deductive arguments are selected, it should be easy to prove that they will not do the work of inductive. But it is wonderful that so few should have perceived how absurd were the attempts to turn the so-called imperfect modes into perfect ones. It has been shown already (p. 227.), that the modes of each figure in the old arrangement had their proper use, that the first served for deducing facts from laws, the second for establishing differences, and the third for bringing in examples and exceptions. Yet logicians have persisted in torturing syllogisms of the second and third figures into the first, by the help of Conversion, without perceiving that they turned a natural argument into a distorted monster. To say (A A I, Fig. ш.) Lead is fusible, Lead is a metal; Therefore some metal is fusible is natural enough; but it partakes far more of the nature of induction than deduction, because it is advancing from a single observation towards a more general statement, which may end probably in a universal. Now to establish the erroneous assertion that all syllogisms are deductions, logicians are bound either to deny that such an argument is a syllogism, or to attempt to reduce it to one of the deductive modes. They adopt the latter alternative, thus (A II, Fig. 1.) Lead is fusible, Some metal is lead; Therefore some metal is fusible. But this unnatural form is no more like deduction than before; there is no reasoning from a law to facts, from a general to a particular statement, and all that has been done is to give us for a second premiss an unnatural judgment such as logicians have taught us already to avoid as much as possible. The syllogism is not confined to deductive arguments. Every one of the inductive methods already described, falls easily into an appropriate syllogistic form ; and we can no more reason without making syllogisms than we can speak and argue without forming sentences. What Grammar does for speech Logic does for thought; it ascertains its simple elements and exhibits them, and if it be found that the inductive processes do not fall readily under the old forms, it would be right to consider first whether the forms could be amended or enlarged, rather than to abandon at once one half the territory of thought, the whole of which Logic has always by its names and definitions seemed to claim. To assign one half the domain of Logic to Induc tion is not strictly correct. There is in truth a third process, of some subordinate advantage in investiga tion, whereby no advance is made towards general laws, as in Induction, nor towards the application of laws to facts, as in Deduction, but the matter of knowledge is exhibited under a new and more convenient form. It has been appropriately named Traduction.* The modes UU U in all the figures are those which exemplify it most perfectly. § 120. Employment of defective Syllogisms. The difficulty in answering the question-how does Logic aid by the syllogism in adding to our stock of knowledge? has been caused principally by studying only the complete forms of syllogism, whereas in discovery it is necessary to accept defective forms, only suspending our adoption of them until they are fortified by other evidence. The fact that such suspense is necessary proves that the forms are imperfect; the fact that we have attained new truths from evidence formally insufficient to establish them by itself, proves their usefulness. This will appear from * By Mr. James Broun, in an able letter in Prof. De Morgan's Formal Logic, p. 332. a description of some of the best known forms of defective syllogism. The RHETORICAL ENTHYMEME as described by Aristotle, is "a syllogism from probable propositions or from signs." The probable proposition (ɛiкòç) is that sort of statement which must satisfy us in matters where universal assertions are impossible; as in human affairs, that "injured men will seek revenge men are active where their interest is concerned," and the like. Any syllogism into which a proposition of this sort, general but by no means universal, enters, can only supply a general and therefore uncertain conclusion. The sign (onpeior) according to Aristotle, is a proposition in which some one fact or mark that accompanies, precedes or follows, another fact or conception, is adduced as a necessary or probable indication that the other is present. (Pri. An. ii. 27.) In describing a sign as "a proposition," some violence is done to language, since it can always be expressed as a single term. As no account is taken of negative signs, indications, that is, that a given thing does not exist, all the Enthymemes based on signs will be positive or affirmative; and as they are to prove the existence of a given fact without limitation, their conclusions will also be universal. Now some of them are found to furnish demonstrative proof of the point they would establish; and these are called Proofs. Others only afford a presumption more or less valid that the conclusion is true. This difference becomes manifest from the use of the three Figures; the Proofs will only be found, where the mode and figure of the syllogism, made out of the terms of the question with the sign for a middle term, are logically valid. Where they are invalid, the sign will fall short of a Proof to the extent of that invalidity. Thus, of three Enthymemes; (1.) Dionysius must fear because he is a tyrant; (II.) This man is the murderer, because he was near the murdered man ; (III.) As we see from the case of Lord Bacon, contemplative men are competent to the affairs of life ;— each falls into a different figure. (1. А А А.) All tyrants fear, Dionysius is a tyrant; ... He must fear. (п. А А А.) The murderer would be near, This man is near; He is the murderer. (111. A A A.) Lord Bacon was a practical man, Lord Bacon was contemplative; All contemplative men are fit for practical life. Of these the first alone is formally conclusive, because it violates no syllogistic rule; it amounts therefore to a scientific proof. Not so the second; it has not distributed the middle term; it should have shown |