In perhaps Plato’s most unusual, and certainly his most technical, dialogue, he presents a scene in which Parmenides, the great philosopher from Elea in Italy, visits Athens in company with his famous disciple, Zeno at the time of the Great Panathenaea Festival. Plato offers an elaborate account of how the story was preserved by Antiphon, who was Plato’s half-brother, introduced to the narrator by Plato’s brothers Glaucon and Adeimantus.[6] In the story, Parmenides is about 65 years of age, Zeno about 40, and Socrates quite young (no age is given).[7] The visitors from Elea are staying at the house of Pythodorus, who years later reported the conversation to Antiphon. However elaborate the stage-setting, the meeting of minds is fictional. Plato has a problem to discuss, and he needs to bring out the big guns of Elea to make his point.
In the dialogue, Socrates has just heard Zeno read from his book the arguments designed to refute pluralistic philosophies that opposed the views of his mentor Parmenides. The young Socrates observes that whereas Zeno’s mentor Parmenides had argued that everything is One (the thesis philosophers call Monism), Zeno had supported him by arguing that the Many things are both like and unlike, which is impossible; so they do not exist (a refutation of the thesis of Pluralism). Zeno grants Socrates’ point, but provides some historical context: he used this tactic to reply to those who had criticized Parmenides’ position. He was showing to the pluralists that their pluralistic theses were no less problematic than the monism of Parmenides. Furthermore, he wrote the book as a young man eager to advance his views, not as an established expert.[8]
Socrates now offers his own theory: there is a Form of Likeness and another Form of Unlikeness. The Many things can participate of both Forms at the same time, so that, for instance object a is like object b but unlike object c, without contradiction. The Forms themselves can never partake of each other, but sensible objects can partake of both. Similarly, one person can be at the same time one (person) and many (bodily parts), without contradiction.[9]
Pythodorus was worried that the visitors from Elea would be offended by Socrates’ arguments. But, to the contrary, they seemed impressed by his precocious intellect. Parmenides asked him if he had developed his theory of Forms himself. Socrates admitted he had. (At this point the character Socrates is representing not the historical figure, but Plato’s alter ego, since the Theory of Forms is Plato’s invention.) Do you believe in a Form of Likeness? he asks. Yes. “And are there others such as a Form of Justice itself by itself, and of Beauty, and Goodness, and the like?” Yes. How about a Form of Man and of Fire and Water? Socrates is not so sure. How about disgusting things like hair and mud and dirt? Is there a Form of each of these? Surely not; they are just what we see.[10]
Here Parmenides presents with full force what we may call the Population Problem: of just what sorts of properties and kinds are there Platonic Forms? For virtues and ideals, young Socrates gives his full endorsement. For biological species and physical objects, he is in a quandary. For base matter, he has only contempt, and will not consider assigning Forms. At the time of the writing of the present dialogue, Plato’s Forms have been under discussion for perhaps twenty years. Yet never has Plato given his readers a definitive answer to the Population Problem. Here we are, to be sure, dealing with a very young “Socrates,” who has evidently not worked out all the details or the ramifications of his glorious new theory. So he is not in a position to announce Plato’s present commitments on the topic. But he does address an ongoing problem for Plato’s theory.
In the event, Parmenides himself cuts the young man some slack. “You are still young, Socrates,” Parmenides says, “and philosophy has not yet taken hold of you, as, I believe, it someday will; then you won’t despise any of these objects. Now, however, because of your youth you are worried about other people’s opinions.”[11] Parmenides suggests that the young Socrates will be less fastidious about the Forms when he is more mature. What seems to matter is that all general features or properties will be explained in the very same way, by the existence of Forms in which sensible objects participate. Parmenides, in fact, show himself to be more optimistic about the Forms than the young Socrates.
[6] Plato Parmenides 126a-127a. For Plato’s family connections, see Nails 2002, s.v. Plato.
[7] Plato Parmenides 127b-c.
[8] Plato Parmenides 127d-128e.
[9] Plato Parmenides 128e-130a.
[10] Plato Parmenides 130b-d.
[11] Plato Parmenides 130e.