HoPwaG: Plato IX (Parmenides)

Question of whether the Parmenides reaffirms or refines Plato's doctrines (and questions about the chronology of the dialogues).

Starts with Zeno reading his paradoxical arguments. Recall, the point of the paradoxes is to affirm the Eleatics' doctrines.

Socrates rejects Eleatic doctrines: things are one and many. But that doesn't mean there's no oneness and manifoldness: the Forms, e.g., since they don't feature compresence of opposites, are oneness.

Socrates posits Forms to explain why things are similar--explain presence of shared characters in some things: they explain both why things are similar and dissimilar.

Parmenides poses problems for the theory of Forms, which Socrates is unable to resolve.

The problems:

1. Which things have Forms?

• Socrates says there are Forms of goodness, beauty, largeness, etc. Is there also a Form of man? Of every animal? Of hair, dirt? Man-made things?
• This a serious problem. If there are Forms, how are we to know what they are? Sometimes Plato seems to suggest there are Forms of man-made things, but in the Parmenides   

2. What is it to share in or partaking in a Form?

•  E.g. does each large thing have a piece of the Form of largeness? Then each part of the Form of largeness would be small by comparison with the Form as a whole.
• Or, e.g., is the whole Form of largeness present in each large thing? Then the Form would be separate from itself (the largeness of the giraffe is spatially distinct from the largeness of the Eiffel Tower).
• Socrates' reply: Metaphor of the same day being present in different places.

3. The Third Man argument

• Recall Socrates posits a Form to explain similarity. Eg: there are several large things, so the Form of largeness is posited to explain their similarity.
• But if the Form of largeness is itself large, then there are {large things, Form of largeness}, so we need another Form to explain their similarity. 
• To explain largeness, we need to posit an infinite number of Forms.
• Reply option 1: 'So what?' What contradiction follows from the need for an infinite number of Forms (e.g. they are immaterial!)
• Problem: the idea was that one thing was to explain the similarity of many things. It spoils that aim to have to have not just one, but an infinity, of Forms before we can explain the similarity of all large things. [In fact, it doesn't really advance the explanation at all.]
• Reply option 2: Deny that the Form of largeness is large. But this awkward. Recall: the Form of largeness was not supposed to be small: it was supposed to differ from physical things that feature compresence of opposites. If he also denied that the Form was large, the Form would be neither large nor small. Also, recall the self-exemplification thesis from before. And also, physical things are supposed to be large by virtue of resembling or partaking in the Form. If we're now saying that the Form itself isn't large, then how do they resemble it? [That last problem seems to me fatal for this reply option.]
• But there also seems to be good reason to deny that the Form of largeness is large. Forms are immaterial; immaterial things can't be large; so, the Form of largeness can't be large. [This seems disastrous.]
• Reply option 3 (Socrates): Forms are not "separately existing objects". Rather, they are thoughts. Not clear how this solves problem, but as thought, Form wouldn't be large, so wouldn't get infinite regress.
• Objection: Thoughts have referents. The referent of the Form-thought would be outside our mind and subject to the argument. 
• Even if they're "paradigms that exist in nature", which other things resemble, they're independent of us, etc., and subject to the Third Man argument. And also...

4. Third Man argument, redux

• The Form of largeness is invoked to explain why large things are similar to each other: large things are similar to the Form of largeness. But then we have: {similarity of large things to Form of largeness, similarity of Form of largeness to itself, similarity of Form of similarity to itself}. So we need another Form of similarity to explain the similarity that these things partake in. Again, an infinite regress.
• This time the infinite series of Forms are Forms of similarity, not largeness.[Not clear why that's worse than the first Third Man argument?]

5. Impotence of Forms

• If Forms are separate [from us?], they can relate to each other but not to us ('mastery' example supposed to show this: the master is master of the slave; the Form of mastery doesn't master the slave).
• The upshot: two disconnected realms--the Forms and what is supposed to participate in them.
• If nothing in our world can relate to the Forms, then there are no relations between physical world and Forms; knowledge is a relation; so we can't have knowledge of Forms. But they were supposed to be the objects of knowledge.

Question of what the upshot of this is. Is there a reply available on behalf of the theory? Suggestion that the sequence of questions is a list of desiderata for the theory of Forms: we want an account of which ones there are, how they can be different enough from physical things to explain their similarity, but not so different that they are radically disconnected from physical things (and so unable to explain their similarity).