Socrates, Aristotle says, was the first to fix attention on definitions, and the Socrates of the Socratic dialogues does that. But he does not simply say: let's define (say) piety. He doesn't have the word “define”: this is discussed in § 2.1.

Nor does he simply look for definitions as an abstract intellectual enterprise. He expects definitions to solve certain problems. So we must look at the problems (§ 2.2), and at the reason Socrates thinks definitions are required for solving them (§ 2.3).

PRELIMINARY: ON THE VOCABULARY FOR “DEFINING”

The Socratic dialogues do not consistently employ terms for “define” or “definition.” Aristotle has a technical terminology here, but this is after the arteries have hardened considerably. Some of his words appear in the Socratic dialogues. His favored noun, ʿορισμός, does not appear anywhere in Plato, but an alternative, ὅρος, does, as does the associated verb ʿορίζειν. All these words have to do originally with (spatial) boundaries, and the transition to technical philosophical terminology is only just under way in the Socratic dialogues. Of the six occurrences of ὅρος in these dialogues, that in the first book of the Republic is the one for which the translation “definition” is the most comfortable. There Socrates, having raised the question (331c1–3) “whether we are to say that this itself, justice, is, without qualification, truthfulness and giving back what one has taken from someone,” gives a counterexample, and says (331d2–3): “So this is not {a} definition of justice, saying the truth and giving back what one has taken.