reasons for the rejection of this Principle of equality, which will appear in the sequel.

v. It would be obviously out of place here to enter upon a discussion touching the merits of this theory in its relation to the logical science. Suffice it to say that, as applied to the forms of thought, it seems to have even less verisimilitude than as applied to concepts or to the reality which constitutes their object.

-

THE PRESENT PROPOSITION IS THUS DECLARED.

The fundamental Principle, on which all philosophical thought in ultimate analysis absolutely reposes, must explicitly exhibit the necessity that Being should be, if it is. Without perfect security for this, all process of thought would become nugatory, nay, impossible. But the Principle of identity, even understood in a nontautological sense, does not explicitly exhibit the necessity that a Being should be, if it is. That which it does explicitly exhibit, is the identity of a thing with itself; and perhaps, as a consequence, its reality. Yet the idea of the identity of Being with itself, or even of the reality of Being, does not explicitly represent the necessity that Being should be, if it is. Thus,-to take an example in the concrete, it is said that Two and three are five. The Principle of identity assures us, (we will suppose), that 2+3 and 5 are one and the same thing. Be it so; but what security does it give that 2+3 may not at once be 5 and 7, or any other number? Yet, without such security, multiplication-tables, arithmetic, algebra, are a simple farce. Similarly: It has been maintained in a former Proposition, that the concept of change, under whatever form, necessarily carries with it the idea of an efficient cause. But why? Is it because change is change; or because Being subject to change is identical with inceptive or contingent Being? By no means. If the analysis there instituted be carefully considered, it will be seen that the concept of change includes the idea of an efficient cause, because it is impossible that any entity should be at once new and not new. In other words, the Principle of causality, like every other Judgment analytical or synthetic, reposes on the above mentioned motive, viz. on the necessity that a thing should be, if it is.

COROLLARY.

It follows from the preceding declaration, that the Principle of identity cannot be, even co-ordinately, an ultimate in order of

reduction. The insertion of this Corollary has been rendered necessary by the peculiar theory under review. Sir William Hamilton does not, in fact, claim for the said Principle an exclusive priority or, in other words, the position of a solitary ultimate; however inconsequent he may occasionally prove himself to be. For he says, 'The law of Identity and the law of Contradiction are co-ordinate and reciprocally relative, and neither can be educed as second from the other as first; for in every such attempt at derivation, the supposed secondary law is, in fact, almost necessarily supposed. These are, in fact, one and the same law,-differing only by a positive and negative expression'.' It is plain, then, that this author maintains the precedency of two co-ordinately ultimate Principles, each independent of the other :-the one lying at the root of all affirmative, the other at the root of all negative, analytical Judgments. It has been already seen that Sir William Hamilton does not limit their application to analytical Judgments; the restriction has been here adopted, in obedience to the requirements of the metaphysical science. The same declaration, which has been made in proof of the Proposition, will serve equally for the present Corollary. It was with a view to this, that the illustrations were exclusively taken from affirmative Judgments.

DIFFICULTIES.

I. The Principle of identity, understood in a sense not tautological, is the ultimate in order of reduction; so far as regards all affirmative analytical Judgments. The Antecedent is thus proved. That Principle, which is the fundamental reason for truly affirming the synthesis of predicate and subject in such Judgments, is the ultimate in order of reduction, so far as regards affirmative Judgments. But the Principle of identity is the fundamental reason for such affirmation. The Minor is thus declared. In every affirmative Judgment and, à fortiori, in every affirmative analytical Judgment, the fundamental reason why the predicate is truly affirmed of the subject, is this; that the reality, conceptually represented by the predicate, is objectively identical, (partially, at least), with the reality conceptually represented by the subject. Thus, to take an instance,—in the Judgment, All plants are living things, the ultimate basis for the truth of the affirmation is, that

Logic, Lect. V. pp. 82, 83.

living thing is objectively identified with plant. This identity finally and absolutely establishes the truth of the affirmation. If I should be asked, why I assert that Plants are living things, my only answer will be, Because they are. There is an objective identity, if only partial, between plants and life in plants, which the mind recognizes as the final justification of its assertion. It is impossible to proceed further. Whatever objection, therefore, may be made to the formula or formulas by which the Principle is symbolized, (and this is a matter of comparatively small importance); it would be difficult to deny the efficacy of the Principle itself in the case of affirmative Judgments.

ANSWER. The Antecedent is denied. As touching the proof, the Major requires to be distinguished. That the Principle, which is the fundamental reason for truly affirming the exclusively necessary synthesis of predicate and subject in such Judgments, is the ultimate in order of reduction,-granted. That the Principle, which is the fundamental reason for truly affirming the simply actual synthesis, is the ultimate,-I subdistinguish: The formal and conceptually fundamental reason,-let it pass; the material, as it were, and objectively fundamental reason,-again I subdistinguish: Such fundamental reason is the ultimate basis for the objective truth of the Judgment, let it pass; such fundamental reason is the ultimate Principle upon which the true Judgment conceptually rests in final analysis,-denied.

The Minor is contradistinguished. That the Principle of identity is the fundamental reason for truly affirming the exclusively necessary synthesis of predicate and subject in affirmative Judgments,denied; that this Principle is the fundamental reason for truly affirming the actual synthesis,-I subdistinguish: That it is the material and objectively fundamental reason,-let it pass; that it is the formal and conceptually fundamental reason,-denied.

This answer, given briefly in form, needs explanation. So, then; a given Principle may, or may not, be the fundamental reason why the predicate in a Judgment should be truly affirmed of the subject; and yet not include any, or at least sufficient, reason why it could not possibly be otherwise, or why simultaneous affirmation. and negation should be an absurd impossibility. This it is precisely that is intended by the phrase, exclusively necessary. But, if the Principle proposed does not exhibit a sufficient reason for this exclusively necessary synthesis, it cannot lay claim to be the ulti

mate in order of reduction. Again: If a Principle is the fundamental reason for truly affirming the simply actual synthesis of predicate and subject, it may be such in two ways. It may be formally and conceptually the ultimate reason for the true affirmation. In such case, it may be open to doubt whether it could not be the ultimate Principle; because the formal motive in the mind of the thinker, which justifies the affirmation, might perhaps virtually include a reason, implicit at least, for the affirmation of an exclusively necessary synthesis. But, if the said Principle is only materially and objectively the fundamental reason for truly affirming such synthesis, i. e. if the reason is in the object only, not in the concept; it is false to say that such a Principle can be the ultimate Principle in order of reduction, albeit it may possibly be an ultimate reason for the ontological truth of the object as presented to the mind.

Now, the Principle of identity is not, even virtually, the fundamental reason for truly affirming the exclusively necessary synthesis of predicate and subject; but only the actual synthesis. For, simply because A is A, it in no wise follows that A cannot at the same time be not-A. Moreover, if it should chance to be the ultimate reason for truly affirming the actual synthesis of predicate and subject; it is not such, as a Principle formally sustaining the Judgment, but as a Principle of Being which is really undistinguishable from ontological unity. For identity is simply the unity of Being with itself. Wherefore, the Principle of identity is rather the ultimate reason (if ultimate reason at all) of the truth of the object, than of the truth of the synthesis in the Judgment. It is true for instance, objectively, that All men are animals; because animality in man is objectively the same as rational animality. Accordingly, the so-called Principle of identity is nothing more or less than the reality, truth, or unity of Being, affirmed by a reflex Judgment; and contains nothing which had not been previously contained in the idea of Being and its attributes. It is not a Principle at all, strictly speaking. For a Principle is a Judgment; and, as such, postulates two terms. The above explanation will suffice to explain the contradistinctions embodied in the answer to the Minor of the objection.

II. It will not improbably be objected by a disciple of the Hamiltonian views, that a grave injustice has been committed against their learned author in the present Thesis. For the simple

fact is, that Sir William Hamilton has been solely occupied, in the passages quoted, with the task of determining the primary law of the affirmative syllogism, and of discovering a substitute for the, to him at least, unsatisfactory Dictum de omni et nullo; whereas it has been gratuitously assumed, that he is claiming for the Principle of identity a co-ordinate supremacy within the sphere of ontology. Thus the two spheres of Metaphysics and Logic have been confounded, apparently for the mere purpose of bringing in a bill of indictment against this illustrious writer. The mistake, moreover, is the less excusable, because Sir William Hamilton, in the very places which have been selected, expressly disclaims the pretension that the law of contradiction is a metaphysical Principle, and asserts that it can only boast of a logical value.

ANSWER. It seems necessary to observe, first of all, that philosophical inquiry abscinds from that which is purely personal. Whether, in his treatment of this question, Sir William Hamilton did, or did not, confine himself within the strict limits of Logic, is a matter of comparatively small importance. Nor would one, who is endeavouring to recall the mind of England to the old philosophy of the School, be too ready to quarrel with one that laboured so effectively in a similar direction. Yet, even supposing that a wrong interpretation has been given to his words, the possibility that his doctrine may be so misinterpreted makes it a matter of duty for the metaphysician to guard the student against the supposed error and its consequences. But, again, Sir William Hamilton has certainly given just occasion for the interpretation complained of. For (a), he is perpetually introducing the object of thought, though at the same time protesting against its relevancy within the sphere of Logic. Constituent qualities,' 'characters,'' constituent characters,'' notes of the object,' are terms which point to Metaphysics, not to Logic. When he speaks of thinking of a thing by the attribution of constituent qualities or characters,' and adds that the concept of a thing is the whole, the characters are the parts of that whole,' when he further declares that the law of identity may be thus enounced, -Everything is equal to itself, he is, plainly enough, passing beyond the boundaries of pure Logic, which has nothing to do with 'thing,' or characters,' or with attribution of constituent qualities' (because these constitute the matter of thought and belong to it as representative), but limits itself to a contemplation of the laws, or forms, of ideas and concepts only, abstracting wholly from the matter.