The theory of forms is probably the most characteristic, and most contested of the doctrines of Plato. In the background lie the Pythagorean conception of form as the key to physical nature, but also the sceptical doctrine associated with Cratylus (said by Aristotle to have been one of the teachers of Plato) that in the heaving confusion of the perceptible world nothing is fixed, so thought can gain no foothold and nothing can be said. In escaping from this impasse Plato attempts to present a way in which the forms of things are intelligible but abstract shared features. Ordinary things gain their natures by either ‘imitating’ forms (which then become thought of as transcendent and somehow independent of the sensible world) or ‘participating’ in them (in which case they are immanent, present in things, and perhaps less mysterious). The train of thought is illustrated with both geometrical and ethical examples. The plate that the potter makes is not itself perfectly round, but perfect roundness is an ideal. It may not be found in the world, but it is something to which things approximate, and it plays a role in rendering intelligible the world in which they do so. Similarly actual human institutions may only approximate to the ideal of justice, but the ideal or form provides an intelligible dimension of description and criticism. Of course, to apply it means having the special knowledge of the geometer, in the case of roundness, or of the thinker who has attained knowledge of what justice consists in, in the case of ethics. Knowledge of the forms thus becomes itself an ideal towards which philosophers strive (see line, image of the). It is this line of thought that ends up with Plato echoing the Eleatic distinction between the real world, in this case the world of the forms, accessible only to the intellect, and the deceptive world of unstable perception and mere doxa or belief. The world of forms is itself unchanging, as change implies development towards the realization of form. But whereas Parmenides thinks of the real, eternal world as a kind of physical world, in Plato it becomes entirely non-physical.

The transcendental element in Plato’s thought is most visible in the Symposium, the Phaedo, and the Republic. The problem of interpretation is however confused by the question of whether Socrates’ voice is also that of Plato (again, according to Aristotle, Metaphysics M, xiii. 1078 b, Socrates did not make universals separate, but others, i.e. Plato, did). In the later dialogue Parmenides, Plato squarely confronts the problems of thinking of forms either as transcending particular things (see third man argument), or as partaken of by particular things, and therefore divisible. What is needed is an accommodation between the idea that universals are present in particulars, and the idea that they are merely imitated by them. See also conceptualism, nominalism, universals.