception cannot 
 give the idea of space, but some other power 
 called intuition or the reason. 
 
 4. Reasoning from Analogy is arguing with 
 premises made up of principles and judgments 
 respecting similar things, or things that are alike 
 in some relations. This definition would in- 
 clude induction, as treated by most writers on 
 
90 EliEMENTS OP LOGIC. 
 
 the subject; but I consider the difference to 
 be very important, because the principles on 
 which Induction is based -are certainties, but 
 "■hose of Analogy are but probabilities. 
 
 Some of the principles on which reasoning by 
 Analogy is based are : 
 
 Sirrdla/r causes will "be likely to ^produce simir 
 la/r effects. 
 
 Things that resemble each other in certain at- 
 i/Hhutes or relat/ix)ns will he likely also to resem- 
 hU each other in some other attributes or relations. 
 
 An att/rihute found in several individuals be- 
 longs to their class. [This is the old principle of 
 /nduction.] 
 
 Thus, horned animals have cloven hoofs, is a 
 law in natural history, and is proved thus : 
 
 Animals that resemble each other in some attributes are 
 likely to resemble each other in other attributes ; 
 
 All horned animals resemble the ox, sheep, etc., in being 
 horned ; 
 
 Therefore, they will be likely to resemtle them in other 
 attributes as having cloven hoofs. 
 
 In the following example the conclusion dis- 
 agrees with facts : 
 
 An attribute of a, b, and c clovers is likely to belong to 
 
DISTINCTIONS OF REASONING. 91 
 
 5. Keasoning a Priori is reasoning from 
 antecedents to consequents. Thns, the idea 
 of God, the perfect and infinite One, is proved 
 true by the pre-existing ideas of infinity and 
 perfection. 
 
 Every necessary and universal idea of the human mind 
 must indicate a reality; 
 
 The ideas of the perfect and infinite are necessary and 
 universal in the human mind ; 
 
 Therefore, they indicate a reality. 
 
 6. Eeasoning a Posteriori is reasoning from 
 consequents to antecedents. 
 
 Whatever exhibits marks of design proves an intelligent 
 author ; 
 The world exhibits marks of design ; 
 Therefore, the world proves an intelligent author. 
 
 7. Eeasoning a Fortiori is inferring a judg- 
 ment from premises which have already been 
 admitted to prove a point less probable. 
 
 If robbery deserves imprisonment, much more doea 
 highway robbery. 
 
 If God foresees contingent events he must foresee neces- 
 sary events. 
 
92 ELEMENTS OF LOGIC. 
 
 8. Reduotio ad absurdum is proving that a 
 certain proposition is true, because its contra- 
 diction involves an absurdity. 
 
 9. Reductio ad impossibile is proving a pro 
 position to be true by showing that its contra 
 diction is inadmissible. 
 
 These are often employed in mathematics. 
 
 10. Probable reasoning is drawing infer- 
 ences from premises that are not certain, but 
 more or less probable. 
 
 When both premises are of this character 
 then the result is not so probable as either pre- 
 mise, but as a fraction of one of them. 
 
 Thus, if the probability of the arrival of ocean 
 mail to-day may be represented by |, and the 
 probability of your receiving letters by it is J, 
 then the probability of your receiving letters 
 to-day is but J of |, that is, }. 
 
 The rule is to represent the jprobability of 
 each premise as compared with certainty hy a 
 fraction^ and multiply these fractions together 
 for a result, 
 
 EXAMPLES, 
 
 1. Thirty-two degrees Farenheit will always 
 freeze water. 
 
DISTINCTIONS OF REASONING. 98 
 
 2. Swans are white. 
 
 3. Jupiter is inhabited. 
 
 4 If one straight line cross another straight 
 line the opposite angles are equal. 
 
 5. The freedom of the will is proved by the 
 
 idea of liberty. 
 
 6. The shadow of the earth upon the moon 
 
 proves that it is round. 
 
 7. If highway robbery and murder deserve 
 
 death, piracy deserves death. 
 
 8. A certain reporter is generally correct, 
 
 say five times out of six. A certain 
 statement is probably his report, the 
 probability being represented by two 
 fifths, what is the probability of the 
 report being true ? 
 
 9. If the probability of your winning a game 
 
 be one half, what is the probability 
 of your winning three games in suc- 
 cession ? 
 
 10. The law of terrestrial gravitation is proved 
 
 by an apple falling to the ground. 
 
 11. A certain degree of attention is necessary 
 
 to memory, as experience demonstrates. 
 
 12. Swine have horns, if what is true of 
 
 individuals is true of a class. 
 
94 ELEMENTS OF LOGIC. 
 
 18. This servant will always return in due 
 season, because he always has done so. 
 
 14. The emperor will declare war, becausei 
 
 he never submits to a national insult. 
 
 15. The will is free, and therefore its future 
 
 acts are unknown by even an infinite 
 mind. 
 
 16. Ketribution may be expected in a future 
 
 state, judging from the effects of virtue 
 and vice in this life. 
 
 17. The will never acts without some motive, 
 
 and therefore, if you know a man's 
 motives in any case, you may know 
 how he will choose. 
 
 18. This case is typhus fever, for it exhibits 
 
 many symptoms of that disease. 
 
 19. Mercury, Yenus, and the Earth are 
 
 opaque, and therefore all the planets 
 are opaque. 
 
 20. The bull-dog, terrier, mastiff, etc., bark, 
 
 tlierefore, all dogs bark. 
 
 21. Quadrupeds, birds, fishes, etc., have a 
 
 nervous system ; therefore, all animals 
 have a nervous system. 
 
PART IV. 
 
 OF FALLACIES. 
 
 1. The fourth part of Logic treats of Falla- 
 cies. 
 
 2. A Fallacy is an unsound argument of 
 any kind. 
 
 3. Fallacies are of two kinds; logical falla- 
 cies and material fallacies. 
 
 4. I. Logical Fallacies are those which in 
 form violate any of the rules of syllogism. 
 
 In these the error is entirely in the process 
 of reasoning, and the conclusion does not follow 
 from the premises ; as, 
 
 Every rational agent is accountable; 
 Brutes are not rational agents ; 
 Therefore, brutes are not accountable. 
 
 This violates the third rule of syllogism. 
 
 5. II. Material Fallacies are those which 
 in form do not violate any of the rules of syl 
 
96 ELEMENTS OF LOGIC. 
 
 logism, but the premises either are not wholly 
 true in fact, are unduly assumed, or result in a 
 conclusion not relevant to the question which is 
 argued. 
 
 In material fallacies the fault is entirely in 
 the matter of the propositions, and not in their 
 form or connection. 
 
 All bodies move toward the center of the universe ; 
 All bodies move toward the center of the earth ; 
 Therefore, the center of the earth is the center of the 
 universe. 
 
 In this example there is no fault in the pro- 
 cess of reasoning; the conclusion results from 
 the premises, but the minor premise contains a 
 statement which is not true in fact. 
 
 Some logicians make a third division of 
 fallacies into semi-logical, including those made 
 by ambiguous terms: for if these terms aroused 
 in two senses they make a logical fallacy ; and if 
 they are used in only one sense they make a 
 material fallacy ; and you cannot always tell 
 which. A simple instance is the following : 
 
 Light is contrary to darkness ; 
 
 Feathers are light ; 
 
 Therefore, feathers are contrary to darkness. 
 
OF FALLACIES. 97 
 
 6. Fallacies are rarely presented in the syl- 
 logistic form. They are usually found in enthy- 
 memes, and the error lurks in the suppressed 
 proposition. 
 
 Sometimes they are offered in the form of 
 questions so stated that a false conclusion will 
 be likely to be implied. 
 
 7. Whately remarks, All jests are fallacies. 
 They tend to excite laughter by betraying theii 
 fallacious character while putting on the air of 
 serious argument. The contrast amuses. For 
 example : A gentleman seeing a young man 
 whom he knew going by with a looking-glass, 
 cried out, "Ah, Joseph, don't carry that glass 
 about, it will reflect on you." This, reduced to 
 a syllogism, will be found to violate the first rule 
 of syllogism, by having an equivocal middle. 
 
 8. To determine whether an argument be 
 valid or fallacious, let the following directions 
 be followed. 
 
 EULE. 
 
 Reduce the argument to a syllogistic form.. 
 If it he found incapable of taking that form 
 it is of course a fallacy. If it he reducible to a 
 njllogism^ ohserve carefully the import and the 
 number of its terms am.d 'prepositions^ and apply 
 
98 ELEMENTS OP LOmC. 
 
 the rules of syllogisms. If it violates any of 
 them it is a logical fallacy. If not., observe if 
 either of the Remises he untrue or inadmissible^ 
 or the same as the conclusion., or result in a coti- 
 elusion different from the one required. If so 
 it is a material fallacy. 
 
 SECTION I. 
 
 LOGICAL FALLACIES. 
 
 9. It is evident that logical fallacies are aa 
 numerous as are the ways of violating the five 
 rules of syllogism. 
 
 Most of those made by ambiguous terms may 
 be classified as follows : 
 
 10. I. The Fallacy of Equivocation, arising 
 from an equivocal word, or from the ambiguous 
 structure of the sentence. 
 
 This class will be found to violate the first 
 rule of syllogism ; as, 
 
 All that believe shall be saved ; 
 
 The devils believe ; 
 
 Therefore, the devils shall be saved. 
 
 Every one desires happiness; 
 
 Virtue is happiness ; 
 
 Therefore, every one desires virtue. 
 
LOGICAL FALLACIES. 09 
 
 In the first example the term believe is equiv 
 ocal, having two different senses. There is, 
 therefore, in reality, two terms ; and the syllo- 
 gism, consequently, has four terms, which is con- 
 trary to Eule I of syllogisms. In the second 
 example the minor premise is ambiguous. 
 
 11. II. The Fallacy of Similar Expression 
 arises from words that are derived from the 
 same root and are similar in sound, but not in 
 sense; such as art, artful; faith, faithful,' 
 design, designing. As, 
 
 **^ Designing men should be avoided : 
 
 ^ This man has many designs ; 
 
 ^ Therefore, he should be avoided. 
 
 Z This violates Rule I of syllogism, for there are 
 
 ^ in reality four terms. 
 
 'S 12. III. The Fallacy of Composition or Di- 
 
 ^ VISION is when the middle term is used collect- 
 ively in one premise, and not collectively, but 
 distributively, in the other. As, 
 
 Two and three are even and odd ; 
 Five is two and three; 
 Therefore, five is even and odd. 
 
 Tliis is a fallacy of composition. Two and 
 three is the middle term, and it is used distrib- 
 
100 ELFMENTS OF LOGIC. 
 
 atively in the major premise, and collectively 
 in the minor premise. Hence there are properly 
 four terms in this argument, which is contrary 
 to Rule I of syllogism. 
 
 The planets are seven ; 
 Mercury and Venus are planets ; 
 Therefore, Mercury and Venus are seven. 
 
 This is a fallacy of division. The middle 
 term is used distributively in the minor premise, 
 and collectively in the major. 
 
 13. lY. The Fallacy of Accident is when 
 the middle term is understood simply and as to 
 its essence, in one premise, but in the other is so 
 used as to imply that something, which does 
 not belong to it essentially, but accidentally^ is 
 
 taken into account with it. As, 
 
 » 
 
 Whatever is bought in the shambles is eaten by man ; 
 Raw meat is bought in the shambles ; 
 Therefore, raw meat is eaten by man. 
 
 Here the middle term is hought in the 
 shambles^ and it is used in the minor premise, 
 as considered simply, and as to its essence ; but 
 in the major premise it should be understood in 
 connexion with something else, as, when prop 
 
LOGICAL FALLACIES. 101 
 
 efrby cooked. Hence, four terms are empJoyed 
 in reality in this argument which violates Rule J 
 of sj^llogism. 
 
 EXAMPLES. 
 
 1. ]^o one is rich who has not enough ; 
 No miser has enough ; 
 Therefore, no miser is rich. 
 
 2. All that glitters is not gold ; 
 Tinsel glitters ; 
 Therefore, tinsel is not gold. 
 
 3. He who calls you a man speaks truly ; 
 He who calls you a fool calls you a man ■, 
 Therefore, he who calls you a fool speaks 
 
 truly. 
 
 4. W"arm countries alone produce wine 
 Spain is a warm country ; 
 Therefore, Spain produces wine. 
 
 5. What we eat grew in the fields; 
 Loaves of bread are what we eat ; 
 Therefore, loaves of bread grew in the 
 
 fields. 
 0. What is universally believed is true^ 
 The existence of a God is true; 
 Therefore, the existence of a God is uni- 
 versally believed. 
 
102 ELEMENTS OF LOGIC. 
 
 7. Whatever is universally believed must 
 
 be true ; 
 The immortality of the soul is not imi 
 
 versally believed ; 
 Therefore, it is not true. 
 
 9. What I am you are not ; 
 But I am a man ; 
 Therefore, you are not. 
 
 SECTIOlSr II. 
 
 MATERIAL FALLACIES. 
 
 14. Material fallacies may be as numerous as 
 errors of learning, mistakes of judgment, or 
 willful duplicity can make them. 
 
 The most common may bt included in th^ 
 following classes: 
 
 15. I. The Fallacy of begging the ques- 
 tion is that of inferring a conclusion from pre- 
 mises substantially the same as the conclusion, 
 or depending upon the conclusion ; as ivhen we 
 attempt to prove a thing by itself, or by a 
 synonymous word, or by something which is 
 itself to be proved by the very point you seek 
 to establish. As, 
 
MATERIAL FALLACIES. 103 
 
 God is eternal, because he is without beginning or end* 
 Opium produces sleep because it is soporific. 
 We know the Scriptures are true from the infallible 
 testimony of the Church, and we know the Church is in- 
 fallible by the declaration of the Scriptures. 
 
 The last example is what is called reasoning 
 kn a circle. 
 
 16. II. The Fallacy of false assumption is 
 when the premises are unduly or unwarrant- 
 ably assumed ; as when we attempt to prove a 
 thing by something that is false, or unknown, or 
 partially stated. As, 
 
 All bodies that move themselves are animated ; 
 All stars and heavenly bodies move themselves ; 
 Therefore, the stars and all the heavenly bodies are 
 animated. 
 
 Meteors have a volcanic origin ; 
 
 For they cannot otherwise be accounted for. 
 
 "We hold this doctrine to be true by the authority of 
 St Paul in such and such texts. 
 
 This is a fallacy, if these texts do not contain 
 the whole of the apostle's testimony to the point 
 in question, and is sometimes called the fallacy 
 of partial reference. 
 
 17. III. The Fallacy of mistaking the ques- 
 noN is that in which the premises are such as 
 
104 ELEMENTS OF LOGIC 
 
 result in a conclusion diflPerent from the one 
 required, but apparently the same. As, 
 
 Alfred the Great was a scholar ; 
 
 For he founded the University of Oxford. 
 
 18. The sophist will not always draw out the 
 conclusion, but leave it to be inferred, for in 
 that case its irrelevancy will be less likely to be 
 detected. 
 
 19. This fallacy is often conveyed in appeals 
 to prejudice, to the passions, or to personal 
 considerations; sometimes in the form of ob- 
 jections, and sometimes by implication, in ar- 
 guments, which go to prove a part of what is 
 required. As, 
 
 Gentlemen of the jury, this man is a friend to the rights 
 of the people. Will you convict him ? 
 
 This work is not evangelical. Look at the statements 
 made in the eighth chapter. Are these warranted by the 
 New Testament ? 
 
 These objections are many and weighty. Can such a 
 science be worthy of credit? 
 
 EXAMPLES. 
 
 1. The soul occupies the whole body, for if 
 resides in every member. 
 
MATERIAL FALLACIES. 105 
 
 2. The plant is capable of much growth, for 
 
 it has great vegetative powers. 
 
 3. The soul suffers dissolution with the body 
 
 at death. See Ecc. iii, 18, 19, 20 ; Job 
 xxxiv, 15 ; Psa. cxlvi, 3, 4. 
 
 4. The Bible cannot be the rule of faith, foi 
 
 men understand it very differently. 
 
 5. We may expect some dreadful disaster, for 
 
 the sky last night was full of falling 
 meteors. 
 
 6. The appearance of strange birds flying 
 
 south in the highest northern latitudes 
 which have been explored, and of float- 
 ing plants, as well as men who declare 
 by signs that they come from the far 
 north, indicate that the earth is concave 
 about the poles, and the interior of the 
 earth is inhabited. 
 
 7. Mohammed is a prophet, for the Koran de- 
 
 clares it ; and the Koran is true, for Mo- 
 hammed received it from God, as he 
 affirms. 
 
 8. Whatever is contrary to experience is not 
 
 to be believed. 
 Miracles are contrary to experience ; 
 Therefore, miracles are not to be believed 
 
106 ELEMENTS OF LOGIC. 
 
 9. Paul was not a Komaii citizen, for he was 
 
 born at Tarsus in Cilicia. 
 
 10. Job was a great sinner, for he was over- 
 
 whelmed with great calamities. 
 
 11. No evil should be allowed that good maj^ 
 
 come of it ; 
 All punishment is an evil ; 
 Therefore, no punishment should be al 
 
 lowed that good may come of it. 
 
 12. "Ho man can possess power to perform an 
 
 impossibility ; 
 A miracle is an impossibility; 
 Therefore, no man can possess power to 
 
 perform a miracle. 
 
 13. Which of you having an ox or an ass fall 
 
 into a pit, will not pull him out on the 
 Sabbath day? 
 The last is a personal appeal, called Ar- 
 gumentum ad hominem, and is allow- 
 able when your object is to silence the 
 captious. As offered to prove the 
 point in question, it is a fallacy. (19.) 
 
SUPPLEMENT 
 
 SECTION I. 
 
 MOODS AND FIGURES OF SYLLOGISMS 
 
 This subject may be advantageously studied 
 after the scholar has become perfectly familiar 
 with the foregoing, and is expert in the applica 
 tion of all the rules of logic. In that case it 
 may serve to discipline the mind, otherwise it 
 will only perplex. One may be an able logician 
 without the doctrine of moods and figures. 
 
 1. The Mood of a Syllogism is the deaigna 
 tion of the quantity and quality of its proposi- 
 tions. 
 
 This is done by the symbols A, E, I, and O, 
 which stand respectively for the universal al 
 tirmative, universal negative, particular affirma- 
 tive, and particular negative. 
 
108 ELEMENTS OF LOGIC. 
 
 Tlie following, for example, is A, A, A 
 
 A. All animals are mortal; 
 
 A. All men are animals ; 
 
 A. Therefore, all men are mortal 
 
 The following is E, A, E. 
 
 E. No human invention is perfect ; 
 A. Language is a human invention 
 E. Therefore, no language is perfect. 
 
 2. The whole number of the moods of valid 
 syllogisms is only eleven. A, A, A, — A, A, I, — 
 A, E, E,— A, E, O,— A, I, I,— A, O, O,— E, A, 
 E,— E, A, O,— E, I, 0,-1, A, 1,-0, A, O 
 
 3. As there are sixty-four different ways in 
 which it is possible for A, E, I, O to be com- 
 bined to form a syllogism, there might be fifty- 
 three other moods formed, as E, E, A, — I, I, I, 
 etc. ; but they would offend against one or more 
 ^f the five rules of syllogism. As, 
 
 L Some birds are animals ; 
 
 I. Some fish are animals ; 
 
 I. Therefore, some fish are birds. 
 
 E. No human invention is perfect ; 
 
 E. No language is perfect ; 
 
 A. Therefore, language is a human invention. 
 
MOODS AND FIGURES OF SYLLOGISMS. 109 
 
 These examples are contrary to the fifth rule 
 of syllogisms. Two negative or two particular 
 premises prove nothing. 
 
 4. The Figure of a Syllogism denotes the 
 situation of the middle term, in respect to the 
 major and minor terms. 
 
 5. Figure First is when the middle term is 
 the subject of the major premise and the pre- 
 dicate of the minor premise. As, 
 
 A. Every wicked man is miserable ; 
 
 A. Every tyrant is a wicked man ; 
 
 A. Therefore, every tyrant is miserablev 
 
 E. No discontented man is a happy man ; 
 A. Every wicked man is a discontented man ; 
 E. Therefore, no wicked man is a happy man. 
 
 A. All the faithful are dear to God; 
 I. Some that are afflicted are faithful ; 
 I. Therefore, some that are afflicted are dear to God. 
 
 E. No virtue is an evil ; 
 I. Some difficult things are virtues ; 
 O. Therefore, some difficult things are not evils. 
 
 6. To this figure the logical axiom applies 
 directly ; and to this figure all the other figures 
 may be reduced. 
 
no ELEMENTS OF LOGIC. 
 
 \M, Figure Second is when the middle term is 
 jJ^G predicate of both the major and the minor 
 if jpremises ; as, 
 
 xr E. No happy man is discontented ; 
 
 /A. Every wicked man is discontented ; 
 vV E^y^Therefore, no wicked man is a happy man. 
 
 xA.. Every wicked man is discontented i 
 L ^. No happy man is discontented ; 
 
 y Jfe. Therefore, no happy man is a wicked man. 
 
 . f^ ^ E. No evil is a virtue; 
 y Vs I. Some difficult things are virtues ; 
 
 (). Therefore, some difficult things are not evils. 
 
 A. Every good man is afflicted:/ 
 
 0. Some rich men are not afflicted ; 
 
 0. Therefore, some rich men are not good men. 
 
 8. Figure Thisd is when the middle term is 
 the subject of both the premises. As, 
 
 A. All the faithful are dei\r to G-od ; 
 A, All the faithful are aMicted ; 
 I. Therefore, some that are afflicted are dear to God. 
 
 I. Some of the faithful are afflicted ; 
 A. All the faithful are dear to God ; 
 I. Therefore, some that are dear to God are afflicteil 
 
 
MOODS AND FIGURES OF SYLLOGISMS. Ill 
 
 A, All the faithful are dear to God ; 
 r. Some of the faithful are aflQicted ; 
 L Therefore, some that are afflicted are dear to God 
 
 El No virtue is an evil ; 
 
 A. All virtues are difficult ; 
 
 O. Some difficult things are not evils. 
 
 O. Some called Christians are not true believers ; 
 A. All called Christians profess faith ; 
 
 0. Therefore, some who profess faith are not true 
 Delievers. 
 
 E. No virtue is an evil ; 
 I. Some virtues are difficult. 
 O. Therefore, some difficult things are not evils. 
 
 9. Figure Fourth is when the middle term is 
 the predicate of the major and the subject of 
 the minor premise. 
 
 10. This is the reverse of the first figure and 
 is the most awkward of all. As, 
 
 A. Every tyrant is a wicked man ; 
 A. Every wicked man is miserable , 
 
 1. Therefore, some that are miserable are tyrants. 
 
 A , Every wicked man is discontented ; 
 
 E. No disomtented man is happy; 
 
 E. Therefore, no happy man is a wickcq man. 
 
112 ELEMENTS OF LOGIC. 
 
 I. SoDic afflicted are faithful ; 
 A. All the faithful are dear to God ; 
 
 I. Therefore, some that are dear to God are alBicled. 
 
 E. No evil is a virtue ; 
 
 A. All virtues are difficult ; 
 
 0. Therefore, some difficult things are not evils* 
 
 E. No evil is a virtue ; 
 I. Some virtues are difficult ; 
 O. Therefore, some difficult things are not evils. 
 
 II. Each of the eleven allowable moods will 
 not go in every figure, for it will violate some 
 of the rules of syllogism in one figure, though 
 not in another. For example. A, A, A, which 
 goes in the first figure will not go in the third 
 figure. 
 
 Figure 1st. All wicked men are miserable ; 
 All tyrants are wicked men ; 
 Therefore, all tyrants are miserable. 
 
 Figure 8d. All wicked men are miserable ; 
 All wicked men are tyrants ; 
 Therefore, all tyrants are miserable. 
 
 This violates Kule III of syllogism, for the 
 term tyrants is distributed in the conclusion, 
 though not in the premises. Besides, the minor 
 premise is incorrect. 
 
MOODS AND FIGURES OF SYLLOGISMS. 113 
 
 12. Some of the moods, also, which might be 
 admitted in some of the figures are useless, as 
 having a particular conclusion when the uni- 
 versal might be drawn. 
 
 For example. A, A, I will go in the fourth 
 figure, but in the first figure it is useless. 
 
 Figure 4th. A. Every tyrant is a wicked man ; 
 
 A. Every wicked man is miserable ; 
 
 I. Therefore, some that are miserable are 
 tyrants. 
 
 Figure Ist. A. Every wicked man is miserable ; 
 
 A. Every tyrant is a wicked man ; 
 
 A. Therefore, every tyrant is miserable. 
 
 But, 
 
 I. Therefore, some tyrants are miserable; 
 
 would be a useless conclusion, for a universal 
 conclusion is legitimate. 
 
 13. For these reasons, out of the forty-four 
 allowable moods, which mighty possibly go into 
 the four figures, only nineteen are retained. 
 Examples of all the nineteen are found above 
 unier the definitions of the four figures. 
 
 14. To assist in remembering these moods, 
 and the figure in which they are found, the fol- 
 lowing mnemonic lines have been invented : 
 
114 ELEMENTS OF LOGIC. 
 
 First. bArbA'rA, cElA'rEnt, dArll, f Erl'O. 
 SecoTid. cEsA'rE, cAmE'strEs, f Estl'iiO, bArC/kO. 
 Third, dArA'ptI, dlsA'inls, dAtl'sI, fElA'ptOn, 
 
 bOkA'rdO, f Erl'sO. 
 Fourth. brAmA'ntlp, cAmE'nEs, dIraA'rIs, fEsA'pO, 
 frEsI'sOn. 
 
 Here, it will be seen, are only ten moods, 
 but some are employed in more than one figure, 
 as E, 1, O, making nineteen in all the four 
 figures. 
 
 15. If any syllogism be not found in these 
 lines it cannot be a valid syllogism ; it is a 
 logical fallacy. 
 
 16. The utility of the mnemonic lines is like 
 that of duly certified weights and measures, by 
 which we test the size or weight of bodies with- 
 out the necessity of a minute and tedious calcu- 
 lation. 
 
 SECTION II. 
 
 REDUCTION. 
 
 17 The process by which the moods of the 
 last three figures are changed into a mood of 
 the first figure is called Heduction. 
 
 18. This is done in two ways; by Ostensive 
 Reduction and by E-eductio ad impossibile. 
 
REDUCTION. 1 16 
 
 19. OsTENSivE Eeduction is performed by 
 the conversion of one of the premises, A into 
 r, E into E, I into I, and bv transposing the 
 premises when occasion requires. 
 
 For example, take Cesare of the second 
 figure. 
 
 cEs. No happy man is discontented ; 
 A. Every wicked man is discontented; 
 rE. Therefore, no wicked man is a happy man. 
 
 This may be converted into Celarent of the 
 first figure by the simple conversion of the 
 major term, thus: 
 
 cE. No discontented man is a happy man ; 
 lA. Every wicked man is a discontented man ; 
 rEnt. Therefore, no wicked man is a happy man. 
 
 Take now Camestres of the second figure and 
 convert that also into Celarent. To do this you 
 will only have to convert the minor premise 
 and transpose the premises,, as will be seen in 
 the following examples. 
 
 cAm. Every wicked man is discontented ; 
 Es. No happy man is discontented; {convert and 
 transpose.) 
 trEs. Therefore, no happy man is a wicked man 
 
il6 ELEMENTS OF LOGIC. 
 
 cE. No discontented man is a happy man ; 
 lA. Every wicked man is discontented ; 
 rEnt. Therefore, no wicked man is a happy man. 
 
 20. In like manner all the moods of the lasf 
 three figures can be reduced into one of the four 
 perfect moods of the first figure. 
 
 21. In the mnemonic lines the initial letters 
 b^ G, d^ y, show to which mood of the first figure 
 the reduction is made, namely, harhara^ celarent^ 
 darii, or ferio. The letter m signifies that the 
 premises are to be transposed, as above, in 
 Camestresj the letter s denotes that the propo- 
 sition, which the preceding vowel stands for, is 
 to be converted by simple conversion, and jp, 
 by particular conversion ; but p in Bramomtvp 
 marks that the premises, when changed, warrant 
 a universal conclusion instead of a particular. 
 The symbols A E I O mark the moods, that is, 
 the quality or quantity of the propositions. 
 
 22. Reductio ad Impossibile is when you 
 reduce a mood to the first figure, by substitut- 
 ing the contradictory of the conclusion for one 
 of the premises ; by which an absurdity follows 
 which proves not directly that the conclusion is 
 true, but that it cannot be false. 
 
 Thus Baroko^ in the second figure. 
 
REDUCTION. 117 
 
 b Ar. Every good man is afflicted ; 
 Ok. Some rich men are not afflicted; 
 O. Therefore, some rich men are not good men. 
 
 bAr. Every good man is afflicted ; 
 bA. All rich men are good men ; 
 r A. Therefore, all rich men are afflicted. 
 
 Which conclusion is notoriously false, and the 
 original conclusion which you had drawn is, 
 therefore, true. 
 
 23. The letter Jc in the mnemonic lines de- 
 notes that the proposition indicated by the 
 vowel immediately preceding is to be substi- 
 tuted by the contradictory of the conclusion ; 
 the other letters, not above explained, have no 
 signification. 
 
 EXAMPLES. 
 
 1. Whoever has reflection and volition has 
 
 the essential properties of mind ; 
 
 Mankind has reflection and volition ; 
 
 Therefore, mankind has the essential prop- 
 erties of mind. 
 
 2. Whatever is universally believed must be 
 
 true ; 
 The existence of God is not universally 
 
 believed ; 
 Therefore, it is not true. 
 
118 ELEMENTS OF LOGIC. 
 
 3. Whoever is capable of deliberate crime is 
 
 responsible ; 
 An infant is not capable of deliberate 
 
 crime ; 
 Therefore, an infant is not responsible. 
 
 4. Some philosophers reckon virtue good in 
 
 itself ; 
 
 The Epicureans did not reckon virtue good 
 in itself; 
 
 Therefore, the Epicureans were not phil- 
 osophers. 
 
 5. Prudence has for its object the benefit of 
 
 individuals; 
 But prudence is a virtue ; 
 Therefore, some virtue has for its object 
 
 the benefit of individuals. 
 
 6. Whatever is expedient is conformable to 
 
 nature. 
 . Whatever is conformable to nature is not 
 hurtful to society. 
 Therefore, what is hurtful to society is 
 never expedient. 
 
 7. No man is happy who is not secure ; 
 No tyrant is secure; 
 
 Therefore, no tyrant is happy. 
 
EXAMPLES. 119 
 
 S. All true patriots are friends to religion ; 
 Some great statesmen are not friends to 
 
 religion ; 
 Therefore, some great statesmen are not 
 
 true patriots. 
 
 9. All true Christians have peace ; 
 
 Some afflicted men are true Christians ; 
 Therefore, some afflicted men have peace. 
 
 10. No uncandid man is fit to reason correctly; 
 Some infidels are uncandid ; 
 Therefore, some infidels are not fit to 
 
 reason correctly. 
 
 11. E, E, E,— I, O, 0,—I, E, O. 
 
 12. I, A, I,— A, E, E, in the first figure. 
 
 13. A, A, A in the third figure, A, E, O. 
 
120 ELEMENTS OF LOGIC. 
 
 QUESTIONS IN A GENERAL REVIEW. 
 
 1 . What is Logic ? 
 
 2. What does it assume as its foundation ? 
 
 3. What are first truths ? 
 
 4. What are first principles ? 
 
 5. What is the true process of reasoning ? 
 
 6. What is Aristotle's dictum ? 
 
 7. What is a distributed term ? 
 
 8. What are the rules of distribution? 
 
 9. What is opposition? 
 
 10. What is conversion ? 
 
 11. What two canons have logicians invertoc 
 
 to test the validity of arguments ? 
 
 12. What five rules must be observed ? 
 
 13. What are hypothetical syllogisms? 
 
 14. What two kinds of these? 
 
 15. Can they be reduced to one? 
 
 16. Can they be reduced to categoricals ? 
 IT. What is a dilemma. 
 
 18. What is the special advantage of it? 
 
 19. What distinctions of reasoning art 
 
 found ? 
 
 20. Are these different in principle? 
 
 21. What division of fallacies is made? 
 
APPE^ DIX, 
 
 THE PHILOSOPHY OF INDUCTION.* 
 
 It has long been the fashion to decry the 
 logic of Aristotle, because, its legitimate use 
 not being understood in the medieval schools, 
 it served to divert the minds of men from the 
 study of nature, and set them whirling about in 
 dialectic circles to educe the principles of science 
 and the laws of the universe ; and Bacon and 
 Des Cartes have been lauded to the skies, be- 
 cause they taught that nature reveals her laws 
 only in the passing phenomena of matter and 
 mind, as presented to the senses and the con- 
 sciousness, which must be carefully analyzed 
 
 •First delivered before the Philosophical Society of Dickinson 
 College. 1853. 
 
122 ELEMENTS OF LOGIC. 
 
 and then generalized by the process of induction, 
 A comparison has been made between the or- 
 ganon of Aristotle and the organon of Bacon, 
 or, to speak more precisely, between the method 
 of deduction and of induction, altogether to the 
 disparagement of the former, until at length it 
 has come to pass that it is no longer regarded 
 by many as of vital importance to scientific in- 
 vestigation, while induction is considered as not 
 merely an indispensable auxiliary to the dis- 
 covery of new truths and principles, but as the 
 only fundamental process of inference — the 
 ouly process by which, from facts perceived by 
 the intelligence, you can advance to the determ- 
 ination of the laws and principles which are 
 the objects of science. 
 
 It is remarkable that, notwithstanding the 
 exaltation of induction, since Bacon directed 
 the attention of philosophers to it, no thorough 
 attempts were made to expound its philosophy 
 and to institute its canons until very recently.. 
 Dr. Whewell, Mr. John Stuart Mill, Dr. Henry 
 Tappan, and Sir William Hamilton, and writers 
 in other tongues, have supplied the desideratum 
 by works profoundly investigating the whole 
 subject of logic, and particularly induction. 
 
THE PHILOSOPHY OF INDUCTION. 12b 
 
 We have, therefore, the means by which we 
 may sit in judgment upon the question and 
 rendei an enlightened verdict. 
 
 COUSIN'S VIEW OF INDUCTION. 
 
 The particular aspect of the question which 
 It is the design of this paper to examine, is 
 clearly presented in the following remarks in 
 Cousin's critique of the philosophy of Locke. 
 Cousin wonders, as well he may, that a leader 
 in the sensual and Baconian school of philoso- 
 phy should so far be warped from his appropri- 
 ate sphere of thought as to lose sight altogether 
 of induction as one of the legitimate modes of 
 knowledge, while, at the same time, casting 
 contempt upon the syllogism as the proper type 
 of the reasoning process ! 
 
 "Thus intuition and demonstration are the 
 different modes of knowledge, according to 
 Locke. But are there no others? Have we 
 not knowledge which we acquire neither by 
 intuition nor demonstration? How do we ac- 
 quire a knowledge of the laws of external 
 nature? Take which you please, gravitation for 
 instance. Certainly there is no simple intuition 
 and immediate evidence here, for experiments 
 
124 ELEMENTS OF LOGIC. 
 
 multiplied and combined are necessarj to give 
 the slightest law ; and even this will not snilice, 
 since the slightest surpasses the number, what- 
 ever it be, of experiments from which it is 
 drawn. There is need, therefore, of an inter- 
 vention of some other operation of mind besides 
 intuition. Is it demonstration? Impossible, for 
 demonstration is the perception of the relation 
 between two ideas by means of a third ; but it 
 is upon the condition that the latter should be 
 more general than the two others, in order to 
 embrace and connect them. To demonstrate 
 is, in the last analysis, to deduce the particular 
 from the general. Now, what is the more gen- 
 eral physical law from which gravitation can be 
 deduced ? We have not deduced the knowledge 
 of gravitation from any other knowledge an- 
 terior to it, and which involves it in the germ. 
 How, then, have we acquired this knowledge, 
 wliich we certainly have ? and, in general, how 
 do we acquire the knowledge of physical laws? 
 A phenomenon having been presented a num* 
 ber of times, with a particular character and in 
 particular circumstances, we have judged that 
 if this same phenomenon should occur in similar 
 circumstances, it would have the same character; 
 
THE PHILOSOPHY OF INDUCTION. 125 
 
 that, is to say, we have generalized the particular 
 character of this phenomenon. Instead of de- 
 scending from the general to the particular, we 
 have ascended from the particular to the gen- 
 eral. This general character is what we call a 
 law : this law we have not deduced from a more 
 general law or character; we have derived it 
 from particular experiments in order to transfer 
 it beyond them. It is not simple resumptior 
 nor a logical deduction ; it is what we call in- 
 duction. It is to induction that we owe all 
 conquests over nature, all our discoveries of the 
 laws of the world." 
 
 PEOBLEM TO BE SOLVED. 
 
 This clear and eloquent exposition of the 
 order of thought in the two processes of deduc- 
 tion and induction, as it has commonly been 
 apprehended, enables us to present, without 
 danger of being misunderstood, the problem 
 which we wish to solve, namely, that there is 
 no fundamental difference between induction 
 and deduction ; but in both cases the mind pro- 
 ceeds from the more general to the less general, 
 or from the general to the particular ; and that 
 the opposite process of proceeding from the 
 
126 ELEMENTS OF LOGKJ. 
 
 particular to the general is utterly inipossible. 
 All inference, I maintain, is of one kind— -it is 
 deductive. You may take as many particulars 
 as you can gather together, and they will be 
 perfectly barren of any consequence, unless you 
 can attach them to a general principle. Yon 
 may sum them up and call it generalization, 
 but you can never infer a universal law, you 
 can make no scientific generalization by means 
 of them, unless you can put them upon some 
 broader general principle than that which you 
 wish to educe from them. Take the instance 
 of scientific induction referred to by Cousin, 
 that of the law of gravitation, and analyze it 
 thoroughly, and you will see that it is at bottom 
 deduction. A philosopher observes a material 
 substance — a body — say, an apple, fall to the 
 ground ; he observes another body, a leaf, in 
 like manner disengaging itself from the ^ree 
 and following the apple ; he casts a stone into 
 the air, it takes the same direction ; he casts a 
 feather upon the winds, and, though for a time 
 it is resisted by the currents of air, yet, when 
 these obstacles cease, it directly in like manner 
 falls to the earth. From these- particulars he 
 observes that it is the material substance in 
 
THE PHILOSOPHY OF INDUCTION. 127 
 
 Lhese different bodies that exliibits the phe- 
 nomenon of falling to the earth, and not any 
 particular qualit}' of the apple, or the leaf, or 
 the Stone, or the feather; and this is his analysis. 
 Thereupon he proceeds to infer that all bodies — 
 all material substances — in all parts of the globe 
 will behave in like manner ; in other words, he 
 infers the law of terrestrial gravity. This is his 
 induction. He seems, indeed, merely to pro- 
 ceed from the particular to the general ; but 
 how? by what authority? on what ground? To 
 answer this question is to solve the problem of 
 induction. 
 
 DE. WHEWELL'S SOLUTION. 
 
 Di Whewell, who has elaborated this point, 
 says that the conclusion is not a mere summing 
 up of these particulars, and of all known par- 
 ticulars of the same nature ; it is something 
 more, a conception which, while it expresses 
 these particulars, transcends them ; it reaches 
 all possible cases of the same kind. But how 
 do we get this conception ? He says we leap to 
 it: "Induction mounts the ladder by a leap, 
 which is out of the reach of method." But 
 then it can turn round and verify itself by de- 
 
128 ELEMENTS OF LOGIC. 
 
 scending the ladder, step by step, by the de- 
 ductive process. But how do we make the 
 leap? By a sort of philosophical "sagacity — 
 a scientific instinct — " which is the rare gift 
 of some superior minds. But this explains 
 nothing. 
 
 ANALYSIS OF INDUCTION, BY J. S. MILL. 
 
 Now, if this inference of the general law 
 from observed particulars be a legitimate pro- 
 cedure, and it cannot admit of any solution, 
 then it must be regarded as ultimate, and we 
 may call it induction, and mark it as the oppo- 
 site of deduction. But it happens that we can 
 analyze the process in this instance and in all 
 instances of induction ; and this analysis will 
 show that the subtle movement of the reasoning 
 faculty from the particulars to the general is 
 upon the broad basis of a universal and intuitive 
 principle ; and thus the whole process could 
 easily be put into the form of a syllogism, 
 with the principle for its major premise, 
 and these observed particulars for its minor 
 premise. 
 
 Happily the desired analysis of this process is 
 furnished to our hand by Mr. Mill, who not only 
 
THE PHILOSOPHY OF INDUCTION. 129 
 
 goes with Cousin in maintaining that induction 
 is one fundamental mode of investigation, but 
 advances far beyond him, contending with great 
 ability that inference is always fundamentally 
 from particulars to generals, and that deduction 
 is only an intermediary process, which may be 
 resorted to for convenience, but is of no avail 
 for original discovery. 
 
 And here I can scarcely refrain from remark- 
 ing how happily opposite systems conspire to 
 advance the light of truth! By their conflict 
 they bring to view the vital points of inquiry, 
 and clear the ground for those who would ap- 
 proach to determine the merits of the case. If 
 Mr. Mill has taken the wrong side of this ques- 
 tion, yet it will ever be to his praise that his 
 thorough comprehension of the subject and his 
 precise and candid statements have placed the 
 controversy in the clearest light; and if logicians 
 differ it will not be because the point in dis- 
 pute is misapprehended, but because their dif- 
 ferent systems of philosophy drive them to op- 
 posite conclusions. Hear what he says : " We 
 must first observe that there is a principle im- 
 plied in the very statement of what induction 
 
 is, an assumption with regard to the course of 
 9 
 
180 ELEMENTS OF LOGIC. 
 
 nature and the order of the universe ; namely , 
 that there are such things as parallel cases, that 
 what happens once will happen again, and not 
 only again but always." — YoL i, p. 370. 
 
 It is evident that Mr. Mill has thoroughly 
 elaborated the opinion, for he has profoundly 
 criticised the statement of it as made by Reid 
 and Stewart, namely, that it is an intuitive con- 
 viction that the future will be as the present. 
 He remarks : " Time, in its modification of past, 
 present, or future, has nothing to do either with 
 tho belief itself or the grounds of it. We be- 
 lieve that fire will burn to-morrow, because it 
 burned to-day and yesterday ; but we believe 
 on precisely the same grounds, that it burned 
 before we were born, and that it burns at this 
 very day in Cochin China. It is not from the 
 past to the future, as past and future, that we 
 infer, but from the known to the unknown, from 
 facts observed to facts unobserved, from what 
 we have perceived or have been directly con- 
 Bcious of, to what has not come within our ex- 
 perience. In this last predicament is the whole 
 region of the future, but also the vastly greater 
 portion of the present and the past." 
 
THE PHILOSOPHY OF INDUCTION. 131 
 
 THE ERROR OF MILL. 
 
 Thus far his criticism is just ; but in whai 
 follows he denies that this principle is intuitive, 
 and herein lies the whole error of his system. 
 His empiricism forbids him to acknowledge that 
 any universal principles, even the first principles 
 of mathematics, are intuitive. Hesays: '• What- 
 ever be the most proper mode of expressing it, 
 the proposition that the course of nature is uni- 
 form, is the fundamental principle or general 
 axiom of induction. It would yet be a great 
 error to consider this large generalization as any 
 explanation of the inductive process. On the 
 contrary, I hold it to be an instance of induc- 
 tion, and induction by no means of the most 
 obvious kind. Far from being the first induc- 
 tion we make, it is one of the last, or, at all 
 events, one of those which are latest in attain- 
 ing strict philosophical accuracy. As a general 
 maxim, indeed, it has scarcely entered the 
 minds of any but philosophers, nor even by 
 them, as we shall have many opportunities of 
 remarking, have its extent and limits been al- 
 ways justly conceived. It is this principle, 
 thougU so far from being our earliest induction, 
 
182 ELEMENTS OF LOGIC. 
 
 wh.»cli must be considered as our warrant for all 
 others in this sense, that unless it" were true, all 
 other inductions would be fallacious." 
 
 Thus this ingenious reasoner disclaims what 
 he at first seemed to affirm. He disclaims 
 making this principle any explanation of the 
 process of induction as being founded upon it, 
 or proceeding through it ; but he now regards 
 it as only the sine qua non of correct induction, 
 so that no induction could be valid were its 
 truth not admitted! And why? Because he 
 thinks this principle is itself an induction, and 
 that not the earliest in science. But if so, how 
 could the earliest inductions have been made if 
 their truth depends wholly upon this as their 
 "fundamental principle?" And if itself be an 
 induction how could it be made at all ? It then 
 must have been founded upon itself, or else 
 here is one induction, and that the greatest of 
 all, which is not formed on this principle. Good 
 reason in these paralogisms to modify his state- 
 ment! But take his qualified statement, that 
 this late induction is the warrant of all other 
 inductions, then it follows that all scientific in- 
 ductions up to the time when this was formed, 
 were without any warrant ; and that warrant 
 
THE PHILOSOPHY OF INDUCTION. 133 
 
 itself is without any warrant, except it be war- 
 ranted by itself; and if this be impossible, then 
 itself and all other inductions warranted by it 
 are without authority I 
 
 But if we read on we shall find that what he 
 calls "warrant in a certain sense" is what all 
 who believe in deductive reasoning will call 
 proof: "Archbishop Whately has well remarked 
 that every induction is a syllogism, with the 
 major premise suppressed ; or, as I prefer to 
 express it, that every induction may be thrown 
 into the form of a syllogism by supplying a 
 major premise. If this be actually 'done, the 
 principle which we are now considering, that 
 of the uniformity of the course of nature, will 
 appear as the ultimate major premise of all in- 
 ductions, and will, therefore, stand to all in- 
 ductions in the relation in which, as has been 
 shown at so much length, the major premise 
 always stands to the conclusion, not coni/i^ibutr 
 mg at all to jprove it^ but being a necessary con- 
 dition of its being proved, since no conclusion 
 is proved in which there cannot be found a true 
 major premise." 
 
 But why will not Mr. Mill allow that a true 
 major premise of a true syllogism proves its cod- 
 
184 ELEMENTS OF LOGIC. 
 
 elusion ? Because the major premise contains the 
 conclusion, and itself was formed by the addition 
 of particulars, or induction from particulars of 
 which that very conclusion was one. Passing 
 this for the present, it is enough for our purpose 
 that he admits that the principle of the uniform 
 course of nature is the foundation of every in- 
 duction in the very tjense in which the major 
 premise of a valid argument is the proof of its 
 conclusion. 
 
 INDUCTION FOUNDED ON INTUITION. 
 
 The question now is, Where did we get that 
 fundamental principle? It is absurd to con- 
 sider it an induction, as we have seen, on Mr. 
 Mill's own principles ; it must then be a deduc- 
 tion or an intuition. It cannot be a deduction, 
 for, as Mr. Mill has clearly seen, that would 
 suppose a principle beyond it more general 
 from which it was derived. Il is an intuition, 
 and is given by the reason in its primitive un- 
 foldings, and on the very first occasion of ihe 
 recurrence of any cause whose effect we have 
 experienced, or of any cause similar to that 
 primary cause. We see its manifestations in 
 the very first rational actions of the child. Let 
 
THE PHILOSOPHY OF INDUCTION. 185 
 
 bhe child put his finger upon a coal of fire, and 
 he learns by experience that it causes pain. 
 Can you get him voluntarily to touch it a second 
 time ? He sees another similar coal beside it ; 
 can you get him to touch that? He will no 
 sooner touch the second than the first. Why 
 not, seeing that he has no experience but that 
 the first coal was once the cause of pain ? He 
 knows by experience nothing about its powei 
 to burn a second time, and nothing at all about 
 the power of the second coal to burn. The 
 only explanation is, that his reason obliges him 
 to conclude as he does; and this law of the 
 reason, this principle of mental order, when 
 rendered into language, is the belief that like 
 causes produce like eflPects. It is the province 
 of the philosopher to look at this necessary 
 movement of the reason and to abstract from 
 it the axiom involved in it, and to lay it as the 
 basis of all formal disquisitions upon the laws 
 of nature. But the child is guided, nay, he is 
 governed by it in all his future inductions. It 
 transpires in the reason immediately after that 
 great first principle of causality, that every 
 event has a cause, which is as early as our first 
 consciousness of sensation, and which is the oc- 
 
136 ELEMENTS OF LOGIC. 
 
 casion of our primitive ideas of the external 
 world, and of God, the cause of causes, and laya 
 the foundation of all science. 
 
 Nor is the principle of uniform causation in 
 the human reason alone ; it belongs as much to 
 the instinct of animals of every grade — the fish, 
 the bird, the insect, seems infallibly guided by 
 it. It pervades the whole animated world, which 
 without it, would rush on instant destruction. 
 Indeed, the instinct of animals goes beyond this, 
 and reveals the causative character of many 
 objects before any experience can take place of 
 their power to bless or to harm. It is not so 
 with man ; he must test everything himself, or 
 be taught by those who have tested. A babe 
 will as soon put his hand into a flame as snatch 
 at a bouquet of flowers; he will chew the 
 deadly herb as fearlessly as the lamb would 
 pluck the tender grass. 
 
 HUME'S OPINION. 
 
 This fact has been noticed by Mr. Hume with 
 an eagerness which characterizes his devotion 
 to empiricism. He then takes occasion to 
 wonder, with an air of delighted skepticism, 
 how it is, after learning thus the particular 
 
THE PHILOSOPHY OF INDUCTION. 187 
 
 character of causes, we can infer they will con- 
 tinue to produce the same effects. 
 
 "All our reasoning on matters of fact seems 
 to be founded on cause and effect. By means of 
 this relation alone we can go beyond the evi- 
 dence of our memory arid senses. If you were 
 to ask a man why he believes any matter of 
 fact which is absent ; for instance, that his 
 friend is in the country or in France, he would 
 give you a reason, and this reason would be 
 some other fact, as a letter received from him, 
 or a knowledge of his former resolution. A 
 man finding a watch, or any other machine, 
 on a desert island, would conclude that there 
 had once been men in that island. All our 
 reasonings concerning facts are of the same 
 nature. ... If we would satisfy ourselves, 
 therefore, concerning the nature of that evi- 
 dence which assures of matters of fact, we must 
 inquire how we came at the knowledge of cause 
 and effect. I shall venture to affirm, as a gen- 
 eral proposition, which admits of no exception, 
 that the knowledge of this is not m anyinstmic^ 
 attained hy reasonings a priori^ hut arises en- 
 tirely from experience^ when we find any par 
 ticular objects are conjoined with each other. 
 
138 ELEMENTS OF LOGIC. 
 
 Let any object be presented to a man of evei 
 80 strong natural reason and abilities, if that 
 object be entirely new to him, he will not be 
 able by the most accurate examination of its 
 sensible qualities to discover any of its causes 
 or effects. Adam, though his rational faculties 
 be supposed at the very first entirely perfect, 
 could not have inferred from the fluidity and 
 transparency of water that it would suffocate 
 him, or from the light and warmth of fire that 
 it would consume him." 
 
 All this we see no reason to dispute ; but 
 when he advances to the conclusion that it is 
 by repeated or customary experiences that w^e 
 discover the uniformity of causation, we find 
 him as blind to the real working of the human 
 reason as he would be blind to the operation of 
 animal instincts if he should affirm that all 
 animals, like man, discover all noxious food and 
 other hurtful causes by experience. But let 
 Mr. Hume speak for himself upon this point: 
 "As to past experience, it can be allowed to give 
 direct arid certain information of those precise 
 objects only and that precise period of time 
 which fell under its experience ; but why this 
 experience should extend to future times and to 
 
THE PHILOSOPHY OF INDUCTION. 139 
 
 :)tlier objects, which, for aught we know, may 
 be only in appearance similar; this is the main 
 question on which I insist. The bread which 1 
 formerly ate nourished me ; that is, a body of 
 iuch sensible qualities has induced secret 
 powers. But does it follow that other bread 
 must also nourish me at another time, and that 
 like sensible qualities must always be attended 
 with like secret powers? The consequence 
 seems to be no wise necessary. At least it 
 must be acknowledged that there is here a con- 
 sequence drawn by the mind, that there is a 
 certain step taken, a process of thought, or in- 
 ference, which wants to be explained. These 
 two propositions are far from being the same. 
 I have found that such an object has always 
 been attended with such an effect, and I foresee 
 that other objects, which are in appearance 
 similar, will be attended with similar effects. 1 
 shall allow, if you please, that one proposition 
 may justly be inferred from the other. I know, 
 in fact, that it always is inferred. But if you 
 insist that the inference is made by a chain 
 of reasoning, I desire you to produce that 
 reasoning." 
 
 Eureka ! good Mr. Hume, we have found out 
 
140 ELEMENTS OF LOGIC. 
 
 that reasoning, that connecting principle which 
 you despaired of finding. It lay just before 
 your eyes when you penned the observation 
 that one proposition is always inferred from the 
 other. Do you not see that you here struck 
 upon a law of the reason by which it is neceS' 
 sitated to operate thus, and that this law ex- 
 pressed in language is the axiom, Like causes 
 produce like effects? or, as it is generally stated, 
 The course of nature is uniform. What men 
 always think and must think is a primary and 
 essential truth, an ultimate principle of reason. 
 But Mr. Hume has objected to this origin of 
 the principle. " Were it the offspring of the 
 reason, an intuition, it would be as perfect at 
 first and from one instance, as after ever so long 
 a course of experience. But the case is far 
 otherwise. Nothing is so like as eggs ; yet no 
 one, on account of this apparent similarity, ex- 
 pects the same taste and relish in all of them. 
 It is only after a long course of experiments in 
 any kind that we attain a firm reliance and 
 security with regard to a particular event 
 Now, where is that process of reasoning whitjh 
 from one instance draws a conclusion so differ- 
 ent from that which it infers from a hundred 
 
THE PHILOSOPHY OF INDUCTION. 141 
 
 instances, tliat are nowise different from that 
 single one? This question I propose as much 
 for the sake of instruction as with an intention 
 of raising difficulties. I cannot find, I cannot 
 imagine any such reasoning." 
 
 It would be easy to turn off this question 
 with a joke, especially as the example of the 
 eggs is so egregiously puerile ; but it is due to 
 the candor of Mr. Hume to treat it seriously, 
 nay, to admit that the question is one of great 
 importance, and leads to the true science of in- 
 duction. It is not true that bodies having the 
 same or similar qualities produce different ef- 
 fects ; the eggs that have a different taste are 
 different in some particulars, and this is usually 
 sufficiently manifest in eggs; and if your eyes 
 fail to see it, a microscope will abundantly re- 
 veal it. Just here opens to our view the ap- 
 propriate sphere of induction, as far as it may 
 be properly distinguished from deduction ; its 
 office is to analyze phenomena, to mark the 
 different qualities of objects, and to ascertain 
 their precise effects ; but when you have cer- 
 tainly determined what qualities in any case 
 produce what effects, one single instance of 
 causation is sufficient for the widest generali- 
 
142 ELEMENTS OF LOGIC. 
 
 zation. Show me the property of the magnol 
 wliich attracts iron, and I hesitate not to pre- 
 dict that whenever and wherever that quality 
 appears, in like circumstances, it will be followed 
 by the same effect. But if I have not been 
 careful in my observations and mistaken some 
 other property for the real one, then most cer- 
 tainly I shall make a false prediction, and the 
 event will expose the error. It is not in the 
 reason, which assures me intuitively that like 
 causes produce like effect^, but in my observa- 
 tion. 
 
 MERIT OF MILL. 
 
 Science is under no greater obligation to any 
 writer of the present age than to Mr. John 
 Stuart Mill, for the profound and elaborate ex- 
 position of the grounds and process of induction 
 which he has given to the world. "' There is no 
 event," he remarks, " happening in the uni- 
 verse, which is not connected by an invariable 
 sequence with some one or more of the phenom- 
 ena which preceded it." " If we knew all the 
 agents which exist at the present moment, their 
 collocation in space, and their properties, or in 
 other words, the laws or modes of their agency. 
 
THE PHILOSOPHY OF INDUCTION. 148 
 
 we could predict the whole subsequent histoij 
 of the universe; at least, unless some new vo- 
 lition of a power capable of controlling the 
 anivei*se should supervene. And if any par- 
 ticular state of the universe should ever recur a 
 second time, (which, however, all experience 
 combines to assure us will never happen,) all 
 subsequent states would return too, and history 
 would, like a circulating decimal of many 
 figures, periodically repeat itself. 
 
 "Jam redit et virgo, redeunt Saturnia regna, 
 Alter erit turn Tiphys, et altera qii89 vehat Argo 
 Delectos heroas : erunt quoque altera bella, 
 Atque itcrura ad Troiam magnus mittetur Achilles." 
 
 Such undoubtedly is the order of the universe, 
 with the single exception of the free-will of 
 moral agents. But Mr. Mill makes no such 
 exception, for he holds that human volitions are 
 BO far controlled by motives that a man's actions 
 as inevitably result from his character as any 
 elfect follows a cause ; and if we thoroughly 
 knew his character we could certainly predict 
 how he would act in any supposable case. But 
 this we repudiate, for this reason, among many 
 which cannot now be mentioned, that the same 
 
144 ELEMENTS OF LOGIC. 
 
 view must apply to the divine mind ; and then 
 it would follow that the universe, like a circu- 
 lating decimal, actually has been, and will be 
 produced and destroyed, again and again, for- 
 ever. For God is the same in character ; and 
 if, when nothing was but he, his power pro- 
 duced the present universe, it was but the type 
 of a past and a coming eternity. Plato's rem- 
 iniscences are resurrections ; and not only the 
 ideas that now are have been before, but we 
 ourselves, the world's millions, and all their 
 various histories, have been before as now, and 
 will be as they now are, again and again, for- 
 evermore. But, aside from free agents, the 
 idea of Mr. Mill is as true as it is sublime ; and 
 it illuminates and explains the problem of in- 
 duction. The law of causation binds together 
 the universe, and the only difficulty is to dis- 
 cover that chain amid the shifting, and veering, 
 and multitudinous phenomena that move about 
 it and upon it ; but if you can strike that chain 
 at one point it will vibrate throughout its whole 
 direction. " The order of nature, as perceived 
 at iirst glance, presents at every instant a 
 chaos, followed by another chaos. We must 
 decompose each chaos into single facts. We 
 
THE PHILOSOPHY OF INDUCTION. 145 
 
 must learn to see in the chaotic antecedent a 
 multitude of distinct antecedents, and in the 
 chaotic consequent a multitude of distinct con- 
 sequents." What then ? We have to determine 
 which particular antecedent is followed by 
 which consequent, and which consequent is 
 produced by which antecedent; then, by the 
 simplest ratiocination, whose major premise is 
 the principle of causality, furnished by the 
 reason, we generalize the fact, or, in other 
 words, infer a law of nature. To make the 
 requisite analysis we need to observe and ex- 
 periment ; and we require no aid but the simple 
 rules of arithmetic, except in those cases where 
 the effects of various causes are mixed together, 
 as the curvilinear motion of the rocket, which 
 is the result of various causes. Here we re- 
 quire the aid of the higher mathematics tu de- 
 termine the proportion in which the causes 
 mingle in producing the effect. But all mathe- 
 matics is deductive. Hence, nowhere in induc- 
 tion, throughout its whole circuit, can you find 
 any new principle of inference. Inference, 
 therefore, is always one and the same ; it is a 
 passage of tba thought from the more general 
 
 to the less general, or to the particular; and 
 10 
 
146 ELEMENTS OF LOGIC. 
 
 never vice versa, from the particular or from 
 particulars, however numerous, to the general, 
 I repeat, you may sum them up, and call them 
 bj a general name ; but that is no inference, 
 no induction, nothing but generalization. 
 
 CONCLUSION OF THE ARGUMENT. 
 
 Thus, it is demonstrated that the process by 
 which we discover the laws of nature is funda- 
 mentally a deductive process ; and that we are 
 as much indebted to the reason for the major 
 premise as we are indebted to experience for 
 the minor premise. 
 
 ARISTOTLE VINDICATED. 
 
 It is owing to a misapprehension of the in- 
 tuitive developments of the reason that some 
 modern philosophers have rejected the syllo- 
 gism as a type of ratiocination. They suppose 
 its major premise is a general truth obtained by 
 a summation of particulars ; and, consequently, 
 to deduce one of these particulars from the 
 general is to reason in a circle. But, great as 
 the mystery of the reason may appear, we hold 
 it to be the source of general principles, and it 
 gises them to us as by revelation. So struck 
 
THE PHILOSOPHY OF INDUCTION. 147 
 
 was Cousin with this function of reason that he 
 seemed well-nigh beside himself, and almost 
 ready to bow down and worship it as a portion 
 of divinity ; and Plato, at the dawn of philoso- 
 phy, declared, "It is the gift of the gods to 
 man which, as I conceive, they sent down by 
 some Prometheus in a blaze of light." But it 
 is no enthusiasm to say that the reason is the 
 brightest aspect of the image of God in man. 
 Were the human mind destitute of this power 
 of intuition it would be impossible to vindicate 
 the logic of Aristotle. This he clearly saw and 
 stated in his exposition of the process of deduc- 
 tion. Indemonstrable truths, he aflSrms, make 
 the basis of all reasoning ; for if your premises 
 be demonstrated, then they must have been de- 
 monstrated by something beyond them, and if 
 they were demonstrable though not demon- 
 strated, it only extends the chain indefinitely 
 back. Hence there must be indemonstrable 
 truths at the foundation of every reasoning pro- 
 cess, or it is without foundation. And these 
 indemonstrable truths are particular intuitions 
 of sense, of consciousness, and of the reason, and 
 also the general intuitions or principles of the 
 reason. Thus sense gives us direct knowledge 
 
148 ELEMENTS OF LOGIC. 
 
 of the qualities of bodies ; consciousness, of the 
 phenomena of mind; and reason, ideas of sub* 
 stance, space, time, cause, right and wrong, and 
 the principles of causality, mathematical prin- 
 ciples, etc. The principle of contradiction, 
 namely, a thing cannot be and not be at the 
 same time, Aristotle considered the first of these 
 indemonstrable principles, which lay at the 
 foundation of demonstration. 
 
 ERROR OF THE SCHOOLMEN". 
 
 The error of the schoolmen, which plunged 
 them into the vortex of abstract speculation, 
 and for which Plato is to be blamed rather than 
 Aristotle, was in the supposition that all truth 
 lay wrapped up in a priori principles, and 
 could be educed by ratiocination : they failed 
 to perceive that they yielded no consequences 
 of scientific value, but as they were attached to 
 facts. Bacon reclaimed science from folly by 
 turning her eye upon the actual phenomena of 
 nature. But it is an illusion as great as that of 
 the scholastics, to suppose that facts can of 
 themselves give science; for they are as incon- 
 sequential without the principles of intuition as 
 these are barren without them ; they lie scat- 
 
THE PHILOSOPHY OF INDUCTIOK. 149 
 
 tered about like pebbles on tbe shore, antil they 
 are bound together by some a priori principle 
 or general truth ; then we see in them the path 
 of the mighty laws that clasp and encircle tho 
 universe. A falling apple sheds a ray of light 
 through immensity, and a drop of rain marking 
 the clay pours its illuminations down the chasms 
 of a past eternity. 
 
 And is not here the answer to Mr. Mill's earn 
 est inquiry: " Why is a single instance in some 
 cases sufficient for a complete induction ; while in 
 others, myriads of concurring instances, without 
 a single exception, known or presumed, go so 
 little way toward establishing a universal prop- 
 osition ?" The difference in the cases is that 
 the former stands in the relation of cause and 
 effect, and the latter does not. " Whoever," he 
 adds, " can answer this question knows more 
 than the wisest of the ancients, and has solved 
 the problem of induction." Let him add the 
 true theory of the origin of primary axioms to 
 his own incomparable analysis of induction, 
 and he may demand the palm. Take away the 
 a priori principles from induction, and you 
 cover with clouds the whole process, and tbe 
 long »7ray of the sciences dependent upon it 
 
150 ELEMENTS OF LOGIC. 
 
 restore these ideas and the movement is attended 
 with certainty, as far as certainty can belong to 
 human knowledge. 
 
 I say as far as certainty belongs to human 
 knowledge, because, after all, it must be con- 
 fessed that absoluta knowledge is not for man. 
 In its very depths what is our knowledge bui 
 faith ? When we talk of certainty what do w€ 
 mean ? Certainty for an individual is but his 
 necessary belief; human certainty is the neces- 
 sary and universal belief of the race. In 
 heaven itself certainty is absolute only in the 
 Throne of Light ; the knowledge of the loftiest 
 archangel nearest that Throne is but a cloudless 
 belief, forced upon his understanding by its own 
 subjective laws. God only knows, and knows 
 he knows ; God only is light. 
 
 SECOND CAUSES. 
 
 This leads us to remark, that the problem of 
 induction being only a question of causation, it 
 matters not what theory any one adopts in re- 
 spect to second causes, if he admits that no 
 event is without a cause, and like causes pro- 
 duce like effects, that is, what seems to us to be 
 causes. To me, however, there 's no more difl5« 
 
THE PHILOSOPHY OF INDUCTION. 151 
 
 culty in supposing that God has put a causative 
 power in nature distinct from his own, than 
 that he has constituted nature, both matter and 
 mind, distinct from his own essence. If matter 
 exists with its various elements distinct from 
 the divine nature, though not independent of 
 it, why may we not suppose that God has en- 
 dued it with a motive property as well as other 
 properties? Secondary causes are the general 
 belief of mankind as well as secondary natures. 
 Still, you may take either hypothesis ; you may 
 think it was the electric fluid which struck the 
 oak when it fell, blasted and blazing with light- 
 ning, or you may regard it as the stroke of the 
 divine thought or volition, and think that all 
 other events are, in like manner, the extempo- 
 raneous movements of the all-pervading mind 
 of Deity. Yet if your reason obliges you to 
 believe that they proceed upon the principles 
 of causality, then induction is the same, and the 
 certainty of its results is the same. Proceeding 
 upon a priori and empirical data conjointly, 
 the process is not to be doubted until the facul- 
 ties of observation and reason are doubted ; and 
 when they are doubted the mind is ruined, and 
 the light of knowledge is set forever. 
 
II. 
 
 MISCELLANEOUS EXAMPLES FOK 
 PRACTICE. 
 
 LESSON I. 
 
 1. That which is followed by repeptanoe h 
 
 not to be desired ; 
 Some pleasures are followed by repentanoe; 
 Therefore, some pleasures are not to be 
 
 desired. 
 
 2. If the world existed from eternity there 
 
 would be records prior to the Mosaic; 
 
 and if it were produced by chance it 
 
 would not bear marks of design ; 
 But there are no records prior to the 
 
 Mosaic, and the world does not bear 
 
 marks of design ; therefore, 
 The world neither existed from eternity, noi 
 
 is it the work of chance. 
 
 3. Every dispensation of Providence is bene- 
 
 ficial ; 
 Afflictions are dispensations of Providence : 
 Therefore, they are beneficial. 
 
EXAMPLES FOR PRACTICE. 153 
 
 s 
 
 4. If tl\ere is* a God he ought to be_SEpr- 
 ^ shiped ; ^- 
 
 '^Bnt there is a Ggd ;^ 
 
 Therefore^ hf ought to be worshiped. P 
 
 5. If God is innnitely wiseTand^acts with per- 
 
 fect freedom, he does nothing but what ia 
 
 best; 
 But God is infinitely wise, and acts with 
 
 perfect freedom ; 
 Therefore, he does nothing but what is best. 
 
 6. If God were not a Being of infinite good- 
 
 ness, neither would he consult the happi- 
 ness of his creatures ; 
 
 But God does consult the happiness of his 
 creatures ; 
 
 Therefore, he is a Being of infinite good- 
 
 7j^ The world is either self-existent, or the work 
 of soniefinite, or of some infinite being ; 
 But it is not self-existent, nor the work of a 
 
 finite„being ; 
 Therefore, it is the work of an infinite 
 ' Being. • ^ j , p 
 
 8. Ko deceitful msLf merits confidence ; 
 All honest men" merit confid^ce ; 
 , Therefore, no honest man is deceitful. 
 
154 ELEMENTS OF LOGIC. 
 
 9 Every human virtue is to be sought with 
 dih'gence ; 
 Prudence is a human virtue; 
 Therefore, prudence is to be sought iili- 
 gently. 
 10. Everything base should be avoided ; 
 Some pleasures are base ; 
 Therefore, some pleasures should be avoided. 
 
 LESSOI^^ n. 
 
 1. He who follows evil counsel will meet with 
 
 trouble ; 
 Rehoboam followed evil counsel ; 
 Therefore, Rehoboam met with trouble. 
 
 2. No good citizen will violate the laws of God 
 
 and man ; 
 Duelists do that which violates the la\^a 
 
 of both God and man ; 
 Therefore, duelists are not good citizens. 
 
 3. Things offensive to delicacy should not be 
 
 used; 
 Therefore, some words should not be used. 
 4/ That which is prudent is commendable ; 
 Moderation is prudent; 
 Therefore, moderation is commendable. 
 
EXAMPLES FOR PRACTICE. 155 
 
 5. We are bound to set apart one day in 
 
 seven for religious duties, if the fourth 
 commandment is obligatory on us; but 
 we are bound to set apart one day in 
 seven for religious duties ; and hence it 
 appears that the fourth commandment is 
 obligatory on us. 
 
 6. A desire to gain by another's loss is a viola- 
 
 tion of the tenth commandment ; all 
 gaming, therefore, since it implies a de- 
 sire to profit at the expense of another, 
 involves a breach of the tenth command- 
 ment. 
 
 7. All the fish that the net inclosed were an 
 
 indiscriminate mixture of various kinds : 
 those that were set aside and saved as 
 valuable, were fish that the net inclosed; 
 therefore, those that were set aside and 
 saved as valuable were an indiscriminate 
 mixture of various kmds. 
 
 8. No one who lives with another on terms of 
 
 confidence is justified on any pretense in 
 killing him ; Brutus lived on terms of 
 confidence with Cesar; therefore, he was 
 not justified, on the pretense he pleaded 
 in. killing him. 
 
156 ELEMENTS OF LOGIC. 
 
 9. Seeing that I have experienced calamity in 
 the snares of pleasure, 1 should abandon 
 its pursuit. 
 10. The principles of justice are variable; the 
 appointments of nature are invariable ; 
 therefore, the principles of justice are no 
 appointment of nature. 
 
 LESSON in. 
 
 1. All good Christians are saved ; 
 All good Christians have sinned ; 
 Therefore, some who have sinned will be 
 
 saved. 
 
 2. Knowledge is better than riches ; 
 Virtue is better than knowledge ; 
 Therefore, virtue is better than riches. 
 
 3. Christianity requires us to believe what the 
 
 apostles wrote ; 
 
 St. Paul is an apostle ; 
 
 Therefore, Christianity requires us to believe 
 what St. Paul wrote. 
 t. It is necessary that a general should under- 
 stand the art of war ; 
 
 But Caius did not understand the art of war, 
 
 Therefore, it is necessary that Caius should 
 not be a general. 
 
EXAMPLES FOR PRACTICE. 157 
 
 5. A total eclipse of the sun would cause dark- 
 ness at noon : 
 It is possible that the moon at that time may 
 
 totally eclipse the sun ; 
 Therefore, it is possible that the moon may 
 cause darkness at noon. 
 6 The fogs vanish as the sun rises ; 
 
 But the fogs have not yet begun to vanish 
 Therefore, the sun is not yet risen. 
 
 7. The sun is a senseless being ; 
 
 What the Persians worshiped is the sun ; 
 Therefore, what the Persians worshiped is a 
 senseless being. 
 
 8. If every creature be reasonable every brute 
 
 is reasonable ; 
 But no brute is reasonable ; 
 Therefore, no creature is reasonable. 
 
 LESSON rv. 
 1 . God is omnipotent ; 
 
 An omnipotent being can do everything 
 
 possible ; 
 He that can do everytliing possible can do 
 
 whatever involves not a contradiction ; 
 Therefore, God can do whatever involves 
 not a contradiction. 
 
168 ELEMENTS OF LOGIC. 
 
 2. If we love any person, all emotions of hatred 
 
 toward him cease ; 
 
 If all emotions of hatred toward a person 
 cease, we cannot rejoice in his mis- 
 fortunes ; 
 
 If we rejoice not in his misfortunes, we cer- 
 tainly wish him no injury ; 
 
 Therefore, if we love a person we wish him 
 no injury. 
 
 3. A thinking substance is a spirit; 
 A spirit has no extension ; 
 
 What has no extension has no parts ; 
 
 What has no parts is indissohible ; 
 
 Therefore, the mind is immortal. 
 4r. If God did not create the world perfect in 
 its kind, it must either proceed from w^ant 
 of inclination or from want of power ; 
 
 But it could not proceed from want of in- 
 clination or from want of power ; 
 
 Therefore, God created the world pertect in 
 its kind, or, which is the same thing, it is 
 absurd to say that he did not create the 
 world perfect in its kind. 
 5. Whatever is immaterial is indissoluble ; 
 
 The mind of man is immaterial ; 
 
 Therefore, the mind of man is indissoluble 
 
EXAMPLES FOR PRACTICE. 169 
 
 6. Whatever perceives, judges, and reasons, is 
 
 a thinking substance; 
 The human mind perceives, judges, and 
 
 reasons ] 
 Therefore, the human mind is a thinking 
 
 substance. 
 
 7. Things equal to the same thing are equal to 
 
 one another ; 
 Therefore, these two triangles, each equal 
 to the square of a line of three inches, 
 are equal between themselves. 
 
 8. What is not a being, since it can have no 
 
 attributes, can be no agent nor act, cannot 
 produce anything ; 
 What is called nothing is not a being, has 
 no attribute, is not an agent, nor can it 
 act; therefore, what is called nothing 
 cannot act or produce anything. 
 
 9. The order and constitution of things estab- 
 
 lished and maintained in the universe, i? 
 
 the law of Supreme intelligence ; 
 Nature is the order and constitution ol 
 
 things established and maintained in the 
 
 universe; therefore. 
 Nature is the law of Supreme intelligence 
 
160 ELEMENTS OF LOGIC. 
 
 LESSON V. 
 
 1. No man can possess power to pertonn im 
 
 possibilities ; 
 
 A miracle is an impossibility •; 
 
 Therefore, no man can possess power to per- 
 form a miracle. 
 
 2. War is the source of numerous evils ; 
 Some wars are just ; therefore, 
 
 Some just actions are the source of numer- 
 ous evils. 
 
 3. Protection from punishment is plainly due 
 
 to the innocent ; therefore, as you main- 
 tain that this person ought not to be 
 punished, it appears that you are con- 
 vinced of his innocence. 
 
 4. All the most bitter persecutions have been 
 
 religious persecutions ; among the most 
 bitter persecutions were those which oc- 
 curred in France during the Eevolutiou' 
 therefore, they must have beer, religious 
 persecutions. 
 
 5. Of two evils the less is to be preferred ; oc 
 
 casional turbulence, therefore, being a 
 less evil than rigid despotism, is to be 
 preferred to it. 
 
EXAMPLES FOR PRACTICE. 161 
 
 6. The early and general assignment of the 
 
 Epistle to the Hebrews to St. Paul as its 
 author, must have been either from its 
 professing to be his, and containing his 
 name, or from its really being his ; since, 
 therefore, the former of these is not the 
 fact, the epistle must be Paul's. • 
 
 7 . All the miracles of Jesus would fill more books 
 
 than the world could contain ; the things, 
 related by the evangelists are the miracles 
 of Jesus; therefore, the things related by 
 the evangelists would fill more books 
 than the world could contain. 
 
 8. According to theologians, a man must 
 
 possess faith in order to be acceptable to 
 the Deity ; now he who believes all the 
 fables of the Hindoo mythology must 
 possess faith ; therefore, such a one 
 must, according to theologians, be ac- 
 ceptable to the Deity. 
 
 9. If Abraham were justified, it must have 
 
 been either by faith or by works ; now, 
 
 he was not justified by faith, (according 
 
 to St. James,) nor by works, (according 
 
 to St. Paul ;) therefore, Abraham was not 
 
 justified. 
 
 11 
 
l$t ELEMENTS OF LOGIC. 
 
 to. He who cannot possibly act otherwise than 
 he does has neither merit nor demerit in 
 his action ; a liberal and benevolent man 
 cannot possibly act otherwise than he 
 does in relieving the poor ; therefore, 
 such a man has neither merit nor demerit 
 in his action. 
 
 LESSON VI. 
 
 1. Smollet, in a town in France, having met at 
 an inn with a scolding chambermaid and an 
 awkward red-haired hostler, who had engrossed 
 his whole attention, immediately wrote in his 
 journal: "The men in this town are all red- 
 haired, and the women are all scolds." 
 
 2. The Stoics proved that the world was a great 
 animal, thus : That which has the use of reason 
 is better than that which has not. Now, there 
 is nothing better than the world ; therefore, the 
 world has reason and is a great animal. 
 
 3. The Sophists used the following argument 
 against marriage : If a woman that marries be 
 lovely she will create jealousies ; if she be ugly 
 she will not delight ; therefore, it is not good to 
 marry. 
 
EXAMPLES FOR PRACTICE. 168 
 
 4. An Irishman, hearing much of the charms of 
 a feather bed, took a feather and laid it on a 
 rock for a pillow. He awoke with a headache. 
 '' Arrah," said he, "if these be your feathers give 
 me my straw." 
 
 5. Warm countries alone produce the Banian- 
 tree. Spain is a warm country; therefore, 
 Spain produces the Banian-tree. 
 
 6. A canal boat was passing under a bridge, 
 and some one on deck cried out, "Look out!" 
 A Dutchman lying in his berth heard the cry, 
 and stuck his head out of the window, and re- 
 ceived a severe blow on his forehead. "Vat 
 for," cried he, in a passion, " did you tell me to 
 'look out?' vy did you not tell me to Mook 
 in?'" 
 
 7. As I would not trifle with the prejudices of 
 the poor, because it is illiberal, so I would not 
 always yield to them, because it is unwise. 
 
 8. Books are seldom correct, because human 
 nature is fallible. 
 
 9. Fugitive cant, which is always in a state of 
 increase or decay, cannot be regarded as any 
 part of the durable materials of. a language, and 
 therefore must be suffered to perish with other 
 things unworthy of preservation. 
 
164 ELEMENTS OF LOGIC 
 
 10. Pleasures are deceitful; therefore, young 
 men should curb their Inclinations 
 
 LESSON vn. 
 
 Let the learner analyze the following, giving, 
 Ist, the terms; 2d, the propositions; 3d, the 
 syllogisms. 
 
 Ye men of Athens, I perceive that in all 
 things ye are too superstitious. For as I passed 
 by and beheld your devotions I found an altar 
 with this inscription : " To the Unknown God." 
 Whom, therefore, ye ignorantly worship him de- 
 clare I unto you. God that made the world and 
 all things therein, seeing that he is Lord of 
 heaven and earth, dwelleth not in temples made 
 with hands; neither is worshiped with men's 
 hands, as though he needed anything, seeing 
 he giveth to all life, and breath, and all things ; 
 and hath made of one blood all nations of men 
 for to dwell on all the face of the earth, and 
 hath determined the times before appointed, 
 and the bounds of their habitation ; that they 
 should seek the Lord, if haply they might feel 
 after him and find him, though he be not fai 
 from every one of us :• 
 
EXAMPLES FOE PRACTICE. 166 
 
 For in him we live, and move, and have our 
 being ; as certain, also, of jour own poets have 
 said, for we are also his offspring. 
 
 Forasmuch, then, as we are the offspring of 
 God, we ought not to think that the Godhead is 
 like unto gold, or silver, or stone, graven by art 
 and man's device. 
 
 And the times of this ignorance God winked 
 at, but now commandeth all men everywhere to 
 repent ; 
 
 Because he hath appointed a day in the 
 which he will judge the world in righteousness 
 by that man whom he hath ordained ; whereof 
 he hath given assurance unto all men in that he 
 hath raised him from the dead. 
 
 LESSON VHL 
 
 Arguments from uivpubUshed documents. 
 
 1* If the Mosaic doctrine of the absolute crea- 
 tion of the world out of nothing, by the 
 divine decree, were unreasonable, ft 
 would have shocked the common mind. 
 
 2. If Pantheism be true, and all things are but a 
 development of the Deity, then the idea 
 of cause in the human mind is an 11- 
 
t66 ELEJfENTS OF LOGIC. 
 
 liision, for in that case it is nowhere fully 
 realized, as modifications are not abso- 
 lute causations. 
 
 8. Though we cannot, with Plato and Cousin, 
 regard the reason in man as itself divine, 
 it is certainly perfect ; and is, therefore, 
 as a perfect creation, evidence of a per- 
 fect Creator. 
 
 4. Kg interpretation of the Bible is to be con- 
 sidered correct which is directl}^ opposed 
 to the absolute principles of reason, for 
 this would be suicidal, inasmuch as every 
 argument for the divine inspiration of the 
 Bible is based upon those very prin- 
 ciples. 
 
 6. If the New Testament be ngt a true history 
 of Christ, it is the greatest romance in all 
 literature; and if it be the greatest ro- 
 mance ever written, its author could not 
 have been unknown to his cotempo- 
 raries. 
 
 6. If the story of the resurrection be true, the 
 Christian religion is proved to be of di- 
 vine origin ; if it be false, no explanation 
 can bfe given of the sudden and extensive 
 spread of the Christian faith. 
 
EXAMPLES FOR PRACTICE. 167 
 
 7, The Bible must be of divine origin, for its 
 production is beyond all example of human 
 genius 
 
 The remamder are from notes of Dr, Whedon. 
 
 8. Every necessary, universal, and perpetual 
 
 idea is a truth ; 
 Immortality is such an idea ; 
 Therefore, immortality is a truth. 
 
 9. Nothing is to be held eternal which we can 
 
 rationally conceive once to have not ex- 
 isted, and the infinite space to be vacant 
 of it. 
 
 10. Nothing is by the laws of the mind to be 
 held as having no beginning, which we 
 can rationally conceive to have once non- 
 existed and then begun. Now of the 
 visible material world we can conceive 
 space to have been empty, we can con- 
 ceive that it once nonexisted and then 
 began. Not so of space or of creative 
 mind. In order to the world's beginning, 
 these must have preceded and never 
 have had a beginning. 
 
i68 ELEMENTS OF LOGIC. 
 
 11. The regular organrzation of the world must 
 
 either be eternal, or formed without de- 
 sign, or formed by design ; 
 
 The regular organization of the world can- 
 not be eternal ; for geology shows it to be 
 composed of elements once inorganic. 
 
 The regular organism of the world cannot 
 be without design, for no complex adjust- 
 ment of parts to accomplish an end can 
 exist without design. 
 
 12. The regular organization of the world is by 
 
 design, for it accords with all the laws of 
 design, and with nothing else that we 
 know. 
 
 LESSON LX. 
 
 Sv^osed Exceptions to Rules. 
 
 Hamilton, Thompson, and our own country- 
 man, Mahan, and others, have suggested several 
 alterations in the forms of Logic, as left by 
 Aristotle ; but with deference to these original 
 thinkers, I consider them unnecessary and in- 
 expedient. To try the skill of the advanced 
 student, and to make this book as complete 
 as may be, without an adequate discussion 
 of these topics, the present lesson will contain 
 
EXAMPLES FOR PHACTICE. 169 
 
 specimens of those propositions and arguments 
 which have been supposed to be exceptions to 
 the rules and to require a re-formation of the 
 science. 
 
 Eight Classes of Propositions^ i/nstead of the 
 fouvy A^ E^ /, O^of Aristotle, 
 
 1. Toto- total. All A is all of B. — All men are 
 
 all rational animals. 
 
 2. Toto-partial. All A is some of B. — All men 
 
 are mortal. 
 
 3. Parti-total. Some A is all of B. — Some men 
 
 are all the sailors. 
 
 4. Parti-partial. Some A is some of B. — Some 
 
 men are sailors. 
 6. Toto-total. Any A is not any B. — ^No man is 
 a brute. 
 
 6. Toto-partial. Any A is not some B. — l^o man 
 
 is some brute. 
 
 7. Parti-total. Some A is not any B. — Some 
 
 men are no brutes. 
 8 Parti-partial. Some A is not some B. — Seme 
 men are not some brutes. 
 Thompson makes but six. 
 
 A. All plants grow. 
 
 E. No right action is inexpedient. 
 
1 70 ELEMENTS OP LOGIC. 
 
 I. Sone muscles act without voiition. 
 O. Some plants do not grow in the tropins 
 (J. Commoa salt is chloride of sodium. 
 Y. Some stai"* are all planets. 
 
 Hamilton and Mahan add : 
 
 0). Some X is not some Y. 
 Tf. No X is some Z. 
 
 A is converted into Y. 
 
 E 
 
 U 
 
 u 
 
 E. 
 
 I 
 
 U 
 
 u 
 
 1. 
 
 O 
 
 u 
 
 u 
 
 V' 
 
 U 
 
 (( 
 
 (( 
 
 u. 
 
 T 
 
 u 
 
 ti 
 
 A. 
 
 w 
 
 a 
 
 u 
 
 a. 
 
 <» 
 
 u 
 
 ii 
 
 0. 
 
 If we admit Sir William Hamilton's doctrine 
 of the Quantification of the Predicate^ namely, 
 that if you refer not to the form of expression, 
 but to what is meant by it, \hQ jpredicate has air 
 ways a definite quantity^ and the propositM^i 
 may always he converted simply j still this very 
 difference between the form of a proposition 
 and its meaning, makes it necessary to have 
 lules to determine what is the extent of the 
 
EXAMPLES FOR PKACTICE. 17 J 
 
 predicate and to govern conversion ; and no 
 rules are better than those of Aristotle, if we 
 keep in mind the exceptions to the rules I have 
 made. (See Section on Distribution.) 
 
 EXAMPLES OF IMMEDIATE INFERENCE. 
 
 These supposed inferences will be found to 
 be either the same as the premise in different 
 language, or derived from it by means of 
 another premise understood, or by conversion. 
 
 IMMEDIATE INFERENCE BY MEANS OP PRIVA- 
 TIVE CONCEPTIONS. 
 
 L The Premise^ a PosiUve GoncepUon. 
 
 A. All the righteous are happy ; 
 
 Therefore, none of the righteous are un- 
 happy; 
 And, all who are unhappy are unrighteous. 
 E, No human virtues are perfect ; 
 
 Therefore, all human virtues are imperfect; 
 And, all perfect virtues are not human. 
 I. Some possible cases are probable ; 
 
 Therefore, some possible cases are not im 
 
 probable ; 
 And some probable cases are not impossible. 
 
172 ELEMENTS OP LOGIC. 
 
 0. Some possible cases are not probable ; 
 Therefore, some possible cases are im 
 
 probable ; 
 
 And, some improbable cases are not im- 
 possible. 
 U. The just are [all] the holy ; 
 
 Therefore, all unholy men are unjust ; 
 
 And, no just men are unholy. 
 r. Some happy persons are [all] the righteous ; 
 
 Therefore, all who are unhappy are un- 
 righteous ; 
 
 And, no righteous persons are unhappy. 
 
 IL The Premise^ a Privative Concejption, 
 A. All the insincere are dishonest ; 
 
 Therefore, no insincere man is honest ; 
 
 And, all honest men are sincere. 
 E. No unjust act is unpunished ; 
 
 Therefore, all unjust acts are punished ; 
 
 And, all acts not punished are just. 
 
 1. Some unfair acts are unknown ; 
 Therefore, some unfair acts are not known ; 
 And, some unknown acts are not fair. 
 
 0. Some improbable cases are not impossible; 
 Therefore, some improbable cases are pos- 
 sible ; 
 A.nd, some possible cases are not probable 
 
EXAMPLES FOR PRACTICE. 173 
 
 U. The unlawful is the [only] inexpedient ; 
 
 Therefore, the lawful is the expedient ; 
 
 And the lawful is not the inexpedient. 
 Y Some unhappy men are [all] the unright- 
 eous ; 
 
 Therefore, no happy men are unrighteous ; 
 
 And, some unhappy men are not righteous. 
 
 IMMEDIATE INFEEENCE BY ADDED DETERM* 
 INANTS. 
 
 A servant is a fellow-creature ; 
 
 Therefore, a servant in suffering is a fellow- 
 creature in suffering. 
 
 Virtue deserves respect, and a servant is a 
 fellow-creature ; 
 
 Therefore, a virtuous servant is a fellow- 
 creature deserving of respect. 
 
 IMMEDIATE ESTFERENCE BY CO^IPLEX CONCEP 
 TION. 
 
 Oxygen is an element, so that the decompo- 
 sition of oxygen would be the decomposition of 
 an element. 
 
L74 ELEMENTS OF LOGIC. 
 
 IMMEDIATE Il^TERENOES OF INTERPRETATION. 
 
 All the Gentiles are also called ; that is, all 
 other nations, as well as the Jewish, are called. 
 
 Howard exhibited this high philanthropic 
 spirit ; 
 
 Therefore, snch philanthropy really exists. 
 
 A is B ; therefore, B exists. 
 
 A is B ; therefore, where A is we find B. 
 
 niMEDIATE INFERENCE FROM A DISJUNCTIVE 
 JUDGMENT. 
 
 All teeth are either incisors, canine, bicuspid, 
 or molar ; 
 
 Therefore, the molar teeth are neither incisors, 
 canine, nor bicuspid ; 
 
 And, all teeth which are not molar are either 
 canine, incisors, or bicuspid. 
 
 IMMEDIATE INFERENCE BY THE SUM OF 
 SEVERAL PREDICATES. 
 
 Copper is a metal of a red color and dis- 
 agreeable smell and taste, all the properties of 
 which are poisonous ; which is highly malleable, 
 
EXAMPLES FOR PRACTTCE. 176 
 
 ductile, tenacious, with a specific gravity of 
 about 8.83 ; 
 
 Therefore, a metal of a red color, etc., is 
 copper. 
 
 UNFIGURED SYLLOGISM. 
 
 In the unfigured syllogism of Hamilton and 
 Mahan the terms compared do not stand to each 
 other in the relation of subject and predicate, 
 being in the same proposition either hoth sub- 
 jects or hoth jpredicates. 
 
 All C and some B are equal ; 
 
 All A and all B are equal ; , 
 
 Therefore, all C and some A are equal ; 
 
 Or, C and A are unequal. 
 
 Copperas and sulphate of iron are identical ; 
 
 Sulphate of iron and sulphate of copper are 
 not identical ; 
 
 Therefore, copperas and sulphate of copper 
 are not identical. 
 
 Alio and all B equal Y; 
 All A and all B do not equal Y ; 
 Therefore, and A are not equal to each 
 other 
 
176 ELEMENTS OF LOGIC. 
 
 C and B always coexist, or are universally 
 compatible ; 
 
 A and B never coexist, or are wholly incom- 
 ])atible ; 
 
 Therefore, C and A never coexist, or are not 
 compatible. 
 
 Some of these unfigured syllogisms, upon anal- 
 ysis, will be found to contain one or two other 
 syllogisms with premises suppressed. In the first 
 instance given, ''''Things equal to the sa/me thing 
 are equal to each other^'^ is the implied premise. 
 
 REASONING FROM WHOLES IN COMPREHENSION. 
 
 Sir William Hamilton's discovery is illusory ; 
 an individual cannot comprehend a species, nor 
 a species a genus. This red rose is both in ex- 
 tension and comprehension one, A single rose 
 with its own red; it cannot comprehend red 
 rose^ which is not ordy this^ hut that^ and all 
 other red roses / and it admits of no inference. 
 A thing is itself and not something else how- 
 ever like it, much less its class. So triangle 
 comprehends not figure^ but only the thre& 
 cmgled portion, 
 
 THE END. 
 
VB 
 
 
 95