According to a customary formulation, the principle of identity reads: A = A. The principle holds as the highest law of thought. We will attempt to contemplate this principle for awhile. We hear the principle as an expression about identity. By means of this principle we would like to find out what identity means.
When thinking is addressed by an issue and then goes after this, it can happen that it changes along the way. Thus it is advisable in what follows to attend more to the path and less to the content. To duly linger upon the content would already block the progress of the lecture for us.
What does the formula A = A, which one is obliged to present as the principle of identity, say? The formula names the equivalence of A and A. To an equating there belong at least two. One A is equal to another. Does the principle of identity claim to express such a thing? Apparently not. The identical, Latin idem, is called in Greek τὸ αὐτό. Translated into our German language, τὸ αὐτό means “the same.” When one continually says the same—for instance, the plant is a plant—he speaks in a tautology. For something to be able to be the same, one is enough. Two are not required for this as they are for equivalence.
The formula A = A speaks of equivalence. It does not name A as the same. The customary formulation of the principle of identity thereby conceals precisely what the principle is trying to say: A is A, i.e., every A is the same as itself.
While we circumscribe the identical in this way, there resounds an old word by which Plato makes the identical