The Third Man Argument: A Defense of the Forms

In his dialogue Parmenides, Plato calls into question his own Theory of Forms. The theory describes the sensible world, the one that we experience and exist in as an imperfect reflection of a perfect world; that is, the world of Forms. Each sensible object is an imperfect reflection of a perfect, unchanging Form. The dialogue depicts a young Socrates and two older philosophers: Parmenides and Zeno. The trio works out the logical limitations of the theory of Forms.

One key argument made against the theory of Forms is the TMA. On the basis of three assumptions, the TMA generates infinite regress for the Forms. It first assumes that for any set of things with a common trait, there is a Form of that trait which the set participates in: one-over-many. Additionally, a Form ascribes to the trait which it is associated with the common trait of all its participants: self-predication. Finally, no Form is identical to any of its participants: non- identity. I begin by reconstructing the Third Man Argument:

Suppose that x, y, and z are all beautiful things. In being beautiful, x, y and z participate in the Form of Beauty. The Form of Beauty is itself beautiful, as the self predication assumption says that a form participates in the virtue which it is related to. In being beautiful, the Form of Beauty, x, y, and z would all be participants in a Form of beauty. This “new” Form of beauty can’t be identical to the Form of beauty which participates in it, non identity. There would then be another group of beautiful things including all the participants in the second group along with the “new” Form of Beauty. From that would come a third Form of beauty…

It's reasonable to be at least skeptical about the Forms as literal perfect encapsulations of a state of being. Imagining them literally is difficult and irrelevant to any practical uses they might have. Some sort of mystical beautiful or tall thing is less intelligible than an idea of what beauty or tallness is. Instead of imagining the Forms literally, we can instead use them as means of understanding common traits among the sensible things. In understanding what beauty is, a definition of it that doesn’t rely on examples is useful. That these definitions could be infinite complicates their practical use. Instead of a means of understanding broad qualities, the Theory of Forms would devolve into an infinite series of definitions, each to define the one that came before it. To find a definition of beauty that also encapsulates a lower Form of beauty is unnecessary to the Form. In a set of tall things and the infinite tall Forms which they participate in, there would be some common thread that might be useful. We understand that these things are tall because their base is far from their head. Assuming all Forms of Tall are tall, this would be true for every member of the group. The purpose of understanding what tall is, independent of the sensible things, has been accomplished by understanding the form of tall. But it would have been accomplished just the same without an infinite series of Forms. Infinite regress doesn't contribute to a practical use of the Forms, but it might harm it. The idea of the infinite is impossible to visualise and very difficult to understand. If understanding practical traits relies on understanding each Form and its participants, then practical understanding of the traits which Forms represent would become very difficult or even impossible. The task is no longer “What is this one Form of beauty and how does it apply to all these sensible things, what makes something beautiful?” It would instead be a complex metaphysical problem of Forms of beauty that also have Forms of beauty which participate in them, infinitely so.

Perfection is a final state; something can't be more perfect than what is already perfect. The Forms are perfect encapsulations of what they are associated with. The TMA suggests that there would be a perfect example of beauty (a Form of Beauty) participating in another perfect Form of Beauty. We’ve already established that a participant in a Form can not be identical to the Form it participates in. This means that each of the Forms of Beauty would have to be different from one another. They would both have to be perfectly beautiful but not identical. The secondary Form of beauty would either have to be more perfect or a different kind of perfect from the first Form. If something can't surpass a perfect thing in the trait that it is perfectly, then the second Form of beauty would have to be a different “type” of perfect beauty. This seems plausible for a Form that is as subjective as beauty, however, in the same way that there is only one type of tall, Plato establishes that there is one perfect beauty. In calling it “the beautiful itself” (Symposium, 210e-211e). Additionally, in his Allegory of the Cave in book VII of the Republic, Plato confirms that the participants in the Forms can not be entirely like the Forms. Plato compares the non philosopher viewing the sensible objects to prisoners looking at shadows in a cave. In the dialogue, he asks his interlocutor if he supposes that “these prisoners see anything of themselves and one another besides the shadows that the fire casts on the wall in front of them?” to the response of “How could they,” (Republic, 514b). In its setup, Plato’s Allegory of the Cave implies that a sensible thing can never be perfectly similar to the Form which it participates in. A shadow could almost perfectly outline that which casts it, but the shadow will never be the real thing. The Allegory of the Cave indicates the non- identity assumption as central to the Theory of Forms.

Instead a response to the TMA might be some sort of modification to the one- over- many assumption. For any set with a commonality, there is a Form which is associated with that thing, a Form which the set participates in. The assumption has two parts: a set with a commonality and a Form associated with that commonality. Each relies on the other. Modification of the one-over-many assumption would require modifying one of its parts. The first part: we can assume that there isn't a common group. There is a group, but it is not common. Our group is no longer a group, a group of things is a group because of commonality, a common trait or a commonality in the observance of each participant as part of a group. The second part: the Form is not associated with the common trait in the group. A group of very tall things participates in the Form of short. This seems absurd and would worsen the issue of the practicality of the Forms. Understanding a common trait through another trait that is unrelated or opposite would be counterintuitive. Additionally, there doesn't seem to be much purpose in understanding a group of unrelated things as a group, unless it was to discover a common trait.

That leaves self predication. In Plato’s Symposium 210e- 211e Socrates refers to the beautiful as “the beautiful itself”. This idea that a Form participates in the virtue which it is associated with appears throughout the dialogues. Here, he references the beauty as participating in being beautiful: "It exists for all time, by itself and with itself, unique."(Symposium, 211a) However, as stated earlier, a rejection of one of the premises of the Third Man Argument would struggle not to modify the Forms in some way. In rejecting the self predication assumption, Socrates could instead argue that the Forms act as a “blueprint” for the virtue which they are associated with.

A Form doesn’t necessarily have to participate in the property which is associated with it. A silicone heart mold is not a heart shaped chocolate. It is the means of creating heart shaped chocolates, the blueprint. It has the independent qualities of a blueprint. In the same way, the Form of beauty does not necessarily need to be beautiful to still function as a Form. Instead, it could be independent in the trait which it participates in (it isn't beautiful), while “telling” the beautiful things how they can be beautiful. From it, the beautiful things can become beautiful. In the Allegory of the Cave, the objects which cast the shadows give the shadows their outline. The shape and movement of a tree is what the shadow of a tree is “based on”. The tree is cylindric, wooden, and brown with green leaves. The shadow is flat and grey. The two are very different, but the shape of the leaves and the trunk of the tree are able to dictate what the shadows of the tree will look like.

This response would partially satisfy in defending the forms from the TMA. A form that does not participate in the virtue which it is associated with would not be a participant in its virtue along with the sensible things. There would be no new form because there would be no shared virtue among the group. No longer does “some one thing appear large, by which all…appear large” (Parmenides , 132b). That one thing now has traits independent of large, and the TMA falls apart.

Removing the self predication assumption would also still make sense and not alter the practicality of the forms all that much. A Form acting completely different from its participants would be absurd and irrelevant to the actual purpose of the forms. The forms as blueprints don’t pose this problem. A blueprint is still insightful when understanding what makes a thing that thing. In fact they might be more insightful than observation of the thing itself. Looking at the blueprint of a car, understanding how it works and why teaches you more about a car than just staring at its engine. The idea of a blueprint also makes a lot of sense when understanding what the forms actually are. To say that the form of a tree is some perfect tree lends to the idea that somewhere out there, on this separate plane of perfection, there is this perfectly beautiful tree. When looking at the forms as the way that humans group objects, it makes sense for them to be blueprints, what a tree should be. When looking at a tree, we don't refer to some mystical tree we have imagined, checking for similarities. We look at a tree and decide if it follows the “rules” of what makes a tree a tree.

There are still some issues though, with removing self predication. Plato’s Phaedo dialogue establishes the existence of the forms. Plato “assume(s) the existence of a Beautiful, itself by itself, a Good and a Great and all the rest” (Phaedo, 100b). The arguments concerning the forms that follow all rely on some sort of metaphysical existence of a Form. Traits define the existence or nonexistence of something. Something that exists has traits, even if those traits are negative (a man has the trait of not being a bus). Consequently, the existence of a Form requires it to have traits. Our response to the TMA establishes that the forms don't participate in the virtue which they are associated with. This means that a Form would have to participate in another trait. It seems counterintuitive to the practicality of the Forms for a Form to participate in another virtue. Assuming the point of understanding the form of beauty is understanding beauty beyond examples of beautiful things, it wouldn't make sense for the form of beauty to participate in an unrelated or opposite virtue. To understand what makes a tall thing tall, it would be counterintuitive to try and understand a Form which is short. Maybe opposites could give some insight into the true nature of a trait, but on top of adding an unnecessary step (understanding the opposite and understanding the trait which it is opposite to), it relies on each trait having a perfect opposite. The Form of blue doesn't necessarily have an opposite that everyone who understands blueness can agree on. Plato confirms that a form cannot participate in an opposite trait: “Now it seems to me that only Tallness itself is never willing to be tall and short at the same time, but also that the Tallness in us will never admit to the short or be overcome” (Phaedo, 102e).

A Form can’t participate in an opposite trait, and it would be irrelevant for it to participate in an unrelated trait. Instead, a Form might participate in a trait that is independent to the Forms, a trait of “Formness”. Formness would be entirely unique from all other traits. This means that no form would participate in the virtue which it is associated with. In that sense, there wouldn't be secondary forms of virtues like beauty or tallness.

On the assumptions we've established as true or necessary to the Forms, the trait of “formness” would lead to an infinite regress of forms of forms. If there is a trait that is “formness”, one that all the forms participate in, then there ought to be a form of formness. The form of formness would itself be a form, therefore it would have to partake in the trait of formness. Then, it would share a trait with all the other forms which participate in it, meaning that there would again be a need for a new form of formness.

A rejection of the second assumption of the Third Man Argument would effectively change the process of creating unlimited forms, but could not eliminate it entirely. Removing the second assumption of the third man argument is effective at rejecting the argument, though it fails to not produce a second scenario of infinite regress.