Dialogues of Plato, Vol. 4 (Parmenides, Theaetetus, Sophist)

But in this, as in all the later writings of Plato, there are not wanting thoughts and expressions in which he rises to his highest level (15, 17, 63, 67).

The plan is complicated, or perhaps the lack of a clear plan makes the progress of the dialogue difficult to follow. A few leading ideas seem to emerge: the relation of the one and the many, the four original elements, the kinds of pleasure, the kinds of knowledge, and the scale of the good. These are only partially connected with one another. The dialogue is not rightly entitled "concerning pleasure" or "concerning good," but should rather be described as treating of the relations of pleasure and knowledge—after they have been duly analyzed—to the good.
(1) The question is asked: Whether pleasure or wisdom is the chief good, or some nature higher than either? And if the latter, how are pleasure and wisdom related to this higher good?
(2) Before we can reply with exactness, we must know the kinds of pleasure and the kinds of knowledge.
(3) But we may still affirm generally that the combined life of pleasure and wisdom or knowledge has more of the character of the good than either of them in isolation.
(4) To determine which of them partakes most of the higher nature, we must know under which of the four unities or elements they respectively fall. These are, first, the infinite; secondly, the finite; thirdly, the union of the two; fourthly, the cause of the union. Pleasure belongs to the first, wisdom or knowledge to the third class, while "reason" or "mind" is akin to the fourth or highest.

(5) Pleasures are of two kinds: the mixed and the unmixed. Of mixed pleasures there are three classes: (a) those in which both pleasure and pain are bodily, as in hunger and eating; (b) those in which there is a remembered opposite of the actual bodily affection, such as when you are hungry and remember a former feast; (c) those in which the pleasure and pain are both mental. Of unmixed pleasures, there are also three classes: (a) those of sight and hearing; (b) those of smell; (c) those of mathematics.

(6) The sciences are likewise divided into two classes: mixed and unmixed, creative and theoretical. In each, there is an "architectonic" governing or foundational element. In the creative arts, this is arithmetic and mensuration; arts like carpentry, which have an exact measure, are higher than music, which is for the most part mere guesswork and imitation. But there is also a higher arithmetic, and a higher mensuration, which is exclusively theoretical, and a dialectical science, which is higher still and constitutes the truest and purest knowledge.