CHAPTER VIII. FUNCTIONS AND VALUE OF THE SYLLOGISM. § 1. ACCORDING to Mill the syllogistic process is not the process according to which we reason. "All inference," says he, "is from particulars to particulars: general propositions are merely registers of such inferences already made, and short formulæ for making more. The major premiss of a syllogism consequently is a formula of this description; and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula; the real, logical antecedent or premiss being the particular facts from which the general proposition was collected by Induction1." "The value, therefore, of the syllogistic form, and of rules for using it correctly, does not consist in their being the form and the rules according to which our reasonings are necessarily, or even usually, made; but in their furnishing us with a mode in which these reasonings may always be represented, and which is admirably calculated, if they are inconclusive, to bring their inconclusiveness to light. An induction from particulars to generals, followed by a syllogistic process from those generals to other particulars, is a form in which we may always state our reasonings if we please. It is not a form in which we must reason, but it is a form in which we may reason, and into which it is indispensable to throw our reasoning, when there is any doubt of its validity: though when the case is familiar and little complicated, and there is no sus 1 Logic, Vol. 1. p. 221. CHAP. VIII.] FUNCTIONS AND VALUE OF SYLLOGISM. 251 picion of error, we may, and do, reason at once from the known particular cases to unknown cases 1." The universal type of the reasoning process, according to Mill, is as follows :— "Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute?." This type is not, however, conclusive like the syllogism from the mere form of the expression; but must, in every case, be examined by the canons and rules of Induction. For example, all men now living resemble those men who have heretofore died' in certain attributes; whether from their resemblance in these attributes we may infer also their resemblance in the attribute 'mortality' is a question of Induction, and must be determined by its canons. If we may infer this attribute of 'all men now living,' we may infer it also of all other individuals that resemble the men who have died in the same attributes. This process of inference admits of a division into two steps: (1) "That of ascertaining what attributes are marks of mortality, universally, i.e., under all circumstances, and (2) whether any given individuals possess those marks." Conformably to usage, the first step or process, namely, that of establishing the general proposition, is called Induction, and the second step in "the reasoning operation, which is substantially that of interpreting the general propositions," is called Deduction by Mill. Every process by which any thing is inferred respecting an unobserved case, consists similarly of an Induction followed by a Deduction. According to Mill, the syllogism is thus merely a process by which the real or complete meaning of a general proposition established by Induction is made explicit, and by which the validity of a reasoning is tested. It is, in other words, an interpreter of the general proposition and a test of reasoning. Its rules and canons are merely cautions against false reasoning. They merely help us in interpreting correctly the true meaning of general propo2 lbid. p. 232. 1 Logic, Vol. 1. pp. 227—8. In ordinary sitions, and in applying them to particular cases. discourse the reasoning is never conducted nor stated in the syllogistic form; but whenever there is any doubt about its validity, we may, or rather we must, throw it into the syllogistic form, and if it admits of being so expressed, we may be perfectly sure of its being valid. The syllogistic is not, therefore, the process according to which we usually reason. The universal process of reasoning is, according to Mill, from some particulars to other particulars; and the syllogistic process is merely a test of the validity of this process. § 2. Nor, according to Mill, is the syllogistic mode of arguing a sound one. "For," says he, "it must be granted that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say, 'all men are mortal, Socrates is a man; therefore Socrates is mortal,' it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition 'Socrates is mortal' is presupposed in the more general assumption 'All men are mortal'; that we cannot be assured of the mortality of all men, unless we are already certain of the mortality of every individual man, &c., &c.; that, in short, no reasonings from generals to particulars can as such prove anything; since from a general principle we can not infer any particulars but those which the principle itself assumes as known1." Regarded as a mode of Probation, the syllogism involves, according to Mill, the fallacy of petitio principii, that is, the conclusion is presupposed by the major premiss. The proposition 'all men are mortal' can not be true, unless the conclusion 'Socrates is mortal' is true. The truth of the latter is presupposed by the former, or the former can not be true unless the latter is. When you have assumed the major, you have already taken for granted the conclusion. Thus the conclusion is not really proved by the premisses of the syllogism. It is, on the contrary, proved by those particular cases of observation which 1 Logic, Vol. 1. p. 210. establish the general or major premiss. It is these that are alike the evidence of the major premiss and of the conclusion of the syllogism. The syllogism is thus, according to Mill, neither the process according to which we reason, nor an argument which is sound and free from fallacy. Is it, then, altogether useless? No, says Mill, its proper function is to interpret a general proposition and apply it to particular cases, and its real value consists in being an infallible test of the validity of the true process of reasoning. This process is, according to Mill, from particulars to particulars in accordance with the laws and canons of Induction. But when an inference is drawn from some particulars to some other particulars, we can not be quite certain that the reasoning is valid unless it admits of being thrown into the syllogistic form. That is, if, from 'some particulars,' we can infer a general proposition, and if with this general as a major premiss, and with 'some other particulars' as a minor, we can form a valid syllogism, then the reasoning is valid. If the general can not be inferred, and the syllogism can not be formed, then the reasoning is invalid. For example, the reasoning that "all things now living are mortal, because all men in past ages have died," is completed according to inductive methods; but it will not be valid, unless a general proposition "all men are mortal" can be inferred from the particular cases of men who have died in past ages, and unless all kings now living' are really referable to the class 'man,' that is, the validity of the reasoning which is actually and really conducted from particulars to particulars in accordance with the canons of Induction, may be tested by reducing it to the following syllogism: "all men are mortal, all kings now living are men; therefore all kings now living are mortal." This view of the functions and value of the syllogism, first propounded by Mill, has been adopted by Sir John Herschel, Dr Whewell, Mr Bailey, Professor Bain, and others. It has, on the other hand, been strongly opposed by Mansel, Professor De Morgan, Dr James Martineau, and others. § 3. There are two essential points in Mill's view of the syllogism,—(1) that it is not the usual process of reasoning, (2) that it involves the fallacy of petitio principii. On the first point Mill maintains, that the universal process of reasoning is from particulars to particulars; and on the second point, that the real proof of the conclusion is not the premisses of the syllogism, but the facts of observation and testimony on which the major premiss itself is founded. On these two points the following observations may be made:— 1. It is true that the syllogism is not the process by which we usually reason. But it is equally true that our usual reasonings will not be valid, and therefore not deserve the name, unless they are capable of being reduced to the syllogistic form. Mill seems to make a confusion between the business of Psychology and that of Logic. It is not the business of the latter to give an account of the various processes by which people reason correctly or incorrectly, but to give an account of the processes by which they ought to reason, and must reason if they wish to reason correctly. The former is the business of the Psychology of Reasoning, while the latter is the business of the Logic of Reasoning. Mill confuses these two, and makes both the business of Logic. Recognizing the distinction here drawn, it may be said that the syllogism is the type of all valid reasoning; for no reasoning will be valid, as Mill also allows, unless it can be thrown into the form of a syllogism. As a matter of fact, in daily life, men draw inferences in many different ways, but only those among them will be valid, and properly deserving of the name, which are capable of being ultimately reduced to the syllogistic form, the rest being nothing but suggestions of association, fancy, imagination, &c., wrongly called inferences1. § 4. 2. Secondly,-Does the syllogism involve the fallacy of petitio principii? On this most important subject the following noteworthy remark by Dr James Martineau is well deserving of being quoted; and as the book in which it is con 1 Vide Appendix D. |