This principle is often stated in the form A = A. This, however, is manifestly a formula, and not the enunciation of a philosophic principle. Locke (Essay, Bk. 4, c. 7) enunciates it as 'Whatever is, is,' and this form appears to be philosophically correct. Like the principle of Contradiction, this law is an Analytic proposition explicative of the concept of Being.

Its connection with that principle will appear plainly if we express it as 'A Being which is, is.' In this form we see that the only difference between the two is that in the one case we affirm that things which exist, exist : in the other, that things which exist, cannot not exist.

Like the principle of Contradiction also, it may be enunciated in reference to the nature, which determines the existence.

Leibniz has given expression to the law in this form. He words it 'Everything is what it is.' Leibniz's form will serve us also for the logical order, if it be understood as signifying that every subject of predication is what it is, i.e. that whatever attribute is affirmed of any subject, is in fact an attribute of that subject.

Mill somewhat unnecessarily introduces the question of verbal expression. He enunciates the law as: "Whatever is true in one form of words, is true in every other form of words, which conveys the same meaning" (Exam. of Hamilton, p. 409).

It is the universal practice at present to treat the principle of Identity separately from the principle of Contradiction.

Scholastic authors, however, do not admit its claim to rank as a really independent principle. At most they admit that it is a rudimentary form of the principle of Contradiction.¹ They urge that the predicate of an Analytic proposition must in some way explicate the notion of the subject. This principle does not do so. The predicate and the subject are the same concept. It is mere tautology.

There is, it may be owned, some force in this objection. The principle tells us nothing. Yet we must remember that Being is a concept which does not admit of analysis properly so called. Hence perhaps justification may be found for a tautologous principle here, which could not be adduced in any other case. The form is permissible, because it is indicative of the fact, that we have arrived at the limits of all explanation. But in order for the principle to convey any information, and to be of any service, it must be developed into the law of Contradiction.

The separate treatment of the two principles first became usual after the time of Leibniz. It is true that Parmenides the Eleatic (circa BC. 490) had enunciated the principle Being is eon emmenai as the foundation of his philosophy. But Aristotle emphatically affirms that the law of Contradiction is the first of all principles: and his decision for long went undisputed. Among medieval authors the Spanish Scotist Antonins Andrew (ob. 1320) argues that the first place should belong to the principle 'Every Being is a Being' (Omme Ens est Ens, Qq. in Met. IV., Q. 4). But the authority both of St. Thomas (Met. IV., lect. 6) and of Scotus (Quaest. sup. Met. IV., Q. 3) was against him: and he is expressly refuted by Suarez (Disp. Met. Ill., sect; 3).

Leibniz however makes the principle of Identity, which he gives as 'Everything is what it is,' the first of the primitive truths of reason which are affirmative, and the principle of Contradiction, 'A proposition is either true or false' the first of the negative truths (Nouv. Ess. IV., 2, sect; i). He further says, "the statement that a thing is what it is, is prior to the statement that it is not another thing" (Nouv. Ess. IV.. 7, sect; 9). Here as it would seem, is the real ground for the introduction of the principle of Identity as distinct from that of Contradiction. It appeared impossible that the primary analytic principle should be negative. If however, the view taken in the last section is accurate, the negative form is the necessary consequence of the primary character of the principle. We can only explain the perfectly simple by distinguishing it from that which it is not.

Aristotle enunciates this principle in the form given above, "Of two contradictory judgments, the one must be true and the other false" (Met. III., c. 8, sects 3, 4). He says also, "Between the two members of a contradiction, there is no middle term" (Met. III., c. 7, sect; i).'

As a metaphysical principle, it is stated, 'A thing must either be or not be.' The truth of this is evident from the immediacy of the opposition between being and not- being. The truth of the logical principle is capable of demonstration as follows. Where we have two contradictories, we have affirmation and negation, is and is not.

If the member which constitutes the mental judgment corresponds with the reality, whether it be in affirmation or negation, then the mind has attained truth.

Should it, however, not be in conformity with its object, the judgment is false. That is to say, the mind has either judged that what is, is not, or that what is not, is.

Wherever, therefore, the judgment is false, the contradictory judgment, whether it be the affirmative is, or the negative is not, will be true. Hence of two contradictories, the one must be true, the other false.²

The close connection between the logical principle and the metaphysical at once appears, when we reflect, that in affirmation, we are attributing a certain conceptual being to the subject; in negation, we assert that it does not possess this being. All contradictories therefore present the alternative between being and not being.

The way in which the principle is expressed by certain logicians, "Of any two contradictory predicates, one must belong to every subject," is unsatisfactory. It supposes that the predicater, and not the propositions, are contradictory to each other, and is represented by the formula, 'A is either B or not-B.' But, as we have seen, the primary form of negation is the negative judgment, not an affirmative judgment with a negative predicate; and in the expression of a fundamental law, it is the primary form that we need.

Mill employs the following formula — "It is allowable to substitute for the denial of either of two contradictory propositions, the assertion of the other" (Exam. of Hamilton, p. 416).

It should be carefully noted that the law of Excluded Middle is in no way concerned with Contrary terms.² We have explained Contrary terms as those which express the widest possible difference among classes belonging to the same genus, e.g. 'white, black,' 'convex, concave,' 'love, hatred.' There is, of course, a mean between terms such as these. Objects possessed of any other variety of colour are neither white nor black; a plane surface is neither concave nor convex; and indifference is neither love nor hatred. It is manifest, however, that an object must be either white or not white, convex or not convex; and that in regard to any particular individual, it is either true that we do or that we do not feel love towards him.

The principle has not passed unchallenged. Mill, in the interests of the empiricist philosophy, declared the law to be a mere generalization from experience. We have no grounds, he thought, for regarding it as necessary. Indeed he goes further, and maintains that "it is not even true except with a large 'qualification. . . . 'Abracadabra is a second intention,' is neither 'true nor false. Between the true and false there is a third possibility, the Unmeaning."

Such an argument can scarcely be treated as serious. An unmeaning proposition is not a judgment at all. Of more moment perhaps is the Hegelian objection. The very basis of the Hegelian philosophy is the reconciliation of opposites. Becoming is supposed to owe its origin to the union of Being and Not-Being, and the whole of Nature is regarded as constituted by this dialectic development. Hegel himself argues against the principle of Excluded Middle by pointing out that between + A and -A lies A. As against this view, it is urged that in Hegel's system the opposites are in fact contraries not contradictories, and that the individual does not owe its origin to them, but that they are obtained by abstraction from the individual.

Thus if it be urged that at dawn we can say with equal truth 'It is day' and 'It is not day,' and that the state of dawn is constituted by these opposites, it is answered that the two moments are not, as alleged, contradictory opposites, but the contraries 'dark' and 'light': and that dawn is not in any sense constituted by a dialectic development out of darkness and light, though we can mentally abstract these concepts from the state of dawn.