I am teaching Plato’s Theaetetus right now, and thought I’d share a wonderful little semantics-based reductio that Socrates offers there. It’s really path breaking, I think. The context is Heraclitus’ “flux metaphysics”, according to which there are no enduring objects or properties, but only “flowing”. But, urges Socrates, this entails that there are no meaningful words, and no essences to tie them to via definition. By the time you label something, it would be gone; and asserting doctrines would be impossible (Hence, by the way, the whole project of asking “What is knowledge?”, which is the main question of the dialogue, itself makes no sense. If the doctrine were true, the question of the nature of knowledge — that enduring thing — could not arise. But then the Protagoras-Heraclitus answer to the question is self-defeating!) Here is an excerpt:
Soc: Now if there were only moving through space and not altering, we should presumably be able to say what the moving things flow? Or how do we express it?
Theod: That’s all right.
Soc: But since not even this abides, that what flows flows white; but rather it is in process of change, so that there is flux of this very thing also, the whiteness, and it is passing over into another colour, lest it be convicted of standing still in this respect – since that is so, is it possible to give any name to a colour which will properly apply to it?
Theod: I don’t see how one could, Socrates; nor yet surely to anything else of that kind, if, being in flux, it is always quietly slipping away as you speak?
Soc: And what about any particular kind of perception; for example, seeing or hearing? Does it ever abide, and remain seeing or hearing?
Theod: It ought not to, certainly, if all things are in motion.
Soc: Then we may not call anything seeing, rather than not-seeing; nor indeed may we call it any other perception rather than not – if it be admitted that all things are in motion in every way?
Theod: No, we may not.
Soc: Yet Theaetetus and I said that knowledge was perception?
Theod: You did.
Soc: And so our answer to the question, ‘What is knowledge?’ gave something which is no more knowledge than not.
Theod: It seems as if it did.
Soc: A fine way this turns out to be of making our answer right. We were most anxious to prove that all things are in motion, in order to make that answer come out correct; but what has really emerged is that, if all things are in motion, every answer, on whatever subject, is equally correct, both ‘it is thus’ and ‘it is not thus’ – or if you like, ‘becomes’, as we don’t want to use any expressions which will bring our friends to a stand-still.
Theod: You are quite right.
Soc: Well, yes, Theodorus, except that I said ‘thus’ and ‘not thus’. One must not even use the word ‘thus’; for this ‘thus’ would no longer be in motion; nor yet ‘not thus’ for here again there is no motion. The exponents of this theory need to establish some other language; as it is, they have no words that are consistent with their hypothesis…