Physical identity may be divided into complete and incomplete. It is complete, or total, when a being is compared with itself through the unity of its physical entity, as in the preceding example of the pen. It is incomplete, or partial, when a physical part is compared with a physical whole, or, vice versa, as when we compare the whole man with his soul or with his body.
Metaphysical identity is a relation founded on the unity of a [pg 298] metaphysical entity, and possesses a metaphysical reality. It may be divided into adequate and inadequate. It is adequate when a being is compared with itself through the unity of some metaphysical reality which belongs to it. Such is the personal identity of John when old with John when young; for although he has undergone many physical changes in his body, and therefore has not preserved a perfect physical identity with himself, still his formal personality, which is wholly due to his soul, has not changed at all. The identity will be inadequate when any metaphysical constituent of a complete being is compared with the being itself, or vice versa. Such is the identity of the substantial act with the substance of which it is the act, of the matter with the material being, and of any property or attribute with the thing of which it is the property or the attribute. Such is also the identity of the divine Personalities with the divine essence; for, although the divine Paternity identifies itself perfectly with the divine essence, this latter requires further identification with the divine Filiation and with the passive Spiration; for it must be as whole and perfect in the Second and the Third Person as it is in the First.
Logical identity, or identity of reason, is a relation founded on the unity of a being of reason. It may be divided into objective and subjective. The objective has its foundation in the real order of things; the subjective has no foundation except in our conception. Thus the identity we conceive between a horse and its owner as to their animality is an identity of reason only, although it is grounded on a real foundation; for animality is indeed to be found really in both, but its unity is only a unit of reason; for animality, as common to both, is only a logical entity, which we call “genus.” The same is to be said of the identity between Peter and Paul as to their humanity; for humanity, though real in both, is not numerically, but only specifically, one, and its unity is therefore a unity of reason; for “species” is a logical being. On the contrary, when we say that “a stone is heavy,” the identity between a stone and the subject of such a proposition has no foundation except in our reason, and therefore is purely subjective; and the same is to be said of the identity of the verb is with the copula of the proposition, of heavy with the predicate, etc. It is evident, in fact, that the ground on which these last relations are founded is not a real unity, and not even a unity having anything corresponding to it in the real order; since subject, predicate, etc., are mere conceptions and creations of our mind.
We have thus three kinds of identity: the physical, which is either complete or incomplete; the metaphysical, which is either adequate or inadequate; the logical, which is either objective or merely subjective. Since distinction is the negation of identity, it is obvious that the distinction between two terms always results from the non-unity of the same, and is conceived by the comparison of the one with the other according to something which can be affirmed of the one, and must be denied of the other. Those things, in fact, are said to be distinct of which the one is not the other, or in one of which there is something not to be found in the other.
First, then, to deny real physical [pg 299] identity is to assert real physical distinction. Physical distinction may be either complete or incomplete as well as physical identity. It will be complete, or major, when, comparing two complete wholes with one another, we deny that the one is the other; as when we deny that the sun is the moon. It will be incomplete, or minor, when, comparing together the whole and any of its parts, we deny that the whole is any of its parts, and vice versa; as when we deny that Germany is Europe, or that the roof is the house. It is evident that incomplete physical distinction always coexists with incomplete physical identity.
The true and certain sign of real physical distinction between two things is their separability or their state of actual separation. For when two things are completely distinct as to their physical entity, they are each in possession of their own distinct existence; and consequently the existence of the one does not depend on the existence of the other. On the other hand, although a physical whole cannot exist as a whole, if its parts be separated, yet each of its physical parts can exist separated, as each of them has its own existence independent of the existence of the whole.
Secondly, to deny real metaphysical identity is to assert real metaphysical distinction. Metaphysical distinction may be either adequate or inadequate no less than metaphysical identity. It will be adequate, or major, when, comparing together two metaphysical constituents, we deny that the one is the other; as when we deny that the act is the potency. It will be inadequate, or minor, when, comparing a metaphysical compound with any of its constituents, we deny that the constituent is the compound, and vice versa; as when we deny that existence is the thing existing, or that person is personality. The inadequate metaphysical distinction always coexists with an inadequate metaphysical identity.
Thirdly, to deny an identity of reason is to assert a distinction of reason. A distinction of reason may be either objective or merely subjective, no less than the identity of reason. It will be objective, or major, when, comparing together two entities which are really identical, we find in their identical reality a ground for denying their conceptual identity; as when we deny that God's eternity is God's immensity, or when we deny that in any given being one essential attribute, as animality, is another, as rationality. This distinction is objective, because its ground is found in the object itself; and yet it is not real, because each term represents the same thing under two distinct aspects. Thus, in man, animality really includes a rational soul, and therefore implies rationality. But the distinction will be purely subjective, or minor, when, comparing together two entities, we find no ground whatever for denying their identity, except in our subjective manner of viewing them. Thus, although man is identical with rational animal, we can distinguish man from rational animal as a subject from a predicate; and it is evident that this distinction has no ground but in our conception.
Accordingly, we have three kinds of distinction: the real physical, which is either complete or incomplete; the real metaphysical, which is either adequate or inadequate; the logical, or of reason, which is [pg 300] either objective or merely subjective. This division is exhaustive. Some will say that we have forgotten the modal distinction. But the fact is that we have abstained on purpose from mentioning it in connection with any special kind of distinction, because it may fall under the physical as well as the metaphysical distinction, according as it happens to be understood; for it is differently understood by different writers.
Some authors consider that there is a modal distinction between the spherical wax and its sphericity, between the soul affected by fear and its affection, between the finger inflected and its inflection, and generally between the modified subject and its mode. Others, as Suarez, seem to admit a modal distinction between the wax simply and its sphericity, between the soul simply and its affection, between the finger simply and its inflection, and generally between the subject simply and its mode. And others, again, admit a modal distinction between the wax having a spherical form and the same wax having a different form; between the soul affected by a movement of fear and the same soul affected by a different movement; between the finger inflected and the same finger not inflected; and generally between a subject having one mode, and the same subject having another mode.[88]