Socrates' requests for definitions get no answers that pass his tests, and there are a lot of attempts. The Theory of Forms comes of investing the existence assumptions just considered with metaphysical significance, using a generalization of a pattern of argument that originates as an argument against definitions Socrates rejects. The generalized pattern is the Argument from Relativity (§ 1.2).

We are going to get at this by constructing a theory of definition for Socrates.

A SOCRATIC THEORY OF DEFINITION: PRELIMINARY

The theory is not supposed to be Socrates' (or Plato's) own. Rather, it is derived in the following way. When Socrates rejects definitions he uses certain arguments against them. We ask: what would an answer have to be like in order not to fall to that argument? We identify the assumption, and ask what general claim it might most naturally be taken to instantiate. The assumptions in question are not ones that require reference to any special entities that figure as the objects of these definitions.

This procedure will result in three main conditions of adequacy for a definition:

1. the Substitutivity Requirement: its definiens must be substitutable salva veritate for its definiendum;

2. the Paradigm Requirement: its definiens must give a paradigm or standard by comparison with which cases of its definiendum may be determined;

and

1. the Explanatory Requirement: its definiens must explain the application of its definiendum.

This and the next few chapters lay out these requirements and tie them to Socrates.