This article explores three of the objections which Parmenides raises against Plato’s theory of the forms, in Plato’s eponymous dialogue. This theory, as developed in the Parmenides, is itself an attack on a key tenet of Parmenides’ philosophy. This article firstly situates the Parmenides within Plato’s wider authorship, then explains the argument which the theory of forms is developed in response to, before setting out Parmenides three most significant objections: the ‘whole-part dilemma’, the ‘third man’ argument, and the epistemic problem. How should we interpret Parmenides’ arguments, and how successful are they as a response to the Platonic theory of forms?
Locating Plato’s Parmenides: The Progression of Plato’s Authorship
In the earlier part of his authorship, Plato has the character of Socrates investigating certain specific topics by enquiring into their true nature: “what is x?” being the typical subject of such dialogues – whether the “x” is virtue, piety, or friendship. In what is often called the ‘middle period’ of Plato’s authorship, there is a move away from this tightly focused style of inquiry, and towards a more open-ended, constructive approach.
One consequence of this latter approach is the development of what is commonly known as the ‘Theory of the Forms’. Although certain basic elements of this theory are more or less consistent across the Platonic corpus, this theory is developed in quite different ways in different dialogues.
Because Parmenides’ arguments are a critique of the Platonic theory of the forms as it is stated in the Parmenides, what follows is primarily an account of this theory as it is set out in the Parmenides. It should not be understood as an account of Plato’s theory in general.
Motivating the Forms in the Parmenides
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The forms in the Parmenides are introduced in response to an argument Zeno makes. Zeno is attempting to defend the doctrine of monism advocated by Parmenides amongst others, that all things are – fundamentally – one, and the appearance of multiplicity and variety in the universe is ultimately an illusion.
The dialogue really begins with Socrates’ summarizing Zeno’s argument as involving two premises. First, if the things that are are many, then they are both like and unlike. Second, nothing can be like and unlike. The first premise can be understood as a claim about the problem of different qualities: if things share certain qualities but not the others, then they are both like and unlike, and that presents a contradiction. The theory of the forms is developed in the Parmenides as a response to the second premise: Socrates wants to argue that things can be, at one and the same time, like and unlike.
What Are Forms?
The essential division in Platonic thought is between appearance and reality. Appearance, that is the world of particular things which appear to us, is merely a shadow or reflection of reality, the realm of concepts, of absolutes, of things in themselves. All of the latter constitute partial definitions of the ‘Form’ in Plato’s work, an essentially indefinable idea. Socrates sets out a number of principles and features of the forms, two of which are worth setting out explicitly.
Firstly, there is the principle of causality: things that have a certain quality or are a certain kind of thing, apart from the form of said quality or kind of thing, as so because they ‘participate’ in the Form in question. That is, there is a causal relationship between the Forms and things which appear to us.
Secondly, there is the principle of separation: the Form is independent of the things which participate in it. It is itself regardless of any further facts about things which partake in it. Effectively, these two doctrines designate a hierarchy of reliance between forms and things as they appear.
Socrates’ Response to Zeno
This hierarchy of reliance explains how and why Socrates is able to reject Zeno’s claim that ‘things cannot be like and unlike’. Likeness and unlikeness are qualities which have corresponding forms. Being like means participating in said form, and the same is true of being unlike.
Being like and being unlike might be contrary, but they are not contradictory, because of the direction of travel Socrates sets out. Things participate in forms, and can participate in multiple forms, but forms do not participate in things. Zeno is right to point out that likeness and unlikeness contradict each other when they are applied to things on the same level of existence. The form of likeness participating in the form of unlikeness is nonsensical.
Sensible things are impure in a way that forms are not. Zeno, by failing to distinguish things from forms, has seen a contradiction that isn’t really there, and used this fallacious contradiction to defend the seemingly indefensible view that where there appear to be many things that exist, these are in fact all one thing.
1. Parmenides’ First Argument Against Forms: The ‘Whole-Part Dilemma’
One of Parmenides’ responses to Socrates is to try and cast the pallor of absurdity over the Socratic ‘partaking’ relation: that is, the relation between forms and things.
Parmenides argues that either things partake of Forms in their entirety (that is, in the Forms’ entirety), or they only partake of part of a Form. The dilemma is as follows. If Socrates has the first kind of partaking relation in mind, then the problem is that if we imagine multiple things to partake in the same form in its entirety, then that form must in some way duplicate or separate itself from itself.
If, on the other hand, Socrates suggests that part of each Form ends up in each thing which partakes of it, imagining multiple, simultaneously existent things which partake of the same form, we must therefore imagine numerically distinct parts of each form, which contravenes one of the central doctrines of the ‘Form’.
2. The ‘Third Man Argument’
The Third Man Argument is an attempt to create an infinite regress with respect to the postulation of any form, which many later commentators have deemed to be highly successful.
It all hinges on Parmenides’ example, which is the form of Largeness. Imagine various things which partake of the form of Largeness – we can call this form ‘Largeness A’. The form of largeness is itself large: it predicates itself. Then, we can imagine that these things and ‘Largeness A’ also partake of another form of Largeness, which we can call ‘Largeness B’. If we assume, as Parmenides does, that no form is identical to anything partaking in that form, then Largeness B and Largeness A are distinct.
The infinite regress can then be drawn out, when we realize that this reasoning can be repeated: both Largenesses B and A participate in the same form of Largeness, ‘Largeness C’, and so forth, ad infinitum.
3. The Epistemic Problem
The Epistemic Problem is effectively, two distinct problems. The first concerns whether (if Plato’s theory holds) the forms can be known by human beings, and the second concerns whether the gods can have knowledge of the affairs of human beings.
We will focus on the first argument, which has three premises. First, that nothing among human beings is itself by itself. Second, if something is a form, and it is what it is in relation to something else, then that something else is a form. Third, if something is among humans and is what it is in relation to something else, then that other thing is in humans.
Quite a lot of fancy argumentative footwork goes into drawing the conclusion, but it is reasonably clear what motivates this argument. Things are defined by their contingency, the forms are defined by their absoluteness, timelessness, and non-reliance. Knowledge of the forms goes beyond the scope of human thought.
Defending the Theory of Forms in Plato’s Parmenides
A full response to Parmenides’ argument isn’t possible here. But to offer one general response, it is necessary to firstly argue that the strategy Parmenides adopts is rather similar to that which motivates his monism (his doctrine of absolute oneness). Namely, that the creation of concepts is more difficult than the acceptance of unintelligibility.
Nothing is more difficult than finding some non-contradictory way of characterizing reality in all its apparent variety. As much emphasis is placed on the division between appearance and reality in Plato’s work, it is striking that his forms track the qualities of apparent things perfectly: reality is reflected in appearance.
Plato’s work expresses a faith in human understanding, in the power of enquiry, which Parmenides simply does not possess. For Parmenides, attempting to account for all of the world’s apparent depth and variety in one’s theory leaves one open to endless self-contradiction.
Yet, to do what Parmenides did, to reduce all change to ephemera, to illusion, is to make the world indescribable. To take it seriously at all moments would be to make one’s life basically unlivable.