A paradox is like a pun. It is also like a Delphic oracle. For in all three cases, we escape puzzlement, or spoil the joke, when we interpret, when we follow the tracks of the words and disentangle their meaning. So paradoxes are about words - either about the relation between one word and another, or about the relation between words and the world; and the punch of the paradox is delivered by its verbal content. Thus it is characteristic of a good paradox that its verbal content is vicious: paradoxes are very often self-referential, such as ‘Please ignore this notice’.Paradoxes may be classified according to two main types. Firstly, there are the innocuous paradoxes which tell - or point the way to - a surprising truth. The Socratic Paradoxes, for example, are paradoxical because to say ‘No-one does wrong willingly’ is to contradict the phenomena. But deeper reflection upon Socrates' moral psychology and his account of the good life, might make us concede the truth of his dictum. Certainly it is Socrates' view that we all hold beliefs that entail his thesis. Similarly Heracleitus tells the truth that we cannot step into the same (in all respects) river twice; although if we concede that the waters may flow without damaging the identity of the river, what he says is false. Thus ordinary paradoxes tend to have two faces - their initial, paradoxical one, where they appear false, and their truth, apparent upon reflection.
Paradox in Plato's ‘Phaedrus’