to other parts, to all the parts. The necessity of a number of observations in order to a certain induction, is of extralogical consideration. Logic requires but one. In fact, we are often satisfied with one. We are as much convinced from a single observation of the combination of oxygen and hydrogen to form water, that this combination will in the same circumstances always in like manner form water, as from any number of observations. We multiply, in material, physical induction, our observations only for the purpose of determining that we really have a part of a causal whole. But this is all extra-logical. Logic proceeds on what is given or assumed only; and its principle is: "given one part of a causal whole, and the whole is necessarily inferred;" for, by the necessary laws of thought, the part cannot be without the complementary part, and so cannot be without the whole of which it is a part. The part brings in the whole as truly as the whole the part. This is the necessary, the unquestionable principle of logic. Let the case be brought to which it applies, and its influence holds necessarily. We have precisely the same difficulty in the case of a substantial whole, which is the kind of whole that logicians have almost exclusively regarded, that we have in the case of a causal whole - no more, no less. All their examples, all their specific statements of principles, suppose a substantial whole. Even when treating of induction itself, they have seemed able to represent it to themselves only in the forms of a proper substantial whole. It is hence that Hamilton is justified in declaring their teachings to be utterly erroneous. We may, in few words, indicate the precise relationship of this logical consideration of cause to that of substance, as well as to the science generally.

Logic is of no utility except as applicable to objective being. It must of necessity, therefore, develop itself throughout in reference to this applicability. Being we necessarily conceive as substance and also as cause. The latter conception is as important to us as the other; and logic should as much regard it as the other. It assumes; does not prove,

-does not give us the reality of substance. It deals with notions, thoughts only. But its notion of substance is as a whole containing parts, called attributes or characters. As such, and in this relation only, can it deal with them. Now, all real substance is given us in simple apprehension,- in perception or intuition, in the gross, as a whole. From the whole, as thus given, we proceed, by an act of proper thought, to the parts. Logic, as applied to substance, as realized in it, therefore, more naturally, as more in correspondence with the direction of our ordinary mental activity, proceeds analytically, deductively, from whole to parts. We infer, when dealing with objective being as substance, from the whole to the parts. Cause, as real, on the other hand, is given us by the parts, for its necessary form is succession. The logical consideration of cause, therefore, should more naturally proceed genetically, synthetically, inductively, from the part to the whole. The nature of cause prescribes, a priori, this mode of procedure, which is exactly counter to that in the case of substance. The principle of identity works either way just as naturally. The part implies the whole as truly as the whole contains the part; and we need but one part from which necessarily to induce the whole. In substance and in cause we have the same necessity imposed on us of determining the whole, and the part as pertaining to that whole. If we use the premise in a substantial whole, "man is mortal," we need to assume that the whole of characters denoted by the term "man" contains the character "mortal" as one of them, or that the extensive whole, the class-whole, "mortal" contains under it, as one species, "man"; in other words, man as substance contains the attribute "mortal," or the class of substances "mortal" contains the substance "man." Then we have a valid judgment, from which a second, affirming that "Caius," as a whole of characters, contains among them that of "man," will enable us, on the deductive application of the principle of identity, to derive our conclusion that "Caius is mortal." So, precisely, in a causal whole and in induction: "Caius is mortal; Caius is

a man; therefore man is mortal"; the reasoning, as expli cated, runs thus: "Caius," as effect, is part of the causal whole "mortal"; Caius, so far as such effect in this causal whole, is man; therefore, the effect "man" is part of the causal whole "mortal." If the reasoning proceed in extensive quantity, then we should explicate thus: "Caius, as effect, is part of the class of effects in the causal sphere mortal'; Caius is one part of a class, of which other men are the complementary parts; therefore other men with Caius, that is all men, belong to the class in the sphere 'mortal.'" This is the significance of the principle universally recognized as the one governing and validating principle of induction; that nature is uniform; or that the same cause works, in the same circumstances, ever the same effect. If we verify the existence of the cause thus, as we do when we verify a part of its effect, and if we also determine the sphere within which the cause operates, our conclusion is valid, is necessary for every effect of such cause in that sphere. The causal whole is the cause with its entire effect; a part of that causal whole, on the principle of identity, as applied to the relation of parts to whole, involves the other parts as complementary of that causal whole.

In the application of the logical principle to actual induction in matters of experience, we have difficulties precisely analogous to those which we encounter in deduction. or in substances. We must apprehend the effect as the product of a cause, just as in the deductive process we must apprehend the attribute; we must also apprehend the causal whole or sphere, and the effect as belonging to it, just as in the other case we must apprehend the substance and the attribute as pertaining to it. Whether one or more

facts are necessary to assure us of the cause, and of its embracing the class of effects in question, is to be determined on the same grounds on which we determine whether one or more observations are necessary to assure us of the substance, and of its attributes. But all this is extra-logical. Dealing only with the process of thought, and confining

itself to the exposition of its nature and laws, logic only assumes the facts to which its processes are to be applied; and this as well in inductive as in deductive reasoning. In the one case its one principle is: "Given a whole, a part of that whole, and a part of that part; and the conclusion follows necessarily, that the part of the part is a part of the whole." In the other case, its principle is: "Given a part; a whole of that part; and a whole of which this whole is a part; and the conclusion follows necessarily, that the whole of which the lesser whole is a part is a whole also of the part of this lesser whole." For example, in the first case: given, "mortal," "man" as part of "mortal," and "Caius" as part of "man"; and deduction gives the necessary conclusion, "Caius is part of mortal." In the other case: given," Caius," "man" as whole of which "Caius" is part, and "mortal" as whole of which "man" is part; and induction gives the necessary conclusion, "man is part of mortal." The one form is that which our necessary mode of conceiving substance compels us to adopt; the other is that which our necessary mode of conceiving cause prescribes to us. The one form of application involves the other. Logic, as a complete science, should treat of the one as well as the other. In neither does it transcend its bounds as pure, necessary science. Of the two applications, if there be a preference, that to cause in induction is of superior practical importance. At all events, logic has been onesided in its development, in so far as it has been exclusively in the direction of substantial wholes, and has so far failed in its command of respect and cultivation; just as in giving exclusive consideration to reasonings, to the neglect of concepts and judgments, which are of incomparably greater importance, scientifically and practically, it has become, as a structure, top-heavy, and fallen into ruin.

We are now prepared to enunciate in brief, formal statements, what we conceive to be the form of development which logic as a science should assume; indicating, as we

proceed, what remains to be done even now, after the Herculean achievements of Hamilton, in expurgating the systems as received before his time.

I. Logic must be, throughout, treated as a pure science, developed from necessary principles by necessary methods of thought. Hamilton has done an eminent service in exposing the defects of the logical systems in this respect.

II. Logic, or at least discursive logic, is the science of thought, in the stricter sense, as the product of the discursive faculty. It embraces the whole sphere occupied by this faculty; all its products-concepts, judgments, reasonings. Here Hamilton has achieved a most vital success for the science. He has clearly identified these three products of thought in their derivative affinity and consequent equality of claim to co-ordinate consideration in the science. His exposition of concepts is new to English literature, and has made his system of logic an indispensable necessity in all intellectual training. It will force the study of logic into every reputable institution of learning, as a study without which all training must be regarded as fatally onesided and defective, and thus regain for the science its former distinction, now worthily attained. We go further than Hamilton, who, while he thus identified the three elements-concepts, judgments, and reasonings, -as alike products of thought, yet went little further in unfolding their distinctive natures, as we proceed to indicate the more precise distinction, that in a judgment thought identifies the single character; in a concept, it aggregates single characters, thus separately attained, into one; in a reasoning, it separates this single character into separate constituent characters. The judgment is the original product; the concept arises from the synthesis of thought; the reasoning, from the analysis of thought. Logic, in its fuller developments, we claim therefore, should recognize these specific differences in the elements of thought.

III. The faculty of thought is essentially an identifying faculty. Its one principle, therefore, is that of identity. Hamilton has, in scattered posthumous fragments, pointed