The objections of the selection from Parmenides

I. The theory cannot provide a universal account of meaning and understanding

1. If everything has ideas, then all sorts of vile and undignified things should also have ideas.

2. But the consequent is unacceptable, thus not everything has ideas.

3. Therefore, the theory cannot function as a universal theory of meaning and understanding

II. The theory cannot provide the ontological principles it claims it does

1. Whatever participates in an idea must receive either the whole or only a part of it.

2. If the whole, then the whole will be in separate things, and thus the same one whole will be separated from itself, which is absurd.

3. If the part, then the part received is smaller than the whole.

4. Therefore, what is received from the Large, or from the Equal or from the Small, will be smaller than any of these, and thus what is received cannot make the recipients large, small or equal, which is absurd.

This conclusion undermines the theory’s claim that things of a given kind belong to that kind in virtue of sharing in the idea perfectly exemplifying that kind.

III. The "Third Man"

1. All large things are large in virtue of participating in Largeness.

2. Largeness is large, since any idea is the perfect exemplification of its kind.

3. Thus, Largeness participates in Largeness.

4. But nothing participates in itself, for what participates is inferior to what it participates in, and nothing is inferior to itself.

Thus, Largeness, participates in another Largeness, call it Largeness₂, as opposed to the first, which we shall call Largeness₁, that is to say,

5. Largeness₁ participates in Largeness₂

6. But Largeness₂ is also large.

7. Thus it also participates in Largeness, but not in Largeness₂ because of 4.

8. It cannot participate in Largeness₁ either, because according to 5. Largeness₁ participates in Largeness_2, but

9. Nothing participates in anything that participates in it, since then, again, the same thing would be inferior to itself. (Because, if A participates in B and B participates in A, then A is inferior to B, and B is inferior to A, and so, by the transitivity of inferiority, A is inferior to A, which is impossible.)

10. Thus, Largeness₂ participates in Largeness₃.

The same sort of reasoning can be repeated for any Largeness_n, therefore,

11. There is an infinity of Largenesses

12. But according to the theory of ideas, there is only one Largeness.

Since 11 and 12 conclude to an explicit contradiction derived from statements of the theory of ideas, the theory as it stands cannot be true.

IV. Refutation of an alternative theory:

1. Ideas are thoughts

2. Then an idea must be the thought of something

3. That something, call it the object of the idea, is "one single character" observed by the mind in all particulars sharing in the idea, entering the constitution of these particulars

4. But then, being such "one single character" of all the particulars, that object is an idea itself.

5. Thus the object of the idea is an idea, and hence, by 1.

6. The object of the idea is a thought

But since, according to 3, the object of the idea enters the constitution of the particulars,

7. Particulars are constituted of thoughts, and so

8. Everything in the visible world is just a collection of thoughts, which is absurd.

Thus the modified theory, since it leads to another absurdity, offers no way out.

V. Refutation of another alternative theory:

1. Ideas are "patterns", common likenesses of whatever shares in them

2. If so, then an idea and one of its particulars will have a common similarity (as is the case with all similar things)

3. But then, both the idea and the particular share in a common character, which, by 1. is again an idea.

And so the same infinity of ideas crops up as in III, which contradicts the theory’s postulate concerning the uniqueness of ideas.

VI. Ideas are unknowable

1. Ideas belong to a different world, not ours

2. Relative ideas are related to one another (because, for instance, a human master is not a master of the idea of the Slave, but only of other human slaves, and the same goes for all relative ideas)

3. Therefore, no idea is related to anything in this world

4. Thus, all ideas are related to Knowledge

5. But no idea is related to our knowledge, which is not Knowledge

6. Thus, our knowledge is not the knowledge of any idea, that is to say,

7. We have no knowledge of ideas.

VII. The gods know nothing about us and they are not our masters

1. Relative ideas are related to one another

2. The gods possess the ideas

3. By Knowledge and Mastership they can be related only to ideas

4. Therefore, by these they cannot be related to us, and so

5. The gods know nothing about us and they are not our masters, which is absurd