Deductive Logic

Part Ii. of Propositions, §§ 172-185.

CHAP. I. Of the Proposition as distinguished from other Sentences, §§ 172-185.

II. Of the Copula, §§ 186-201.

III. Of the Divisions of Propositions, §§ 202-273.

IV. Of the Distribution of Terms, §§ 274-294.

V. Of the Quantification of the Predicate, §§ 295-312.

VI. Of the Heads of Predicables, §§ 313-346.

VII. Of Definition, §§ 347-384.

VIII. Of Division, §§ 385-425.

Part Iii. of Inferences, §§ 426-884.

CHAP. I. Of Inferences in general, §§ 426-441.

II. Of Deductive Inferences, §§ 442-448.

III. Of Opposition, §§ 449-478.

IV. Of Conversion, §§ 479-495.

V. Of Permutation, §§ 496-502.

VI. Of Compound Forms of Immediate Inference, §§ 503-532.

VII. Of Other Forms of Immediate Inference, §§ 533-539.

VIII. Of Mediate Inferences or Syllogisms, §§ 540-557.

IX. Of Mood and Figure, §§ 558-568.

X. Of the Canon of Reasoning, §§ 569-581.

XI. Of the General Rules of Syllogism, §§ 582-598.

XII. Of the Determination of the Legitimate Moods of Syllogism, §§ 599-605.

XIII. Of the Special Rules of the Four Figures, §§ 606-620.

XIV. Of the Determination of the Moods that are valid in the Four Figures, §§ 621-632.

XV. Of the Special Canons of the Four Figures, §§ 633-647.

XVI. Of the Special Uses of the Four Figures, §§ 648-655.

XVII. Of the Syllogism with Three Figures, §§ 656-666.

XVIII. Of Reduction, §§ 667-700.

XIX. Of Immediate Inference as applied to Complex Propositions, §§ 701-730.

XX. Of Complex Syllogisms, §§ 731-743.

XXI. Of the Reduction of the Partly Conjunctive Syllogism, §§ 744-752.

XXII. Of the Partly Conjunctive Syllogism regarded as all Immediate Inference, §§ 753-759.

XXIII. Of the Disjunctive Syllogism, §§ 760-765.

XXIV. Of the Reduction of the Disjunctive Syllogism, §§ 766-769.

XXV. Of the Disjunctive Syllogism regarded as an Immediate Inference, §§ 770-777.

XXVI. Of the Mixed Form of Complex Syllogism, §§ 778-795.

XXVII. Of the Reduction of the Dilemma, §§ 796-797.

XXVIII. Of the Dilemma regarded as an Immediate Inference, §§ 798,799.

XXIX. Of Trains of Reasoning, §§ 800-826.

XXX. Of Fallacies, §§ 827-884.

EXERCISES.

INDEX.

INTRODUCTION.

§ 1. LOGIC is divided into two branches, namely--

(1) Inductive,

(2) Deductive.

§ 2. The problem of inductive logic is to determine the actual truth or falsity of propositions: the problem of deductive logic is to determine their relative truth or falsity, that is to say, given such and such propositions as true, what others will follow from them.

§ 3. Hence in the natural order of treatment inductive logic precedes deductive, since it is induction which supplies us with the general truths, from which we reason down in our deductive inferences.

§ 4. It is not, however, with logic as a whole that we are here concerned, but only with deductive logic, which may be defined as The Science of the Formal Laws of Thought.

§ 5. In order fully to understand this definition we must know exactly what is meant by 'thought,' by a 'law of thought,' by the term 'formal,' and by 'science.'

§ 6. Thought, as here used, is confined to the faculty of comparison. All thought involves comparison, that is to say, a recognition of likeness or unlikeness.

§ 7. The laws of thought are the conditions of correct thinking. The term 'law,' however, is so ambiguous that it will be well to determine more precisely in what sense it is here used.

§ 8. We talk of the 'laws of the land' and of the 'laws of nature,' and it is evident that we mean very different things by these expressions. By a law in the political sense is meant a command imposed by a superior upon an inferior and sanctioned by a penalty for disobedience. But by the 'laws of nature' are meant merely certain uniformities among natural phenomena; for instance, the 'law of gravitation' means that every particle of matter does invariably attract every other particle of matter in the universe.

§ 9. The word 'law' is transferred by a metaphor from one of these senses to the other. The effect of such a command as that described above is to produce a certain amount of uniformity in the conduct of men, and so, where we observe uniformity in nature, we assume that it is the result of such a command, whereas the only thing really known to us is the fact of uniformity itself.

§ 10. Now in which of these two senses are we using the term 'laws of thought'? The laws of the land, it is plain, are often violated, whereas the laws of nature never can be so [Footnote: There is a sense in which people frequently speak of the laws of nature being violated, as when one says that intemperance or celibacy is a violation of the laws of nature, but here by 'nature' is meant an ideal perfection in the conditions of existence.]. Can the laws of thought be violated in like manner with the laws of the land? Or are they inviolable like the laws of nature?

§ 11. In appearance they can be, and manifestly often are violated-for how else could error be possible? But in reality they can not. No man ever accepts a contradiction when it presents itself to the mind as such: but when reasoning is at all complicated what does really involve a contradiction is not seen to do so; and this sort of error is further assisted by the infinite perplexities of language.

§ 12. The laws of thought then in their ultimate expression are certain uniformities which invariably hold among mental phenomena, and so far they resemble the laws of nature: but in their complex applications they may be violated owing to error, as the laws of the land may be violated by crime.

§ 13. We have now to determine the meaning of the expression 'formal laws of thought.'

§ 14. The distinction between form and matter is one which pervades all nature. We are familiar with it in the case of concrete things. A cup, for instance, with precisely the same form, may be composed of very different matter-gold, silver, pewter, horn or what not?

§ 15. Similarly in every act of thought we may distinguish two things--

(1) the object thought about,

(2) the way in which the mind thinks of it.

The first is called the Matter; the second the Form of Thought.

§ 16. Now Formal, which is another name for Deductive Logic, is concerned only with the way in which the mind thinks, and has nothing to do with the particular objects thought about.

§ 17. Since the form may be the same, whilst the matter is different, we may say that formal logic is concerned with the essential and necessary elements of thought as opposed to such as are accidental and contingent. By 'contingent' is meant what holds true in some cases, but not in others. For instance, in the particular case of equilateral triangles it is true to say, not only that 'all equilateral triangles are equiangular,' but also that 'all equiangular triangles are equilateral.' But the evidence for these two propositions is independent. The one is not a formal consequence of the other. If it were, we should be able to apply the same inference to all matter, and assert generally that if all A is B, all B is A, which it is notorious that we cannot do.

§ 18. It remains now for the full elucidation of our definition to determine what is meant by 'science.'

§ 19. The question has often been discussed whether logic is a science or an art. The answer to it must depend upon the meaning we assign to these terms.

§ 20. Broadly speaking, there is the same difference between Science and Art as there is between knowing and doing.

Science is systematized knowledge; Art is systematized action. Science is acquired by study; Art is acquired by practice.

§ 21. Now logic is manifestly a branch of knowledge, and does not necessarily confer any practical skill. It is only the right use of its rules in thinking which can make men think better. It is therefore, in the broad sense of the terms, wholly a science and not at all an art.

§ 22. But this word 'art,' like most others, is ambiguous, and is often used, not for skill displayed in practice, but for the knowledge necessary thereto. This meaning is better conveyed by the term 'practical science.'

§ 23. Science is either speculative or practical. In the first case we study merely that we may know; in the latter that we may do.

Anatomy is a speculative science; Surgery is a practical science.

In the first case we study the human frame in order that we may understand its structure; in the second that we may assist its needs. Whether logic is a speculative or a practical science depends entirely upon the way in which it is treated. If we study the laws of thought merely that we may know what they are, we are making it a speculative science; if we study the same laws with a view to deducing rules for the guidance of thought, we are making it a practical science.

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