CHAPTER VIII. THE HAMILTONIAN DOCTRINE OF SYLLOGISMS. IR William Hamilton's innovations in the doctrine 15, generally up to this time, are not limited to such as are the direct consequences of his theory of the thorough-going quantification of the Predicate. On several minor points, also, he has considerably modified the Aristotelic doctrine. These changes, it is true, were probably suggested by his system of quantifying the Predicate; but they are not so closely connected with it as to prevent them from being received, even by those logicians who, wholly or in part, reject that system. All of them deserve consideration, as they involve a discussion of some incidental questions of much interest, affecting the whole theory of Logic. As to the order of enouncement, the old doctrine was, that the Premises, as their name imports, should precede the Conclusion. Hamilton observes that the reverse order is more natural, that it more faithfully represents the progress of the mind in the investigation or discovery of truth, and that it effectually relieves the Syllogism from the imputation, which has been thrown upon it for more than three centuries, of being founded upon a mere petitio principii, or a begging of the question. "Mentally one," he says, "the Categorical Syllogism, according to its order of enouncement, is either Analytic, if what is inappropriately styled the Conclusion' be expressed first, and what are inappropriately styled the Premises' be then stated as its reasons; or Synthetic, if the Premises precede and, as it were, effectuate the Conclusion." In the Analytic order, the "Conclusion" would be more properly called the Quæsitum, and the "Premises" should be denominated the Proofs. Now, the Analytic order, it is argued, is the more natural, because the Problem or Question, which it is the purpose of the Syllogism to solve or answer, and which is therefore the leading thought in the mind, is propounded first. When we are in doubt whether A is, or is not, B, it is surely more natural to argue, A is B, because A is C, and all C is B, than to reason in the old order, placing the solution of the Problem last. "In point of fact, the Analytic Syllogism is not only the more natural, it is even presupposed by the Synthetic." As already stated, the Syllogistic process in the mind is really one and undivided, consisting only in the inference of the Conclusion from the Premises. But in order to state this single process in words, we must analyze it, and therefore the Conclusion, which is the compound result, ought to be stated first, so as to admit of analysis. It may be stated generally, that a process of investigation or research, looking towards truth not yet discovered, is always Analytic. The most that can be said for the Synthetic method is, that it may be successfully used for teaching, or proving the truth that is already known. To adopt an old illustration, in order to find out for ourselves how a clock is made and how it does its work, we must take it to pieces; having done this, the best way to teach another person how to make a clock is to take those pieces and put them together again. The common objection to the validity of the Syllogistic process is, that the Conclusion is virtually contained in the Premises, so that we have to assume it to be true in the very propositions by which we attempt to prove it. This objection is thus forcibly stated by Mr. Mill. "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 were previously certain of the mortality of every individual man; that if it be still doubtful whether Socrates, or any other individual you choose to name, be mortal or not, the same degree of uncertainty must hang over the assertion, All men are mortal'; that the general principle, instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it is dispelled by evidence aliunde; and then, what remains for the Syllogism to prove? that, in short, no reasoning from generals to particulars can, as such, prove anything: since, from a general principle, you cannot infer any particulars but those which the principle itself assumes as foreknown." But if the Syllogism be stated in the Analytic form, it is obvious that this objection is inapplicable. When we argue, Socrates is mortal, Because Socrates is a man, we do not assume the point which ought to be proved, but we prove that it is right to predicate mortality of Socrates, by showing that Socrates belongs to the class man, all the members of which are universally admitted to be mortal. We appeal to the admitted Universal truth only after we have established, what is here the main point of the argument, the applicability of the truth to this case, the fact that Socrates is a man. Mr. Mill mistakes the compara tive importance of the two Premises; in Analytic reasoning, in drawing an inference for the purpose of investigation or discovery, -the proof turns chiefly upon the Subsumption; and Aristotle therefore correctly places this Premise first. Thus, if I am in doubt with respect to a new substance which I have found, whether it be fusible or not, the doubt may be resolved by ascertaining that this substance is a metal. Only after this fact is ascertained, and then only in order to complete the thought, or to silence cavil, I refer to the admitted truth that all metals are fusible. Men usually reason in this manner, as is shown by the frequent recurrence of such Enthymemes as these: This iron is not malleable, for it is cast-iron; The man is dishonest, for he has taken what is not his own; this line is equal to that, for they are both radii of the same circle, &c. There is certainly a mental reference in such cases to a Major Premise, to the well-known truths, that No castiron is malleable, All radii of the same circle are equal, &c. But precisely because such Premises are well known and obvious, though thought, they are not usually expressed. The bald truisms which are usually taken as examples of the Syllogistic process are unfortunately chosen, as they render more plausible the imputation that this process itself is futile and needless. Any kind of reasoning appears puerile, when it is applied only to establish a puerile Conclusion. Nobody wishes any proof of the fact that Socrates was mortal. Adopt any supposition which will make it appear that there was a real doubt in the case, and that the point to be determined was one of some importance, and the Syllogism employed loses its frivolous aspect, and seems grave and pertinent. Suppose that the impulsive Athenians of his day had made the same mistake in relation to Socrates, that those of a later time committed in regard to Paul and Barnabas, and had begun to offer sacrifices to him as an immortal being; it would have been dignified and conclusive on his part to argue with them, as the Apostle did, by saying, "We are men of like passions with you," and worship is due only unto God. The first question for the inquirer or disputant is, not whether this case has already been decided, and therefore included under this General Rule, which is supposed to be already found; but under what Class-notion can this case be put, which shall afford a General Rule that will be applicable for the solution of the doubt. The difficulty is, how to find the right Rule, and not, as Mr. Mill supposes, how to interpret it when found. The astronomer proceeds in this manner, when he seeks to know whether a comet, which has just appeared in the heavens, will return at a future period, or disappear forever. By determining three or more points in its path, he ascertains either that its orbit is an ellipse or an hyperbola; this is the Subsumption, and when found, the question is really answered, for the application of the Sumption—that the ellipse is a curve which returns into itself, while the hyperbola does not is so obvious, that it is unnecessary, except for a child, to be reminded of it. But though not expressed, the thought without it is certainly incomplete, and the main question is not answered. Mr. Mill's doctrine is, that "we much oftener conclude from particulars to particulars directly, than through the intermediate agency of any general proposition." For example, "it is not only the village matron, who, when called to a consultation upon the case of a neighbor's child, pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her Lucy." We have already observed (page 9) that a Concept may be derived from one object, as well as from many similar ones; that is, it may not represent an actual, but only a possible, class or plurality of things. The hasty and sweep |