John asked:

How did Plato’s Theory of Forms answer Heraclitus and Parmenides?

Answer by Helier Robinson

This question could be the opening of a book on the history of western philosophy.

First of all, an explanation of why Heraclitus and Parmenides held the views they did. This arises from the problem of identity and change, which is the problem that one thing logically cannot change with time and remain one (identical).

Although this contradicts common sense, the logic of it is quite simple: it arises from the fact that qualitative change entails quantitative change. This can be proved quite easily: whatever A and B might be, if there is a qualitative difference between them then there is some quality, Q, such that A is Q and B is not-Q (or vice versa); so if A and B are one then one thing is at once Q and not-Q, which is impossible; hence A and B must be two, they cannot be one. In particular, one thing cannot travel through time and change as it goes: either it remains one, in which case it cannot change, or else it changes and loses its oneness, its identity.

Heraclitus took the position that only change is real, there is no identity. ‘You cannot step into the same river twice’ he said; because the river, having changed, is a new river, and you, having changed, are a new you. ‘Nothing is permanent except the fact of change’ is another of his sayings. Change is real, identity is illusion. And Parmenides took the opposite position: ‘All change is illusion, only the One [identity] is.’

Plato tried to resolve this problem by saying that there are two worlds. There is the ‘real’ world of the Forms, which are perfect and unchanging, and the sensible world that we all perceive around us, which is an imperfect copy of the world of forms, and insofar as the copy is imperfect so is it illusory. Included in among these illusions are the appearances of change, as well as familiar illusions such as visible space shrinking with distance, in all three dimensions.

If we now fast track to modern times, we still have two worlds: the sensible world we perceive around us, which is called the empirical world and which is the object of study of empirical science, and the world of theoretical science, which physicists describe as the world of underlying causes of empirical phenomena and which is is imperceptible, or non-empirical (which is what ‘theoretical’ and ‘underlying’ mean). (To describe causes is to explain their effects, so theoretical science explains what empirical science describes.) The empirical world is an imperfect copy of the theoretical world, and insofar as it is imperfect so is it illusory. Thus visible space shrinks with distance and all secondary qualities (i.e. sensations) are illusory, but the sense data that yield scientific laws are not. Particularly noteworthy is one similarity between theoretical science and ancient Greek philosophy: Einstein’s space-time is surprisingly similar to Parmenides’ One: if time is a dimension within space-time then there is no passage of time and our sensation of such passage is illusory.

The original problem is not yet solved, of course. In particular, to claim that something is an illusion requires that the fact of the illusion be explained, and the illusion of passage of time is so far inexplicable. However there is a lesson to be learned from all this. It is the problem of how much truth there is in common sense. English language philosophy has always preferred common sense to logical argument. John Locke, for example, worked out his philosophy very logically but always retreated when he got too far from common sense, and A. J. Ayer repeatedly said that any argument that went too far from common sense must be wrong. And one cannot help sympathise: common sense is the cumulative practical experience of centuries of living in a hostile world, and therefore only to be gainsaid reluctantly. On the other hand, if Ayer is right then Einstein’s theories of relativity, all of quantum mechanics. and all of modern mathematics must be wrong.