same, one is always enough. Two are not needed, as they are in the case of equality.

The formula A = A speaks of equality. It doesn't define A as the same. The common formulation of the principle of identity thus conceals precisely what the principle is trying to say: A is A, that is, every A is itself the same.

While we are circumscribing in this fashion what is identical, we are reminded of an old word by which Plato makes the identical perceptible, a word that points back to a still older word. In the dialogue The Sophist, 254d, Plato speaks of στάσις and κίνησις, rest and motion. Plato has the stranger say at this point: οὐκοῦν αὐτῶν ἕκαστον τοῖν μὲν δυοῖν ἕτερόν ἐστιν, αὐτὸ δ᾽ ἑαυτῷ ταὐτόν.

"Each one of them is different from the (other) two, but itself the same for itself." Plato doesn't just say: ἕκαστον αὐτὸ ταὐτόν, "each itself the same," but says ἕκαστον ἑαυτῷ ταὐτόν, "each itself the same for itself."

The dative ἑαυτῷ means: each thing itself is returned to itself, each itself is the same for itself with itself. Our language, like the Greek, offers the advantage of making clear with one and the same word what is identical and again clarifying that word in the unity of all its various forms.

The more fitting formulation of the principle of identity "A = A"


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Identity and Difference (GA 11) by Martin Heidegger