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analytical, requires subdistinction. That which simply or absolutely affirms the existence of the subject and predicate,-granted; that which affirms simply and absolutely the existence of some other third, -here there is need of further subdistinction: If it so affirms such existence explicitly and distinctly,- granted; implicitly and confusedly,-no.

This answer likewise stands in need of some explanation. Wherefore let it be observed that, if a Judgment absolutely affirms the existence of its subject and predicate, it cannot be an analytical Judgment; because all existence, save that of necessary Being, is contingent. Neither can the solitary exception just mentioned give rise to an analytical Judgment or Principle; because the existence of necessary Being is not within the range of our actual intuition, but is synthetically deduced from the existence of contingent beings. Nevertheless, an analytical Judgment may affirm existence in two ways, viz. explicitly and implicitly. In its explicit affirmation of existence, the existence would necessarily be conditioned, so as not to exceed the limits of the ideal order. Thus, for instance, in the Judgment, If contingent Being exists, necessary Being must likewise exist, (which is purely analytical), existence is not predicated simply and absolutely either of contingent or necessary Being; but of contingent Being it is presupposed, not in act, but merely as not repugnant; while of necessary Being it is explicitly predicated,-not simply however, but conditionally ; i. e. the existence of the latter is affirmed to be a metaphysical necessity, on the supposition that contingent Being exists. The existence of contingent Being is not affirmed; though its nonrepugnance, is, of course, implied. In the implicit affirmation of an analytical Judgment, the existence supposed to be affirmed is absolute; nevertheless, such affirmation affects neither the subject nor predicate, but another whose existence is confusedly latent in the concept. Thus, The idea of the possible includes both internal and external possibility, is an analytical Judgment, wherein existence is predicated neither of the subject nor of the predicate; still, the concept virtually, though confusedly, includes the idea of an existing Being, (as we have already seen), Whose necessary Existence is the only real Foundation either of internal or of external possibility. Further Existence, in this last example, is confusedly connoted in subject and predicate,-not as actual, but as not repugnant, or not impossible to either. For all real concepts are representative of real

:

objects which either exist or, at least, are capable of existence, outside the objective representation of the mind.

Now, the Principle of causality does not categorically affirm the In fact, it may be

existence of its subject or of its predicate. adequately represented under the form of a conditional, as thus: If inceptive or contingent Being exists, its efficient cause must exist. In such Judgment, nothing more is contained than the non-repugnance of existence, in the case of both the terms. Besides this, however, it virtually and confusedly includes the existence,-or rather, the idea of the existence,-of a First Cause.

IV. It has been further objected, that the Principle of causality is immoral; because it virtually denies the possibility of free-will. The Antecedent is thus proved. That Principle which affirms the necessity of the effect in presence of its cause, denies the possibility of free-will. But the Principle of causality is of this kind. Therefore, &c.

ANSWER. Of course the Antecedent and Consequent are denied. As to the proof of the Antecedent, the Major must be distinguished. That Principle, which affirms the hypothetical necessity of the effect in presence of its cause, (i. e. supposing the actual influx of the cause into its effect), denies the possibility of free-will,-no. That Principle, which affirms the antecedent necessity of the effect in presence of its cause, denies the possibility of free-will-there is need of a subdistinction: That Principle which includes such a supposition in the case of every cause,-granted; that Principle, which includes such a supposition in the case of some causes only, denies the possibility of free-will,-utterly denied.

This solution, like the preceding, needs explanation. If you conceive a cause, formally qua cause, you must necessarily suppose the effect; because the two terms are essentially relative. It would be a contradiction in terms that a cause, hic et nunc energizing as cause, should be without its effect; which would be tantamount to its being no cause at all. But, if you conceive an entity that is capable of causation, yet is not at present a cause; then, to affirm the necessity of the effect in all cases, would certainly go to destroy the liberty of the human will. But, to affirm such necessity in some cases in which the cause is necessarily determined to one effect, would not, as is plain, interfere with the liberty of the human will. Thus, for instance, it is physically necessary that fire, supposing the required conditions to be verified, should burn dry wood;

because such is the one determined effect of fire, as a cause, on the above-named subject.

NOTE 1. The Principle of causality does not assert the necessity of an existing effect, by virtue of the existence of a potential cause; but, inversely, affirms the necessity of an existing cause, supposing inceptive or contingent Being, (which must, of its very nature, be an effect), to exist.

NOTE 2.

The reader will profit by reading the entire tenth Book on causation in the Fundamental Philosophy of Balmez, There is an English translation of this Work by Brownson (Sadlier and Co., New York).

THE ULTIMATE PRINCIPLE IN ORDER OF REDUCTION.

As ideas, so analytical Judgments, or Principles, are reducible to an ultimate, of which the rest are simple determinations; under which, consequently, these latter are virtually contained. In the order of ideas, i.e. of simple Apprehensions, Being is the ultimate; since all other real concepts are truly determinations and contractions of this primary concept. Wherefore, Being virtually contains every form of reality,-or, to speak logically, every genus and every species, within its transcendental periphery. Now, the present inquiry has been instituted for the purpose of determining which Judgment is,-and at the same time of showing that certain Judgments are not, (though they have been severally supposed to be),—the ultimate in the order of Principles.

To begin with a definition of the subject: The ultimate Principle will be that analytical Judgment which explicitly exhibits the one motive of assent common to all other subordinate Principles; so that these latter may be established against sceptical assault by reduction to the former, as to the evident and immovable foundation of all complex or judicial thought.

PROPOSITION CXX.

The Judgment, which has been designated the Principle of identity, if taken according to the obvious meaning of the word, cannot be a Principle at all, much less an ultimate Principle in order of reduction.

PROLEGOMENON.

Sir William Hamilton has given a prominence in our time to

this so-called Principle of identity. He supposes it to be the 'Law' of all affirmation and definition; just as the Principle of contradiction, according to him, is the 'Law' of all negation and distinction. It is true that his doctrine on this head is ex professo limited to the logical science, and that he has laboured to substitute these two so-called 'Laws,' (a law and a Principle are not altogether the same thing), for the venerable Dictum de Omni et Nullo. And, considered solely under this aspect, it is obvious that any discussion of the theory in question would be out of place in these pages. But it will be seen, on careful examination, that the development of this theory is extra-logical, and lands us within the proper limits of metaphysical inquiry. In fact, as there has been occasion to remark before, the Hamiltonian novelties in Logic can all be traced to an apparent confusion touching the spheres of these two sciences and their respective wholes. In this and the two subsequent Theses, this theory of Sir William Hamilton will be considered under the threefold aspect which it has assumed in the exposition of the author; only, however, so far, as its consideration can fairly claim a place in the metaphysical science.

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For our present purpose it will suffice to introduce a short quotation from this learned author's work on Logic; the detailed exposition of the theory now under review will be reserved for the next Proposition. The principle of Identity, he remarks, 'is expressed in the formula A is A, or A=A; and by A is denoted every logical thing, every product of our thinking faculty,-concept, judgment, reasoning, &c. . . . . This law may, therefore, be also thus enounced,―Everything is equal to itself1.' There is, in this declaration, a seeming confusion of the 'Principle' of identity with that of equality; yet no two Judgments could well be more dissimilar. Accordingly, it will be well, for the sake of clearness, to separate or precise the three proposed formulas, by retaining the first (A is A), omitting the second for the present, and by modifying the third, so as to make it formally equivalent with the first. Wherefore, without prejudice to the theory of its author, it shall stand thus: Everything is itself. From the subsequent exposition it would appear as though Sir William Hamilton did not contemplate the naked tautology which his formula (4 is A) exhibits. Nevertheless, it is necessary first of all to take that formula, as it stands,

1 Lecture v, ¶ 14. Vol. I.

according to its obvious rendering. Afterwards it shall be examined by the light of the explanation with which this author surrounds it. In this Thesis, therefore, the said formula is taken literally, as it stands.

THE PROPOSITION IS THUS DECLARED:

I. A tautological Judgment cannot be a Principle; because a Principle is a Judgment either from which demonstration proceeds or on which demonstration reposes, and demonstration can neither proceed from, nor be founded on the strength of, a tautological Judgment. But the Principle of identity, taken in its obvious meaning, is tautological. The Minor of the above Syllogism is thus proved. Every Judgment, wherein the subject and predicate are in all respects identical, is tautological. But, in the formula, A is A, there is an absolute identity between the subject and predicate, as such; for the formula represents the subjective concepts more directly than the objected reality. The Major is self-evident, to those at least who are conversant with the laws of demonstration. For these laws require three terms, viz. the subject, the passion or attribute, and the definition. In the major premiss, the attribute is predicated of the definition; in the minor premiss, the definition is predicated of the subject. Therefore, in each premiss, there are two distinct terms; and, in the whole syllogism, three. But, in a tautological Judgment, there is only one term (4); and no other is even virtually contained. Therefore, a tautological Judgment cannot be a Principle in any sense; for it cannot actually enter into demonstration, neither could demonstration repose on the foundation of a solitary concept. Further, a Principle must be a Judgment; but A is A is a Judgment in nothing else but its logical form. À fortiori, it could not be the ultimate Principle on which demonstration in every field of science leans for support.

II. It cannot be doubted that the motive or evidence proper to analytical Principles, as such, must be virtually distinct from that which is contained in the simple idea of Being; otherwise, not only would there be an equivalence between the evidence of a simple apprehension and that of a Judgment, but there would be no sufficient reason for denying that a mere idea could become an analytical Principle, which is absurd. But the so-called Principle of identity exhibits a motive, or evidence, which is not dis