My Response to the “Third Man” Argument

***I will leave this up, but there is a much better and more scholarly response on this issue above. If you only have time to read one, I’d recommend that one***

 

Hey guys, so I don’t know if I mentioned this, but I am studying in Scotland for a semester. I must say, the philosophy department here is very different from the one at my school, but I like the fact that I am getting a completely different perspective on pretty much everything. At any rate, this came up in one of the lectures, so I am going to try to give a response to it.

The Argument

This is taken from Plato’s Parmenides. The point is that there seems to be an infinite regression when talking about Forms. Let’s take the sum total of all large things (we are going to look at the ‘Form of Largeness’). Let’s call this set F. So, set contains all large things in the Universe. Now, a Platonist would say that these are instantiations of the ‘Form of Largeness.’ The problem seems to be that the ‘Form of Largeness’ is large, too, so the argument says that it should be grouped with large things as well and that there should be a now Form to describe this second set, say ‘Form of Largeness 1,’ which would in turns also be large and so on and so forth ad infinitum. If this argument is correct, then Plato’s Metaphysics becomes so cluttered that it is a better choice to have no Metaphysics than to uphold this belief.

My Response

It is worthy of note that this argument appears in the Platonic corpus. Philosophers are divided in what it means, i.e. is it there as the issue Plato cannot solve and is left up to future generations to figure out, is it something that Plato did solve and is leaving as an exercise for his students, or is it Plato’s ‘good bye’ to the theory of the Forms? I think it is the second one. However, I think that most people who are committed Platonists are not advanced enough to answer this question the same way as Plato would have answered it. For myself, I am going to cheat and use in the response tools which Plato would not have available to him (i.e. proper descriptions, etc, early 20th century stuff), as to how he would have answered it, I have no clue, but I hope I can reach that level at some point in my life. Alright, the response proper:

Let’s first define our terms clearly so that we may not be confused about what we are talking about. First, our set, let’s call this F(x). This is the set of all things in the Universe which are large. Second, ‘the Form of Largeness.’ This is the Form by which all things that are large are instantiated by in respect to their largeness.

Now, speaking in proper descriptions, all the members of F(x) are things or beings which have the quality of being large. That is to say, they are all the things in which the ‘Form of Largeness’ has instantiated. However, the ‘Form of Largeness’ does not have the quality of being large, it is large in that it is that which both gives large things that quality and the principle of discrimination by which large things are recognized as such. But, surely, the principle of discrimination and the products which are discovered through it cannot fit in the same set. Therefore, it is preposterous to say that the ‘Form of Largeness’ and large things can ever fit into the same set.

Now, a point about the ‘Form of Largeness.’ I presented the argument with using that example because it was the way it was presented to me. However, the reason why I put it in quotations is because I do not think Plato would affirm a ‘Form of Largeness.’ If (as the professor who presented it to me asserts) Plato were to say that every plurality you can think of corresponds to a Form, then there would be things like the ‘Form of the chair.’ However, both Plato and Aristotle are very clear in pointing out that a chair does not have objective ‘Form,’ in that it is not a chair in itself, but wood, or steel, or plastic, or whatever. So, it is not that every plurality corresponds to a Form, but rather those things which are found in nature.

In addition, specifically about largeness, it is not even an objective quality. Things are large in relation to other things. The same thing can be large in comparison to a thing much smaller than it, but not large in comparison to a thing much bigger than it. If largeness were a static/objective/innate quality, then that would mean that the Law of Non-Contradiction would be broken. In addition, you can quite easily imagine in your head a scenario where one thing is larger than the other but smaller than the third. Take for example a cot (presumably you slept there when you were a baby) and your twin size bed, which say you had when you were a teenager, and the queen size bed you sleep in now. The twin bed is ‘large’ when compared to the cot, but it is not ‘large’ when compared to the queen size you have now. However, try to imagine a ’round square’ for example, no matter how much you try, you cannot, because that utterance breaks the Law of Non-Contradiction and you mind is wired to work logically, so try as you might, you cannot imagine a proper round square. His reason for choosing to use the ‘Form of Largeness” may have been to make the issue easier to understand, but it actually makes it harder. Let’s change the scenario from largeness to Justice. Is the Form of Justice just? Well, it’s the criterion of Justice, so I do not know by what criterion you would judge that, because that’s the criterion itself.

At any rate, that’s my stab at it, but I think it does offer a good argument against what some people see as the knock ’em down, drag ’em out argument against Platonism (which I guess Plato was so stupid he put in his own work).

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9 comments on “My Response to the “Third Man” Argument

  1. sammysfood says:

    What do you mean by the principle of discrimination? I’m studying this topic now, and I’m not sure what you mean by that. Great article!

    • A principle of discrimination is a standard by which you decide what is what (a sort of definition), for example, the principle of discrimination regarding males is that they have male genetalia. Basically, what distinguishes this thing from everything else.

    • If you wait a little bit, I need to clear with my study-abroad university that I can publish a paper I wrote for them in my blog, if so, that gives a more detailed and a more thorough examination/solution to the third man argument.

      • sammysfood says:

        That sounds great, I have an exam tomorrow and I found your article as I was scanning the web for different viewpoints – it’s nice to see something more original – the same conclusions about this argument get a little tedious after a while…

      • Glad I could help, I can’t really put the essay up on my blog, but if you want to send en email over to modernplatonist@yahoo.com I could send it to you, on condition that you do not plagiarize, of course.

  2. sammysfood says:

    Thank you very much, but I think I already have too many ideas in my head now 🙂 It’s cruel that you only have two hours to write about such broad topics! It’s kind of you to offer. 🙂

  3. Dr. Günter Bechly says:

    The rejection of self-predication as solution of the Third Man argument was a common strategy by several modern defenders of Platonism. However, this paper suggest that this apparent solution is not feasible, but that there may be another solution: http://faculty.fordham.edu/bfrances/parmenides.pdf

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