Volume 2, 2008
The Diagonalization of Being
Definition and Incommensurability in Plato’s Theaetetus
Plato’s Theaetetus sets the problem of the definition of science; moreover, what there is in question is the problem of the definition in general. Defining means measuring, referring to definite parameters what is initially indefinite. But it is not a case that the dialogue opens with the discussion about the commensurable and incommensurable numbers: the search for what is common to all sciences is the search for their common measure, for the term to which various elements are or can be commensurated. The apories Plato is showing in refuting the Protagorean thesis appear clearly as an objection against the absolute commensurability of all things: each sense is a parameter of a determinate sensible object and then results as quite incommensurable with another sense; a present sensation is incommensurable with a non present one, either past or future; all these facts question the possibility of the definition, for they reduce the knowledge, and the reality, to a set of atomic and quite unrelated elements. In the same way, the other definitions of science are rejected because of their incompleteness. But the negative conclusion of the Theaetetus regarding the definition of science must be assumed in a positive way: every operation of defining constantly presents an excess which belongs to the incommensurability and leaves every definition in a state of incompleteness. Through a comparison with the problem of the commensurable and incommensurable numbers, what is eventually shown is that the Being itself, as a mean between subject and predicate in the proposition, constitutes the diagonal element of every process of definition, irreducible to the elements that come into play. Being is, literally said, the incommensurable.