Plato's Parmenides is a dialogue-form treatise in metaphysics. This dialogue, written about 350 B.C., concerns Plato's most famous theory, that of the Forms. Forms are spiritual entities outside of space and time, and serve as the true and only source of stable knowledge. This dialogue is about Plato criticizing his own theory. Later writers such as Aristotle and Abelard of Paris will use this dialogue to build their own criticism of what is called "metaphysical Realism."
The Parmenides is comprehensible only when you grasp the idea of the Form. The Form is Reality at its highest. It is pure being, pure actuality. The objects of space and time are not forms of knowledge, but only opinion. Only the purified intellect can reach this Form, and reaching it is the sole goal of the philosophical life. The philosopher sees Forms as manifested in particular objects in nature. From the object, his mind can ascend to that which truly represents the object without the distractions of matter. This is Form.
Criticism of the Forms
This dialogue is really about Plato's self-criticism. He has doubts about the Forms. These criticisms revolve around the very nature of a Form, and how such a rarefied entity can ever serve as an object of knowledge.
An important criticism made by Parmenides, the main character in the dialogue, asks the question how a Form can be "in" a particular object. How can an object serve to manifest a form? Is part of the Form in the object? The whole thing? If the whole, then is the Form only in one object? The point is that the nature of a Form is immaterial, but is partially explicated in a particular object found in nature. The "mixing" of these two objects seems to present a difficult problem. Ultimately, the Forms are problematic because they are not actual things. Yet, according to Plato, they have properties. If they do, then they seem to be just one --- albeit unique --- object among others, and hence cannot perform the functions Plato wants them to.
The most famed criticism of the Forms is the idea that the Form should manifest its own qualities. There is a form "large" that can be found "in" all large objects. Is that Form itself large? If not, how could the Form of large not be large? If it is large, then how is it any different from any other particular object? The "Third Man" argument is really about the concept of an "infinite regress." If the Form of large is large, then what is it that makes the Form large? There must be another entity that does this, and so on, to infinity.
Parmenides does not want the theory to disappear. He holds that without Form, knowledge is impossible. Therefore he --- to oversimplify --- proposes that Forms should only deal with specific quantitative things such as relation, time, motion and rest. If Forms remain as mathematical entities, then many of the criticisms would no longer work.
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