Plato (ca. 427 - 347 BC)
In the Parmenides, Plato, represented by Socrates, thinks that objects can be at once both one and many. He thinks this because an object can be shown to partake of oneness when it is shown to be a single entity out of multiple separate entities, and an object can be shown to partake of multitude when it is shown to be comprised of several parts. Socrates tells Zeno that he would be amazed if someone were to distinguish opposite forms (i.e., oneness and multitude) as separate things, and then show that in themselves the forms can mix together and separate.
Parmenides gets Socrates to agree that things partake of forms by being likened to them, and that things cannot be dissimilar to things they are like. This poses a problem because it means that if something were shown to be both one and many, then it has oneness and multitude, so it is similar to both oneness and to multitude, so the thing and its two forms are all similar, so the thing is both forms themselves, so both forms are the same.
Plato thinks (and has Socrates and Parmenides agree) that someone who won’t allow that there are forms will “destroy the power of discourse” because “he won’t have a direction for his thought, since he doesn’t allow that for each thing there is a character that is always the same”. Parmenides argues that there are difficulties and objections involved in trying to make sense of the forms, so people argue that the forms “do not exist, and that, even if they do, they must by strict necessity be unknowable to human nature”.
Parmenides thinks that a form is separate from itself if everything that partakes of a form partakes of it as a whole because the form is separate from the things that partake of it.
This is not a good argument against the forms because Parmenides is thinking of a form as if it were an object of finite size instead of as a property. He seems to think that when several things share the same property, they can somehow use it up and take it away from itself. This is why using the phrase “to get a share of” instead of “to partake of” can be misleading, because “to get a share of” gives the impression that when a thing gets a share of a form, part of the form is lost to the thing, causing the parts of the form to separate.
Parmenides is right to say that Socrates’ example of the day is like his own example of the sail because they both cover many parts at once and part of each covers different places and different things. Those things exist during the day and under the sail, all at once, without the day or the sail having to be divided so that the things can fall under them.
In the dialogue, Parmenides presents the argument that objects partaking of a form have sameness, which makes the observer conclude that the form is one thing. When the observer thinks of the form and the things that partake of the form, the mind’s eye views them all as sharing a form that is different from the first form. Objects partaking of the form largeness and largeness itself partake of a form labeled the “third large.” Each time one thinks of what is common to a form and things that partake of it, a separate, different form is conceived of in the mind. The “fourth large” would be partaken of by the “third large,” largeness itself, and large things, and so on.
Parmenides says, “There is for each thing some being, itself by itself… to begin with” and “the forms are what they are of themselves and in relation to themselves”, which is to say that forms do not originate in the things that partake of the forms. This could provide an escape from the “third large” argument, but another problem is encountered when Parmenides says this argument means we cannot possess the forms themselves, so we cannot possess knowledge itself, but if anything partakes of knowledge itself, it is a god that does so. This is a problem because it contradicts Parmenides’ and Socrates’ earlier agreement that “the forms are what they are of themselves and in relation to themselves”.
Considering the forms thoughts would not help escape the argument. Socrates says, “[E]ach of the forms is a thought of the many… and properly occurs only in minds”. Socrates thinks that the mind recognizes a form when it observes many things partaking of it, and that to partake of a form is to be likened to it. Parmenides says that if Socrates is correct and a thing and a form resemble each other, and if “that which is like… partake[s] of the same one thing as what is like it”, “and if like things are like by partaking of something”, then that something is the form itself. Parmenides ends this argument by concluding that the thing and the form cannot be alike, otherwise “a fresh form will never cease emerging”, so this argument fails to refute the “third large” argument.
I believe that Platonic forms can be salvaged. Considering the forms thoughts comes close to refuting the “third large” argument, but a different approach must be taken. I think it is true that “each of the forms is a thought of the many… and properly occurs only in minds”, but I disagree that to partake of a form is to be likened to it. I think things are what they are in and of themselves, but I think forms are dependent on the things that partake of them.
Each form is a positive or negative value of a dimension, and thus each form has an opposite. For example, large and small are positive and negative values of size, and beauty and ugliness are positive and negative values of aesthetics. Thus, when a thing partakes of a form, it does not get a share of one form or the other; rather, a thing’s size or beauty is relative. It depends on what other thing – something bigger, smaller, more beautiful, or more ugly – it is being compared to.
This conflicts with superexemplification because it rejects the proposal that a form is the thought of a perfect example, which is to say, using my examples, that there is something of ultimate size or beauty, of which everything else large or small or beautiful or ugly is a thought.
If we imagine something with a size, and that size were greater than the size of the smallest conceivable thing and smaller than the size of the largest conceivable thing, this would present no problem because everything besides those two things fits that description. But this is distinct from claiming that the universe is largeness itself, or a subatomic particle is smallness itself. Size is relative. It is possible to conceive of something larger than the universe, and it is possible to conceive of something smaller than a subatomic particle. Every description we can attach to something only exists relative to its opposite.
Originally Written in October or November 2007 as a college essay
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