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.