A Response to Plato\'s Parmenides

Rayyane Shukr
PHIL 213
Prof.Raymond Brassier
Sunday, October 18, 2015
Plato's Parmenides: A Response to the Third Man Argument
Being the most challenging of Plato's dialogues, the Parmenides raised important metaphysical and epistemological questions about the theory of Forms. It is one of the most brilliant dialogues because it entertains the possibility that Plato's most fundamental beliefs may be wrong. Socrates, who tried to defend the theory of forms, was being attacked by Parmenides and Zeno. Socrates claimed that particulars share a certain "likeness" or "resemblance" with a higher character, i.e. "resembled"(Ancient Philosophy, 199). One criticism against the theory of Forms, also known as the Third Man argument, is that it causes infinite regress of likenesses when trying to explain participation in terms of resemblance. A question then arises: is the Theory of Forms trying to explain what things are? Or, is it trying to explain how there is a resemblance between the "Form" and the "particular"? Answering these questions would help in giving a better response to this theory avoiding false assumptions.
In order to have an objective view about the Third Man Argument, let's first define what the "Theory of Forms" is. Going back to Plato's cave in The Republic, the shadows were only an "appearance" to what the reality was. When the prisoner was released outside the cave, he was able to see how real things were. He moved from the state of an "opinion" to a state of "knowledge". The light that was found outside the cave gave the prisoner an idea about how real light is. So, there must be a Form of "Light" that explains how a particular light should be. That being said, Forms explain what things are, and not how there is a resemblance between them and the particulars. Similar things don't share a certain "likeness" but a Form. For example, two large things share the same Form "Largeness". This Form explains how things should be so they could be classified as "large". This doesn't mean that both of the large things are similar; instead, they both participate in the Form "Largeness". Another example would be any two animals. The Form "Animal" explains why these two animals are so called "animals", which is not similar to saying that these animals is like the "Animal"; however, these animals share the same form of an "Animal". The latter explains why both of these animals are classified as such but the former explains how the animals possess likeness.
After defining what the "Theory of Forms" is, it follows to explain what the "Third Man Argument" claims, and how does it attempt to explain participation in terms of resemblance. The Third Man Argument is one of the strongest criticisms against Plato's Theory of Forms. The first version of the argument states that if large things like A,B,C, and D, share Largeness " L", then "L" must be like A,B, C, and D. Then, if "L" is like these particulars, it follows that there is a third character which is "likeness" in which "L" shares with A, B, C, and D. The second version of this argument asserts that if the instances A, B, C, and D, which are called the "resembling", share in "L" i.e." resembled", then there would be an infinite regress of likenesses since a third character " likeness" would appear in order to explain the resemblance between the instances and the Form. The problem here is that Parmenides misrepresented the Theory of Forms, he asked Socrates" do you think, as you say, that there are certain characters, of which these others here have a share and get their names? As, for example, things that get a share of likeness become like, of largeness large, of beauty and justice beautiful and just?"(200). Parmenides was trying to explain participation in terms of resemblance but little did he know that he is misrepresenting Plato's theory, for he later states " when some plurality of things seems to you to be large, there perhaps seems to be some one characteristic that is the same when you look over them all" (201), meaning that it is necessary for the particulars to share a certain resemblance. As explained before, the Theory of Forms explains what things are and not how things participate in terms of resemblance. By confirming to the argument presented, the participants (A, B, C, and D) resemble the Form "Largeness" with an addition to a third character "Likeness" that explains this resemblance. Also, another character "likeness 1" should be introduced between "Likeness" and the participants. Moreover, "likeness 2" should be also introduced between "Likeness" and the Form "Largeness". So, what allows the participants to be like "Largeness" is not largeness, but something else. If this sequence continues, then one has to specify how the participants are like the Form by introducing characters, as Parmenides stated " So another character of largeness will have made its appearance, alongside largeness itself and the things which have a share of it; and over and above all those, again, a different one, by which they will all be large. And then each of the characters will no longer be one for you, but unlimited in multitude" (202). It is not only Parmenides' fault in misrepresenting the argument, but Socrates' too. When Parmenides asked" then if something resembles the character, he said, is it possible for that character not to be like what has come to resemble it, just insofar as it has been made like it?"(202), Socrates then confirmed to what Parmenides stated. By confirming, Socrates is allowing Parmenides to continue with his false reasoning which led to the" infinite regress", this is not very surprising since Socrates was a young man in the dialogue.
Parmenides' criticism to Plato's Theory of Forms results in many consequences. As previously explained, an infinite regress of "likenesses" will result, meaning that if we want to explain participation in terms of likeness, we have to postulate many things. We will have to specify how something is like something and the chain will never end. Instead of unifying the Forms, we would be making things more complex by introducing the unintelligible to the intelligibility. This will prevent us from explaining the difference between the sensible and the intelligible. So, in order for the "Third Man Argument" to win, the Forms should have the same property of their participants. The Form "Largeness" should share the same property as "A, B, C, and D". If the Form "Largeness" is different from the particulars, then the argument would fail because there would be no cause for the infinite regress.
The "Third Man Argument" presents a Straw Man fallacy in which the Theory of Forms is misrepresented. There is a problem in the DEFINITION of the theory of Forms and not in what the theory states. Parmenides moved from an unwarranted assumption that there's a resemblance between the instances and the Form; however, this is not what the theory claims. It clearly explains how things should be. The Form "Color" is different from "red". The Form will help us know how things are classified to have a color "red" but it is not red. Another example, the genus "Antigonia" for the species "fish". The genus will tell us what things are classified to be as "fish" but it is not "fish" itself. However, saying that the genus is the same as the species is a different story, and clearly illogical. This is what caused the infinite regress to occur, as Parmenides stated" another character will always make its appearance alongside the character, and should that be like something, a different one again, and continual generation of a new character will never stop, if the character becomes like what has a share of itself" ( 202). One reason why this infinite regress happens is probably because the Form has almost the same initials as the instances. For example, the Form "Whiteness" has the same initials as the instance "white", causing a false argument that "Whiteness" is like "white". The Form "Whiteness" is the cause for "white" to be as such and not its resemblance. Also, if someone wants to agree with the "Third Man Argument", this person is agreeing with the "infinite regress"; however, he/she is not proving the inexistence of forms. If the "Third Man Argument" is trying to disprove the existence of forms, then it will also fail because the form "Beauty", "Largeness"," Justice", and "Color" still exist.
To conclude, Plato's "Theory of Forms" explains what things are. Stating that it explains how the instances resemble the Form would be a misrepresentation, and would cause an infinite regress. Parmenides' "Third Man Argument" is incoherent and presents a logical fallacy because of its false definition of Plato's theory. This argument should be reconstructed in a way that portrays to the reader the real definition of Plato's theory. Isn't that the main principle of argumentation? To understand what the opponent is saying and then form a thesis opposing it? The "Third Man Argument" should be re-named as "Parmenides' Theory of Forms".









Works Cited
"Parmenides." Ancient Philosophy: Essential Readings with Commentary. Ed. Nicholas Smith, Fritz Allhoff, and Anand Jayprakash. 4th ed. Vol. 1. Malden, Massachusetts: Blackwell, 2008. 445. Print.