well known to logical students, is the quantification of the predicate, a doctrine which naturally enough connects itself with views already presented. As applied by him, it tends powerfully to the expression and simplification of the logical system. It is the grand peculiarity of the new analytic, and really requires a reorganization of the whole scheme of logical forms. As already intimated, this movement was only in part carried out by our author. The doctrine is not discussed in the Lectures, they containing only a faint hint of it, the subject doubtless being regarded as too abstruse for a class of undergraduates. It is, however, treated largely in the Appendix, as also in the Discussions. We do not propose to examine it here in detail, or to do more than briefly indicate its character. are Previous writers on logic have usually maintained that affirmative propositions distribute the subject, and negative propositions the predicate. Thus, in the universal affirmative "All men are animals," we do not mean that "all men "all animals." We take into account the quantity of the subject, but not that of the predicate. It would not do, of course, to convert the proposition so as to say, "All animals are men." We must restrict the wider term and say, "Some animals are men." In the first proposition we think, though we do not say, "All men are some animals." Hamilton insists that, in addition to the generally admitted four kinds of propositions, we may have four others; that is, there may be affirmative propositions with or without the subject distributed, and negative propositions with or without the predicate distributed. Thus: Toto-total: All S. is all P. Toto-partial: All S. is some P. Toto-total: All S. is not all P. Toto-partial: All S. is not some P. Parti-total: Some S. is not all P. Parti-partial: Some S. is not some P. Here is observed the extensive application of his single postulate previously referred to. To state explicitly what is thought implicitly. In other words, to determine what is meant before proceeding to deal with the meaning. Thus in the proposition men are animals, we should be allowed to determine whether the term men means all or some FOURTH SERIES, VOL. XIII.-35 men, whether the term animals means all or some animals; in short, to quantify both the subject and predicate of the proposition. This postulate applies both to propositions and to syl logisms.-P. 512. The views of Inductive Reasoning presented in this volume are worthy of particular attention. The author criticises with much severity the teachings of previous logicians on this topic, charging that almost all, with the exception of Aristotle, have advanced doctrines utterly erroneous. They have usually regarded induction not as regulated by the necessary laws of thought, but as determined by the probabilities and presumptions of the sciences from which its matter has been accidentally borrowed. All inductive reasoning is from the parts to the whole; but this reasoning is one thing in the material and objective sciences, and quite another in the science of logic. In the former take the following example: This, that, and the other magnet attract iron; But this, that, and the other magnet represent all magnets ; Therefore, all magnets attract iron. In this syllogism the minor premise is founded on the principle that nature is uniform and constant, and on this general principle the reasoner is physically warranted in making a few parts equivalent to the whole. But as a logician he knows nothing of any principles except the laws of thought. The induction of the objective philosopher, in so far as it is formal, is, in fact, deductive. But there is a process of purely inductive reasoning, which is governed by its own laws, and which is equally necessary and independent as the other. The rule by which the deductive syllogism is governed is: What belongs or does not belong to the containing whole, belongs or does not belong to each and all of the contained parts. The rule by which the inductive syllogism is governed is: What be longs or does not belong to all the constituted parts, belongs or does not belong to the constituted whole. These rules exclusively determine all formal inference; whatever transcends or violates them, transcends or violates logic. Both are equally absolute. It would not be less illegal to infer by the deductive syllogism an attribute belonging to the whole of something it was not conceived to contain as a part, than by the inductive to conclude of the whole what is not conceived as a predicate of all its constituent parts. In either case, the consequent is not thought as determined by the antecedent; the premises do not involve the conclusion. To take the example previously adduced as an illustration of a material or philosophical induction, it would be thus expressed as a formal or logical: This, that, and the other magnet attract iron; But this, that, and the other magnet are all magnets; Here the inference is determined exclusively by a law of thought. In the subsumption it is said, this, that, and the other magnet, etc., are all magnets. This means, this, that, and the other magnet are, that is, constitute, or rather are conceived to constitute all magnets, that is, the whole, the class, the genus magnet. If, therefore, explicitly enounced, it will be as follows: This, that, and the other magnet are conceived to constitute the whole class magnet. The conclusion is, Therefore, all magnets attract iron. This, if explicated, will give: Therefore, the whole class magnet is conceived to attract iron. The whole syllogism, therefore, as a logical induction, will be: This, that, and the other magnet attract iron; But this, that, and the other magnet, etc., are conceived to constitute the genus magnet; Therefore the genus magnet attracts iron.—Pp. 227, 228. Some have been misled by the objection that the subsumption or minor premise, "This, that, and the other magnet are all magnets," is manifestly false. But this objection is incompetent, as wholly extra-logical. It is not the business of the logician to ascertain the truth or the falsity of his premises. His office does not commence till the premises are furnished, and if they be impossible or false, it is not his business to take any account. He reasons from them, not about them. In the example above, the subsumption has already been explained to mean, not that this, that, and the other, etc., really are all, but that they are thought so to be. The inference proceeding on this supposition is a necessary one. We must pass unnoticed much that is fresh, interesting, and suggestive in its style of treatment, as well as some that is original in thought. On the figure of syllogism we tarry a moment. The four figures commonly recognized by logicians are carefully set forth in all their moods, with the cabalistic literal notation familiar to all students of the science. What is more, they are amply and instructively illustrated by means of diagrams representing the three notions of a syllogism, as including, excluding, or partially including and excluding one another, like so many mathematical quantities. But while presenting these figures and thoroughly explicating them, Hamilton dissents from the doctrine commonly prevailing among the logicians concerning them, and criticises them with much force. The fourth figure was not contemplated by Aristotle, and many writers since it was innovated have striven to disallow it. Its inference, however, has never been invalidated, though felt to be tortuous and perverse. This incompetence on the part of the logicians he avers to come from their neglect of the doctrine of the two quantities in which reasonings may be cast. A cross inference is practicable from one of these quantities to the other in the formation of a syllogism. This is just what takes place in the fourth figure, an occult reasoning being carried on in the mind. This hybrid inference is immaterial, useless, and logically invalid, though valid in itself. It is therefore rejected. But it is further maintained that the second and third, as well as the fourth figures, are only accidental modifications of the first. We cannot do more than present the following paragraph on this point: The three last... figures are merely hybrid or mixed reasonings, in which the steps of the process are only partially expressed. The unexpressed steps are in general conversive inferences, which we are entitled to make, 1. From the absolute negation of a first notion as predicated of a second, to the absolute negation of a second notion as predicated of the first-if no A is B, then no B is A; 2. From the total or partial affirmation of a lesser class or notion of a greater, to the partial affirmation of that greater notion of that lesser-if all (or some) A is B, then some B is A.—P. 309. This view of the syllogistic figure, together with the reduction of Aldrich's twelve rules and Whately's six to three, greatly tends toward a higher simplification of logical forms. After the doctrine of elements, or stoicheiology, comes that of method or methodology. We are to consider thought not only as existing, but as existing in its perfection, and this is as much the object of logic as the possibility of thought. Methodology, then, is conversant with the perfection, the well-being of thought. The end of thought is truth, knowledge, science. "A science is a complement of cognitions having, in point of form, the character of logical perfection; in point of matter, the character of real truth." "Method in general is the regulated procedure toward a certain end." It consists of two processes, correlative and complementary of each other: the analytic, proceeding from the whole to its parts; the synthetic, proceeding from the parts to the whole. Now though there is no ambiguity or disagreement so far in the use of these terms, yet inasmuch as there are different kinds of whole and parts, there is a liability to confusion among different writers. For instance, as we have before seen, the ancients looked almost exclusively to the whole of extension, and with them analysis denoted a division of the genus into species, and of the species into individuals. The moderns, on the other hand, looking at the whole of comprehension, used this term to express a resolution of the individual into its various attributes. Since these quantities or wholes are opposite to one another, it is evident that analysis as applied to one is identical with synthesis as applied to the other, and vice versa. Hence by different philosophers these terms are used in a contrary or reverse sense. This is to be guarded against. The formal perfection of thought is made up of the three virtues or characters: 1. Of clearness; 2. Of distinctness; 3. Of harmony. The character of clearness depends principally on the determination of the comprehension of our notions; the character of distinctness depends principally on the development of the extension of our notions; and the character of harmony on the mutual concatenation of our notions. ... Of these the first constitutes the doctrine of definition, the second the doctrine of division, and the third the doctrine of probation.-Pp. 340, 341. The elucidation of these principles is carried out at great length, and is practical and sensible as well as thoroughly philosophical. We only regret that we are not able to give a larger presentation of the doctrines advanced and their explication. The lectures on Modified Logic are, as already explained, supplementary, the author not recognizing this branch of the subject as properly belonging to the province of logic. Yet, as it seems to us, the course must have been palpably incomplete without a discussion of the topics here embraced. We confess to some disappointment in entering upon this part of the work. The views presented are less original and attractive than was anticipated, yet perhaps they are all we had any right to expect. The treatment, at least, is as thor |