Third man argument

The Third Man Argument (commonly referred to as TMA), first offered by Plato in his dialogue Parmenides, is a possible philosophical criticism of Plato's own Theory of Forms. In Parmenides Plato uses the example of the form of Largeness to demonstrate TMA. Aristotle also discusses TMA and uses the example of man, thereby creating the name "Third man argument." The Parmenides dialogue, thought to be written by an elderly Plato, consists of a conversation between a young Socrates and the Eleatic and monist Zeno of Elea and Parmenides. The Eleatists offer various criticisms of the theory of forms, including the TMA given by Parmenides. The Third Man Argument states that there is a problem with the theory of forms because of the following:

We take a group of things with a common characteristic such as largeness and group them together and place them under the characteristic (here largeness). Largeness itself can be said to contain the largeness characteristic, so it can be placed in the original set as well. Now the set must be grouped under another form, a second largeness (largeness2). Largeness2 also contains the characteristic of largeness, so it may be placed in the set as well. The process of creating new largenesses goes on ad infinitum. Any reliance on infinite categorization reduces the relevance of the theory of forms.

Premises

TMA seems to include the following assumed premises:

1. One-Over-Many Principle, TMA assumes that to define a set of large things, a uniting characteristic must be defined. So, largeness must be created to have a set of large things.
2. Principle of Non-Self Explanation (non-identity), we cannot use largeness to explain largeness itself, so there must be a largeness2.
3. The Principle of Self-Partaking (self-predication), largeness must be included in the set of large things. Largeness has its own characteristic, largeness.

Interpretation

Some have seen Parmenides as a retraction of the Theory of Forms by Plato. The dating of the dialogue Timaeus is crucial to the debate since it relies on the Theory of Forms. If Timaeus was written after Parmenides, Plato may not have rejected the theory of forms. However, Plato's last work, Laws, omits the Theory of Forms, perhaps suggesting he no longer believed his original arguments. Aristotle discussed TMA and concluded that the Theory of Forms was weak. He suggests Plato believed the same. Others have seen Parmenides as a debate, but not one that Plato feels is conclusive. Plato's exact intention of the dialogue has been lost to history.

Modern scholars have debated the soundness of the argument. Among these philosophers, G. Vlastos argued that TMA fell to an ontological regress. Others have challenged the validity of TMA's premises as they are not explicitly stated in Plato's text.