Plato’s Theory of Forms

1. Whenever several things are F, there is a single form of F-ness in which they all participate. (That is to say, all these things are F in virtue of sharing in the characteristics of the form of F-ness.)
2. The form of F-ness is perfectly F.
3. The form of F-ness does not participate in itself. (Because whatever participates in something is inferior to that thing, and nothing is inferior to itself).
4. The form of F-ness has all and only those characteristics which all the things that participate in it (the particulars of the form) have in common, in virtue of being F.

Problems

1. Generality

If this is supposed to be a theory applying to all possible substitutions of F, then we would have to accept the existence of the Forms of perfect Dirt, perfect Stink, etc.

2. The “Third Man”

Several individuals are men. Therefore, there is a form of Man in which they all participate. The form of Man is a man (indeed, the Perfect Man). So all individual men plus the form of Man taken together are all men. So there is a single form in which they all participate. This new form cannot be the form of Man, for then it would have to participate in itself which is impossible, so this has to be a Third Man (besides the singular men and their form). But we can repeat the same reasoning for this Third Man as well, so there would have to be a Fourth, a Fifth, Sixth, etc. to infinity. So for a set of individuals there would have to be an infinity of Forms. But the Theory also states that there is only a single Form for any set of individuals. So the theory is inconsistent, whence it cannot be true.

3. Inconsistency of Characteristics

The perfect Form of F-ness has to have all and only those characteristics, which are common to all its particulars. But all these particulars are necessarily either G or not G. (Say, any triangle must be either isosceles or scalene.) So the Form also has to be G or not G. (Say the Form of triangle must be either isosceles or scalene.) But since not all particulars are G, the Form cannot be G. (Since not all triangles are isosceles, the Form of triangle cannot be isosceles.) And since not all particulars are not G, the Form cannot be not G either. (Since not all triangles are scalene, the Form of triangle cannot be scalene either.) So the Form has to be either G or not G and yet it cannot be G and it cannot be not G. (The Form of triangle has to be either isosceles or scalene, but it cannot isosceles and it cannot be scalene either.) But this is impossible, so the theory cannot be true as stated.