Criticism of Theory of Forms

  1. A review of the essential points of the middle period Theory of Forms

    1. A “Two-Worlds” theory

    2. A Form is a “one-over-many”:

      There’s a Form whenever two or more things have something in common. Cf. Rep. 596a:

      We are in the habit of positing a single Form for each plurality of things to which we give the same name.

    3. Forms are paradigms

    4. Things participate in the Forms by being appropriately related to these paradigms (by resembling them??).

    5. Participation explains predication (cf. Phaedo 100c):
      A thing’s being equal consists in, and is explained by, its participating in Equality.

      In general: x’s being F is explained by x’s participating in F-ness.

    6. A good summary statement is provided at 130e-131a:
      There are certain forms, whose names these other things have through getting a share of them - as, for instance, they come to be like by getting a share of likeness, large by getting a share of largeness, and just and beautiful by getting a share of justice and beauty.

  2. The self-criticism of the first part of the Parmenides

    1. How are these extraordinary criticisms intended to be taken?

      1. As fatal objections to the Theory of Forms ?

      2. As based on misunderstandings of the Theory of Forms that need to be cleared away?

      3. As prima facie problems for the Theory of Forms that demand modifications of the theory?

    2. My view: Some combination of (2) and (3) is probably closest to the truth. Some of the objections are frivolous, but others are meant to be taken seriously.

  3. The Setting of the Parmenides

    1. A discussion involving “the young Socrates” and the two Eleatics, Zeno and his teacher Parmenides.

    2. The Eleatics argued for monism, the view that reality is one: a permanent and unchanging unity. In their view, pluralism, the view that there are many real things, is false.

    3. Socrates offers the Theory of Forms as an alternative to Eleatic monism. It is put forward as a variety of pluralism that does not give rise to the absurdities that the Eleatics find in pluralistic theories.

    4. Parmenides and Zeno’s reply is to attack the Theory of Forms, to show that it leads to puzzling consequences of its own.

  4. The Objections to the Theory of Forms

    1. The Extent of the World of Forms

      What things are there Forms for?

      1. Moral and aesthetic ideals: “just, beautiful, good”

      2. Natural kinds: “human being”

      3. Natural stuffs: “fire, water” [Socrates expresses uncertainty about groups (2) and (3).]

      4. “Undignified” things: “hair, mud, dirt.” [Socrates denies Forms for things in group (4), but Parmenides says that when he gets older he’ll learn not to be so fastidious. This is clearly a point where there is a conflict between the role of Forms as (morally or aesthetically pleasing) paradigms and their role as universals.]

    2. The Nature of Participation

      1. Part or Whole? (131a-c): The dilemma of participation:

        Is (a) the whole Form, or only (b) a part of it, in each participant?

        If (a), then each Form will be “separate from itself” if it is in many things.

        If (b), then the Form is divisible, and hence no longer a unity.

        [The conclusion of this dilemma seems to be that Forms will either be divisible or not shareable. But Forms have to be shareable, that is the whole point of having the theory. So the consequences of making Forms divisible is pursued.]

      2. Puzzling consequences if Forms are divisible (131d-e):

        1. The parts of Largeness are small (with respect to Largeness) but still make the things they are in large. [Note: this conflicts with one of Plato’s requirements in the Phaedo: what makes something F must itself be F.]

        2. A part of Equality which is “less than Equality itself” nevertheless makes what it is in equal.

        3. The parts of Smallness are smaller than Smallness itself! And the addition of such a part to something makes that thing smaller than it was before the addition of that small part!

    3. The Third Man Argument (TMA)

      1. An infinite regress argument: “no longer will each of your forms be one, but unlimited in multitude.” (132b2)

      2. The regress is epistemologically vicious.

        The Theory of Forms is a theory of judgment (by “judgment” I mean the mental state that is common to both knowledge and belief).

        Judging involves consulting Forms: to judge that x is F is to consult the Form F-ness and to see x as being sufficiently like F-ness to qualify for the predicate F. Alan Code suggests that the TMA raises an objection to this theory of judgment:

        The TMA is designed to reduce to absurdity the claim that it is the consultation of forms which enables us to make judgments. It does this by showing that if that were the case, we would have to perform an infinite number of such consultations to make just one judgment.

      3. Since the Theory of Forms tries to explain predication, the TMA is also a challenge to it as a theory of predication. (Recall our examination of the Phaedo : the Form, the F Itself, is the aitia, or explanation. of something’s being F.

        “Participating in a Form” is supposed to explain predication. And the upshot of the TMA is that there is something defective about this explanation:

        Trying to explain predication in terms of the notion of participating in a (paradigmatic) Form leads to an infinite regress, and hence is no explanation at all.

  5. The premises of the TMA

    1. Plato is not explicit about the premises of the TMA. We will have to reconstruct the argument and tease out the implicit premises.

    2. To start, let’s try to see how the argument goes, and what features (or alleged features) of the Theory of Forms are being brought into play.  In the table below, the steps of the “largeness” argument appear on the left; a schematized version showing how the argument can be generalized appears on the right.  The horizontal line separates the Form (above the line, the “one over many”) from the things (below the line) that participate in that Form.

      The Steps of the TMA
      Step One: We assume a number of things are (or “appear to us to be”) large. a, b, c
      Step Two: From this we infer that there is a Form (Largeness) by virtue of which they all appear large. F-ness1
      __________
      a, b, c
      Step Three: We now consider all of the items discussed in Step One (viz., all of the large things we were considering) and Largeness, the Form by virtue of which they all are (and appear to us to be) large. __________
      a, b, c, F-ness1
      Step Four: From this we infer that they all (i.e., the participants and the Form) participate in a Form of Largeness. a form of F-ness
      _________________
      a, b, c, F-ness1
      Step Five: From this we infer that the Form introduced in Step Four is a second Form (Largeness2), distinct from the Form (Largeness1) introduced in Step Two. This second Form is the one by virtue of which the first Form and all of its participants appear large. F-ness2
      _________________
      a, b, c, F-ness1
      Step 6: We now consider all of the items discussed in Step Five, viz., all of the large things we introduced at Step One, the Form we introduced at Step Two, and the second Form we introduced at Step Four (and distinguished at Step Five). ___________________
      a, b, c, F-ness1,
      F-ness2

      And so on, ad infinitum.

    3. By what principles do we proceed from step to step in this argument?

      1. From #1 to #2: A principle that generates a Form for a collection of things that all appear to have something in common (a “one-over-many”).

      2. From #2 to #3: A principle that entitles us to group the Form together with its participants as constituting a collection whose members all have something in common. (Like its participants, the Form is something to which we can apply the predicate large.  That is, a Form can be predicated of itself.)

      3. From #3 to #4: The One-Over-Many principle again.

      4. From #4 to #5: What tells us that we have a second Form? That is, what tells us that #5 shouldn’t be written up this way:

        Step #5

        F-ness1
        _________________
        a, b, c, F-ness1

        The question really amounts to this: What tells us that F-ness1 and F-ness2 are two distinct Forms?

        Roughly: a principle which tells us that a Form is not one of its own participants; that a Form does not participate in itself.

    4. So the argument appears to have three premises.  It has become traditional to call these “One Over Many”, “Self-Predication” and “Non-Identity”:

      1. (OM) There is a Form for any set of things we judge to share a predicate in common. I.e.,

        If a collection of things, a, b, c, etc., are all F, there is a single Form by virtue of participating in which they are all F.

      2. (SP) The Form by virtue of which things are (and are judged to be) F is itself F. I.e.,

        F-ness is F.

      3. (NI) The Form by virtue of which a set of things are all F is not itself a member of that set. (Equivalently, nothing is F by virtue of participating in itself.) I.e.,

        F-nessn does not participate in F-nessn.

      The discovery of these as the three principles underlying the argument is basically due to the ground-breaking efforts of Vlastos [1954]. But his reconstruction of the argument was flawed, since he had the idea that (SP) and (NI) actually contradicted one another. This is important, if true: for if the Theory of Forms is committed to both (SP) and (NI) and these contradict one another, then the Theory is inconsistent! But Vlastos has been shown wrong on this. (Cf. esp. Sellars, Strang, Cohen.)

  6. Reconstructed, Plato’s argument looks like this (with the justification for each step provided):

    1. a, b, and c are all large. premise
    2. There is a Form of Largeness (Largeness1) that they all share in. 1, OM
    3. a, b, c and Largeness1 are all large. 1, 2, SP
    4. There is a Form of Largeness (Largeness2) that they all share in. 3, OM
    5. Largeness2 is not identical to Largeness1. 4, NI
    6. a, b, c, Largeness1 and Largeness2 are all large. 3, SP
    7. There is a Form of Largeness (Largeness3) that they all share in. 6, OM

    And so on, ad infinitum.

  7. Self-Predication vs. Self-Participation

    We must distinguish (as Vlastos did not adequately do) between these two notions.

    Participating in F-ness is supposed to explain being F.

    (SP) tells us that we can apply to the Form F-ness that very predicate (“F”) whose application to sensible particulars is explained in terms of participation in that Form. That leaves us with the problem of explaining this case of predication: F-ness is F.

    (NI) tells us that we can’t explain x’s being F by appealing to x. Hence, the principle is really better called:

    [But the label “NI”, due to Vlastos, has stuck. It’s important to realize that it can be formulated in such a way that it doesn’t contradict (SP).]

  8. The Role of the TMA’s premises as principles of the Theory of Forms

    What would be the consequences for the Theory of Forms of giving up one of these principles?

    Principle abandoned Consequence for Theory of Forms

    (OM)

    		The theory becomes incomplete.

    (SP)

    		Forms will no longer be paradigms.

    (NI)

    		Some explanations become circular.

  9. Forms and Standards

    1. Plato’s Forms as Paradigms

      SP (and along with it Plato’s paradigmatism) have proved to be the hardest of the aspects of TF to make sense of. It helps if we compare paradigmatic Forms to standards of weight and measure.

      Forms are less like properties or universals than they are like standards of measure. That's because a Form's participants are supposed to be compared to , or measured against the Form in the process of judging whether they are entitled to have the Form's name applied (as a predicate) to them.

      In much the same way, a stick is a meter long because it has the same length as the Standard Meter, or to weigh a kilogram because it weighs the same as the Standard Kilogram.

    2. Paradigmatism entails Self-Predication

      In a theory of Standards, self-predication makes sense:

      • The Standard Meter is one meter long.
      • The Standard Kilogram weighs one kilogram.

      That’s because standards of weight and measure are physical objects that play a certain role in a system of weights and measures. They are paradigms against which other things are compared. Although Plato’s Forms are not physical objects, they still are paradigms.

      Does paradigmatism entail self-predication? It’s hard to see how it fails to. How can the paradigmatic F thing fail to be F ? How could the Standard Kilogram fail to weigh one kilogram?

      There are two different approaches one might take here:

      • “The standard pound must weigh a pound; one might say, it weighs a pound no matter what it weighs.” (P. T. Geach)
      • “There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris.” (Wittgenstein, Philosophical Investigations, §50.)

      Neither seems exactly right. Contra Wittgenstein: how could the standard meter not be a meter long? It’s not longer than a meter, and not shorter than a meter, and it does have a length—viz., 39.37 inches. So it’s a meter long. Contra Geach: no matter what it weighs? Suppose we discover that the standard meter—the bar kept locked up in Paris—has shrunk in half overnight. Is it still a meter long? Surely not.

    3. Standards and Change

      The problem with using physical objects as standards is that they are not immune to change. (Notice that Plato's Forms don’t have this problem.) The problem has come to the fore in the case of the Standard Kilogram.

      The kilogram was conceived to be the mass of a liter of water, but accurately measuring a liter of water proved to be very difficult. Instead, an English goldsmith was hired [in 1889] to make a platinum-iridium cylinder that would be used to define the kilogram. … No one knows why it is shedding weight, at least in comparison with other reference weights, but the change has spurred an international search for a more stable definition. … “It’s certainly not helpful to have a standard that keeps changing,” says Peter Becker, a scientist at the Federal Standards Laboratory. … The final recommendation will be made by the International Committee on Weights and Measures, a body created by international treaty in 1875. The agency guards the international reference kilogram and keeps it in a heavily guarded safe in a château outside Paris. It is visited once a year, under heavy security, by the only three people to have keys to the safe. The weight change has been noted on the occasions it has been removed for measurement. ( New York Times , May 23, 2003)

      So we really can’t simply declare that the standard kilogram weighs one kilogram no matter what happens. We need to be sure that it continues to have the same weight that it did. Which means that it must be weighed against something else. This is to admit that the Standard itself requires a distinct standard against which to be compared. So not just SP, but even NI, enter into our account of what to do when a standard undergoes change. Small wonder that scientists are seeking a definition of ‘kilogram’ that does not depend on a physical object of fixed weight as a standard.

  10. Conclusion

    1. The upshot of the TMA is that the Theory of Forms cannot provide a complete account of predication by means of the notion of participation.

    2. But since all three assumptions work together to yield the regress, why single out OM? So long as Plato’s theory likens forms to standards (in their role as paradigms), SP and NI seem correct. OM should then be rejected on the grounds that it is in the nature of a paradigm of F-ness that nothing explains its being F. Rather, it explains other things’ being F. This means that there will always be at least one “many” (at least one set of F’s) to which we cannot apply OM.

    3. What the TMA shows is that a paradigmatic theory of predication cannot be both complete (in the sense of providing an explanation of every case of predication) and non-circular. For the paradigm itself must bear the predicate, and there we have a case of predication that the theory cannot explain without circularity.

  11. Plato’s Reaction

    1. How did Plato react to the TMA? This is a difficult question. We can make some guesses based on the contents of later dialogues. (Our clues do not all point toward a single answer.)

      1. The Timaeus is usually thought to be a later dialogue. And it contains the full-blown, unreconstructed Theory of Forms. (But cf. Owen, “The place of the Timaeus . . .”).

      2. Strang: Plato gave up paradigmatism and the doctrine of recollection. He says (in Vlastos, Plato: A Collection . . ., pp. 198-99):
        In the interval between the second act [the middle period] and the third [late period], which begins with the Parmenides, the paradigmatic eidos and its brother, recollection, have been unmasked as impostors and quietly buried. The TMA is offered by way of justifying the action taken as technically correct. . . .

        The more you become aware of, and enthralled by, the peculiar anatomy of individual Forms, the fewer and the less important become the things that can be said about Forms in general. They remain unchanging (Prm. 135C1), if only to be the subject matter of timeless truths; they remain single (Phlb. 14E5 ff.); but what they do not remain is paradigms.

      3. Evidence from the Sophist:

        1. Self-participation allowed? (cf. 255e, which seems to entail that Difference participates in itself.)

        2. Plato’s talk of blending of kinds (a word he begins to use more and more rather than the middle period’s “Form” or “Idea”) suggests that he’s starting to think of Forms as more like collections. This fits well with Strang’s idea: Forms as kinds are not likely to be thought of any more as paradigms.

      4. Plato abandons or modifies OM? Pol. 262d supports this: Plato contends that it would be a mistake to think that non-Greeks constitute a real class because they all have the common name Barbarian.

References

Cohen, S. M., “The Logic of the Third Man,” Philosophical Review 80 (1971) 448-475. [Jump back to text.]

Geach, P. T., “The Third Man Again,” Philosophical Review 65 (1956) 72-82. [Jump back to text.]

Owen, G.E.L., “The Place of the Timaeus in Plato’s Dialogues,” Classical Quarterly n.s. 3 (1953) 79-95; also in Studies in Plato’s Metaphysics, ed. by R. E. Allen (London: Routledge & Kegan Paul, 1965) 313-338. [Jump back to text.]

Sellars, W., “Vlastos and the Third Man,” Philosophical Review 64 (1955) 405-437. [Jump back to text.]

Strang, C., “Plato and the Third Man,” Proceedings of the Aristotelian Society, Suppl. vol. 37 (1963) 147-164; also in Plato: A Collection of Critical Essays, vol. 1, ed. by G. Vlastos (New York: Anchor, 1971) 184-200, and on reserve in OUGL. [Jump back to text.]

Vlastos, G., “The Third Man Argument in the Parmenides,” Philosophical Review 63 (1954) 319-349; also in Studies in Plato’s Metaphysics, ed. by R. E. Allen (London: Routledge & Kegan Paul, 1965) 231-263. [Jump back to text.]

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