In Metaphysics 19 Aristotle mentions several Platonic arguments for forms. These were set out in detail, along with Aristotle's criticisms, in his essay Peri Ideōn, portions of which are preserved in Alexander's commentary on 19. In this chapter I explore the logic of some of these arguments and the interconnections between them.

Aristotle divides the arguments he discusses into two classes, the less and the more accurate arguments; but he says very little about the basis of this division. I shall suggest that the more, but not the less, accurate arguments are valid arguments for Platonic forms; and I shall claim that although Aristotle is no friend of the forms, he concedes to the Platonists that they are valid arguments for forms. But the concession is coy. For, Aristotle argues, these arguments lead to intolerable results and so cannot be sound. One leads to a vicious infinite regress, the third man, and the other produces forms of relatives, ‘of which we say there is no independent class’ (Metaph. 990b16–17). From this point of view, the less accurate arguments are to be preferred. For although they are invalid arguments for forms, they are valid and, so Aristotle seems to believe, sound arguments for his own universals, the koina.

If this interpretation is correct, it suggests an interesting result: that the overall structure of the Peri Ideōn is neatly dilemmatic. The Platonists can rely on two sorts of arguments for forms, their more and their less accurate arguments.

At the very beginning of Plato's Cratylus Hermogenes explains Cratylus' view by saying that it supposes there to be a certain natural correctness (orthotēs) of names; that this correctness is the same for all linguistic groups; and (very strongly) that it has nothing to do with what name anyone actually applies to anything – so that, he is quoted as saying to Hermogenes, ‘your name would not be Hermogenes, even if everyone called you that’ (383B). This last point implies something which explicitly emerges later, that, for Cratylus, the question whether some word ‘N’ is the correct name of a given item is the same as the question whether ‘N’ is that item's name at all.

The assumption that the answers to those questions must be the same is not shared by everyone in the dialogue. It is shared by Hermogenes, for reasons which are (roughly) the opposite of Cratylus'. It is not shared by Socrates, whose final position requires us to distinguish the questions; or rather, to put it more precisely, it requires us to make a distinction which can be handily put by us in terms of a possible divergence between the name of X and the correct name of X, and is often so put in the dialogue, but which can also be expressed, as we shall see later, in terms of two kinds of correctness.

In trying to give some account of Cratylus' theory of names, I shall particularly emphasise that distinction and Cratylus' denial of it.

At the beginning of Book VII of the Nicomachean Ethics, just before his discussion of akrasia, Aristotle pauses to make some observations about his philosophical method:

Here, as in all other cases, we must set down the appearances (phainomena) and, first working through the puzzles (diaporēsantes), in this way go on to show, if possible, the truth of all the beliefs we hold (ta endoxa) about these experiences; and, if this is not possible, the truth of the greatest number and the most authoritative. For if the difficulties are resolved and the beliefs (endoxa) are left in place, we will have done enough showing (1145b1 ff.).

Aristotle tells us that his method, ‘here as in all other cases’, is to set down what he calls phainomena, and what we shall translate as ‘the appearances’. Proper philosophical method is committed to and limited by these. If we work through the difficulties with which the phainomena confront us and leave the greatest number and the most basic intact, we will have gone as far as philosophy can, or should, go.