Plato's Parmenides: Self-Criticism of the Theory of Forms

Suppose you explain several fair decisions by saying that each answers to the same standard of fairness. Someone then asks what connects that standard to the decisions. If they resemble it, why does resemblance explain anything? If the standard itself is fair, must it answer to a further standard? What looked like an explanation has become something that needs explaining.

This is a modern illustration of the pressure Plato puts on the Forms in the Parmenides. The dialogue examines whether a single intelligible reality can explain many things without becoming another unexplained member of the group. It also asks whether separating that reality from ordinary things threatens the possibility of knowing it. These are challenges to particular assumptions about explanation and participation. They do not amount to an automatic refutation of every theory that recognizes shared properties.

The work gives its reader two tasks. First, follow the objections closely enough to see which assumptions produce them. Then consider why Parmenides responds to the difficulty by demanding more dialectical training. The long exercise that follows does not end with a simple announcement that Socrates has either won or lost.

Plato presents the conversation through a chain of narrators: Cephalus reports Antiphon's retelling of an account learned from Pythodorus. Within that narrated scene, Socrates is very young, Parmenides elderly, and Zeno is reading an argument connected with the problems of plurality. These are features of the dialogue's dramatic construction. The text alone does not establish that the conversation occurred as narrated. See Parmenides 126a–128e.

Socrates distinguishes things that possess contrary characteristics from the Forms themselves. A person can be one person and also many parts. Showing that a person is one and many is therefore less surprising to him than showing a corresponding entanglement within unity and plurality themselves. His proposal moves the difficulty from familiar objects to the intelligible objects through which he hopes to explain them (128e–130a).

A Form, for the account being examined, is a reality such as Likeness itself or Justice itself, distinguished from the many things that participate in it. Participation is the proposed relation by which similar things are similar or just things just. Naming that relation does not yet explain how it works. Parmenides begins to test that gap between an explanatory name and an explanatory account (130a–131a).

This distinction of voices matters. Plato wrote the dialogue, but that does not make every statement by Parmenides a settled declaration of Plato's beliefs. Nor should Socrates' difficulty be turned into a story about a documented crisis in Plato's personal life. The text gives us arguments to assess; its dramatic arrangement does not by itself supply a chronology of the author's intellectual development.

Parmenides first probes the scope of Socrates' distinction. Socrates accepts Forms of justice, beauty and goodness. He is unsure about a separate Form of a human being, fire or water. Asked about hair, mud and dirt, he resists, though he admits being troubled by the possibility that the same reasoning might apply to everything. Parmenides connects this resistance with Socrates' youth and concern for ordinary opinions (130b–e).

The philosophical issue is a demand for a reasoned boundary. If a Form explains what many instances share, why should an unglamorous subject be excluded simply because it seems beneath philosophy? That question does not itself prove that every word has a corresponding Form. A defender might distinguish independently grounded properties or kinds from arbitrary classifications. The point is that dislike or embarrassment cannot do that classificatory work by themselves.

Consider a modern analogy. An organization may want a precise account of excellence but avoid defining what counts as routine failure because the subject feels embarrassing. That preference does not show that failures lack an intelligible structure. The comparison concerns consistency in inquiry. It does not identify organizational categories with Platonic Forms or settle which categories deserve independent metaphysical status.

The scope question also teaches a reading habit. Before asking whether a theory is true, ask what its proponent intends it to cover. An objection to a claim about every shared characteristic may miss a theory restricted to certain kinds. Conversely, restricting the theory only after an awkward example appears can leave the explanatory boundary arbitrary.

The first sustained objection concerns participation. Does each participant receive the whole Form or only a part? If the whole of one Form is present in several separate things, Parmenides asks how it avoids being separate from itself. Socrates answers with the example of a single day present in many places. Parmenides replies with a sail spread over several people, asking whether the whole sail or a different part is over each person (131a–c).

The switch in images deserves attention. A day and a sail need not explain common presence in the same way. Socrates is trying to imagine unity without division; the sail turns the discussion toward different spatial portions. A defender may therefore challenge whether the sail captures what participation was supposed to mean. The dialogue records Socrates accepting the pressure of that image; a reader should still examine the analogy rather than assume that sharing any property must work like distributing fabric.

Dividing a Form produces further difficulties in the exchange. A participant would be large through a part of Largeness smaller than Largeness itself. Smallness would be larger than its own part, even though adding that part would make its recipient smaller. Parmenides uses these consequences to press Socrates on whether participation can be explained through parts at all (131c–e).

The objection can be read as diagnosing an unsuitable picture. If the Form is treated as a quantity parceled out to objects, problems follow about its unity and the relation between the quantity received and the property explained. This does not establish that every possible nonspatial relation is incoherent. It establishes a task for the theory: say what participation is without quietly importing a model that defeats its purpose.

The label Third Man appears in Aristotle's criticism of Forms (Metaphysics 990b). In the passage examined here, however, the example is Largeness. Socrates agrees that looking at several large things leads him to recognize one Form through which they are large. Parmenides then asks him to look together at those things and Largeness itself. If the same explanatory procedure applies to that expanded group, a further Largeness appears. Repeating the procedure produces further Forms without end (131e–132b).

We can reconstruct the pressure through three assumptions. Several things that are large call for one Form explaining their largeness. Largeness itself can be included among things that are large. The Form explaining such a collection must be distinct from the members whose shared character it explains. Keeping those assumptions in play generates another explanatory Form each time the previous one joins the collection.

These assumptions should not be compressed into the assertion that the theory is simply inconsistent. Each does a different job. The first demands an explanation of shared character. The second extends a predicate to the explanatory Form itself; we can call this self-predication. The third prevents the same Form from serving as its own explanation within the expanded group. A reader who rejects one premise changes the argument, and must explain why that rejection is available.

The difficulty is also more precise than a fear of infinity. An infinite collection is not contradictory merely because it is infinite. The problem here concerns the intended explanatory role of a unique Form: the procedure repeatedly supplies another Form where Socrates had expected a single unifying explanation. Whether this makes the regress vicious depends on what the explanation was required to accomplish. The text makes the multiplication explicit without offering a completed theory of explanation.

A possible response distinguishes the way a Form is what it is from the way its participants possess a property. Largeness need not be a large object in the same sense as a mountain. That response blocks the easy move to an undifferentiated collection. It also creates a responsibility: explain the difference in predication rather than use a change of meaning only when the objection appears. This is a proposed defense for the reader to assess, not a solution delivered by Socrates at this point.

Socrates tries another proposal: perhaps Forms are thoughts existing in souls. Parmenides asks whether a thought must be a thought of something, and whether the common object recognized by it would itself be the Form. He also presses the consequences of saying that things participate in thoughts. The proposal therefore has not simply eliminated the original issue by relocating the Form inside a mind (132b–c).

The distinction matters beyond the immediate exchange. The act of thinking about a common property and the property thought about need not be the same thing. Calling an explanation "a concept" leaves open whether the concept merely records a similarity, creates a classification, or identifies something independent of the act. Those alternatives require argument. They cannot be decided simply by replacing the word "Form" with "thought."

Socrates next proposes that Forms are patterns and participants are likenesses of them. Parmenides replies that resemblance is reciprocal: if a thing resembles the pattern, the pattern resembles the thing. If things that resemble each other require a common Form, the pattern and its likeness require another Form, producing another regress (132c–133a).

Here the difficulty concerns the attempt to explain participation entirely through resemblance. An original and its copy may have different roles, but resemblance alone does not explain that difference. A photograph may resemble a face without the face being a copy of the photograph. The modern example illustrates the difference between reciprocal similarity and an asymmetric explanatory relationship; it does not supply a theory of Forms. A defender needs an account of the relevant asymmetry, rather than the word "pattern" alone.

Parmenides then introduces what he calls a greater difficulty. Forms that stand in relations to one another are taken to have those relations within their own domain. Corresponding things among us relate to one another within ours. His example is mastership and slavery: a particular human master is master of a particular human slave, while Mastership itself is related to Slavery itself (133b–134a).

The argument extends this restriction to knowledge. Knowledge itself would know truth itself, while the knowledge among us would concern the things among us. Given that separation of relational domains, our knowledge would not know the Forms. The question is therefore not simply whether we can see a nonphysical object. It concerns the additional assumption that the relevant relations remain confined to each domain (134a–c).

Parmenides presses a troubling consequence in the opposite direction. If the gods possess the most exact knowledge, and that knowledge belongs to the domain of Forms, then under the accepted relational restriction it would not know human affairs. The problem concerns divine knowers under those assumptions. It is not a claim that Forms themselves must be persons who know or fail to know us (134c–e).

This helps locate a possible response. A defender could distinguish independent existence from complete relational isolation. Something need not be created by our thought in order to be an object of our thought. But this defense must explain the bridge that the argument has prohibited. Merely repeating that the Forms are intelligible does not answer a challenge about the conditions under which they could be known.

The payoff for a reader is diagnostic. Whenever an explanation places its object beyond ordinary experience, ask what relation is still supposed to connect inquiry with it. That question alone does not refute the explanation. It identifies work the explanation owes us. The stronger claim that every independently existing object is unknowable would outrun the argument just examined.

After these objections, Parmenides warns against dispensing with Forms altogether. Without a stable object of thought, he says, Socrates would destroy the power of dialectic. He also says Socrates has attempted to define the just, the beautiful and the other Forms before receiving enough training. The response combines criticism with insistence that the inquiry continue (135a–d).

The proposed exercise is systematic. Take a hypothesis and examine the consequences if it holds and if it does not. Consider the subject in relation to itself and to other things, then the others in relation to themselves and to it. The method requires more than collecting objections to a view one dislikes: it also tests what follows from denying it (135d–136c).

Parmenides demonstrates with the one, questioning the young Aristoteles, whom the dialogue identifies as a later member of the Thirty. Socrates does not conduct this extended second part. The topic moves through unity and plurality, relation and difference, motion and rest, and time. The exercise reaches the closing lines without a separate speech telling the reader how every difficulty about Forms has been solved (137a–166c).

A useful modern application is to test both a proposal and the proposed alternative. Suppose a team argues that every exceptional case needs a new rule. That might produce a difficult accumulation of rules. Simply removing rules may produce different difficulties about consistency and discretion. Testing both options helps clarify what must be explained. This is an illustration of the method; it does not make the dialogue an instruction manual for organizational policy.

The opening deduction begins by treating the one as excluding plurality. It therefore cannot have parts; nor can it be a whole composed of parts. The argument excludes shape and location, and goes on to deny further attributes. Eventually it denies participation in time and being, reaching the unsettling result that this one is not. These are consequences within the deduction, not a casual declaration that nothing exists (137c–142a).

The next deduction begins again from the one being. It distinguishes the one from the being in which it participates: being one and having being are not treated as the same account. That difference supplies a route to plurality within the one-that-is. The exercise develops consequences very different from those obtained when unity was isolated from every differentiating feature (142b–143a and following).

One productive reading compares the assumptions at work. Under the first deduction's restrictive treatment of unity, including its exclusions of time, being and relations, the one lacks the differences needed for description. A one that has being already involves differentiation. The deductions can then train the reader to ask what a claim of unity permits us to say. This interpretation does not require accepting every step without scrutiny, or treating apparently conflicting results as straightforward assertions true in the same respect.

The whole second part is longer and stranger than these two examples. Later deductions test consequences of the one's not being and consequences for the others. A complete interpretation must account for those passages as well. Here the representative contrast gives us a way to start reading the exercise, not a substitute for its remaining arguments or a claim that its overall meaning has been settled.

A reader may object that a training exercise is an inadequate response to the first part. If participation remains unexplained, showing greater skill in deduction does not by itself supply the missing relation. That criticism identifies a real burden for any interpretation that treats the second part as a solution. It must show how the exercise repairs the earlier assumptions, rather than merely praise its difficulty.

Another reader may prefer to take the dialogue as a demonstration that separate Forms must be abandoned. That view must also explain Parmenides' warning that rejecting Forms would undermine dialectic. The dialogue puts pressure on both an unexamined defense and an effortless dismissal. We should preserve that tension instead of turning either character's remarks into a final verdict on the whole theory.

For contemporary thinking, the useful discipline is exactness about what has failed. Was it the existence of a shared object, a particular model of participation, an assumption about self-predication, or an isolation of relations? Those failures call for different repairs. The Parmenides gives us an opportunity to distinguish them, and to practice following an objection far enough that our reply answers the argument actually made.

• Plato, Parmenides, translated by Benjamin Jowett. The dialogue consulted here; its introductory essay should be distinguished from Plato's text.
• Plato, Parmenides, translated by Harold North Fowler, Perseus Digital Library. A second translation for comparing passages using Stephanus section numbers.
• Plato, Sophist, Perseus Digital Library. A related dialogue to read when continuing inquiry into being, difference and intelligibility.