If the object formally represented by each of the concepts is one and the same—as, _e.g._ when we compare “_A_” with “_A_,” or “man” with “rational animal,” or, in general, any object with its definition—the identity is both _real and logical_ (or _conceptual_, _formal_). If the concepts differ in their formal objects while representing _one and the same reality_—as when we compare “St. Peter” with “head of the apostles,” or “man” with “rational”—the identity is _real, but not logical_ or formal. Finally, if we represent two or more realities, “John, James, Thomas,” by the same formal concept, “man,” the identity is _merely logical_ or formal, _not real_. Of these three kinds of identity the first is sometimes called _adequate_, the second and third _inadequate_. Logical identity may be _specific_ or _generic_, according as we identify really distinct individuals under one specific concept, or really distinct species or classes under one generic concept. Again, it may be _essential_ or _accidental_, according as the abstract and universal class-concept under which really distinct members are classified represents a common part of the essence of these members or only a common property or accident. Thus John, James and Thomas are essentially identical in their _human nature_; they are accidentally identical in being all three _fair-haired_ and _six feet in height_. Logical identity under the concept of _quality_ is based on the real relation of _similarity_; logical identity under the concept of _quantity_ is based on the real relation of _equality_. When we say that _essential_ (logical) _identity_ (_e.g._ the identity of John, James and Thomas under the concept of “man”) is based on the fact that the really distinct individuals have really _similar_ natures, we merely mean that _our_ knowledge of natures or essences is derived from our knowledge of qualities, taking “qualities” in the wide sense of “accidents” generally: that the properties and activities of things are our only key to the nature of these things: _Operari sequitur esse._ It is not implied, nor is it true, that real _similarity_ is a partial _real identity_: it is but the ground of a partial _logical_ identity,—identity under the common concept of some quality (in the wide sense of this term). For example, the height of John is as really distinct from that of James as the humanity of John is from that of James. If, then, individual things are _really_ distinct, how is it that we can represent (even inadequately) _a multitude_ of them by _one_ concept? To say that we can do so because they reveal themselves to us as _similar_ to one another is to say what is undoubtedly true; but this does not solve the problem of the relation between the universal and the individual in human experience: rather it places us face to face with this problem.