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What the forms are not: Plato on conceptualism in Parmenides 132b–c


Conceptualism—the view that universals are mental entities without an external, independent, or substantial reality—has enjoyed popularity at various points throughout the history of philosophy. While Plato’s Theory of Forms is not a conceptualist theory of universals, we find at Parmenides 132b–c the startling conceptualist suggestion from a young Socrates that each Form might be a noēma, or a mental entity. This suggestion and Parmenides’ cryptic objections to it have been overshadowed by their placement directly after the notoriously difficult Third Man Argument (132a–b), and before the Likeness Regress (132c–133a). However, in the background of 132b–c, we find illuminating assumptions behind Parmenides’ arguments against the Theory of Forms in the first half of the dialogue. We also find in this text a set of implied criteria for Platonic concepthood. While in the Platonic corpus, Forms are explanantia for many of the phenomena explained by concepts in contemporary philosophy, concepts do seem to have an important epistemic role in Plato’s philosophy. An account of Platonic concepthood therefore opens the door for new ways of understanding the Platonic corpus as a whole. My focus in this paper is to uncover these assumptions and criteria through a close reading of Socrates’ conceptualist suggestion and Parmenides’ truncated objections to it at Parmenides 132b–c.

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  1. 1.

    For why the Theory of Forms is not a conceptualist theory of universals see for instance Cherniss (1944, 214–216). That Socrates’ suggestion in this part of the text amounts to conceptualism is defended, for example, by Allen (1983) and Helmig (2007), among many others, and seems to be the dominant view. One exception is the view defended in Bossi (2005), which I discuss in Sect. 2.

  2. 2.

    The Parmenides is an immensely rich dialogue, and all of its difficulties cannot be addressed in one paper. I set aside speculation about the target of Plato’s anti-conceptualism, as well as questions about the dramatic and philosophical allusions or qualifications Plato might intend in making Parmenides the main interlocutor in this dialogue. I also set aside the question of whether the Parmenides of this dialogue is deploying a sincere criticism of the Theory of Forms.

  3. 3.

    The language of numerical and predicational unity belongs to Curd (1986). I will use ‘unity’ and ‘oneness’ interchangeably. The language of ‘bearing’ and ‘acquiring’ a Form, or ‘bearing’, ‘holding’, and ‘expressing’ a predicate is also deliberately ambiguous so as to not beg questions.

  4. 4.

    The text also lends itself to “maybe each of the Forms is a thought of these things” when τούτων is taken as an objective genitive with νόημα. For this reading, see Allen (1983). The placement of τούτων makes this rendering more plausible, though it raises the question of what the referent of τούτων is. So understood, one candidate for the referent would be the participants, so that the Form of Largeness, for example, is a thought of individual large things. But it’s unclear how Forms would do what they are supposed to do (e.g. account for sameness in difference) if they are merely thoughts of individual things. Additionally, if τούτων is meant to refer to something other than the Forms, Socrates would seem to be anticipating Parmenides’ objection to his suggestion, that thoughts are of something.

  5. 5.

    The following discussion of how the LESA and TMA threaten numerical and predicational unity is heavily indebted to the argument in Curd (1986).

  6. 6.

    One problem involves the coherence of considering the Forms to be predicational unities at all. While the Form of Largeness indeed cannot be small or blue, it should be a magnitude. Or while the Form of Greenness cannot be wise or triangular, it is surely a colour, and Justice, in addition to being just, surely is a virtue. It appears in these cases that each Form holds more than one predicate. For a discussion of predicational unity in Plato, see Curd (2004, 228–240). This issue is difficult to adjudicate, but we might still consider the Form of Justice, for example, to be a kind of predicational unity by thinking of it as somehow encoding the properties that are implied by or contained in the property of being just, such as the property of being virtuous. Because one implies the other, we might wonder if it is a true threat to unity. Here, we might also consider Meinwald’s (1991) characterization of pros heauto predication, which she describes as a kind of genus-species tree: “In such a tree, a kind A appears either directly below or far below another kind B if what it is to be an A is to be a B with certain differentia (or series of differentia) added. That is, the natures of A’s and B’s are so related that being a B is part of what it is to be an A.” (68). That justice is a virtue, or that Largeness is a magnitude would be a kind of pros heauto predication. Since these distinctions in modes of predication are primarily introduced in the second half of the Parmenides (starting at 137e4, after the TMA) it is plausible that it signals a revision or refinement of the theory, motivated by the problems raised with respect to predicational and numerical unity in the first half of the dialogue.

  7. 7.

    Cornford (1939) and Helmig (2007) take the active reading, citing the “νόημα…νοεῖ” locution and the Neoplatonic interpretation of the νόημα in this text as active at Proclus in Parmenides. IV 891.22–899.2. See below for a discussion of this. Allen (1983), pp. 147–157 assumes that it has an active sense in [B], also citing the “νόημα…νοεῖ” locution” and a passive sense in [C], though he never argues for this reading, and takes [B] and [C] to constitute one continuous argument.

  8. 8.

    We might consider unity to be a feature that Forms must have owing to the objectivity they provide as explanations, but this would be a strained reading of this section of text.

  9. 9.

    A second piece of evidence that is used in favour of the active reading is the Neoplatonic interpretation of the νόημα in this text as active at Proclus in Parmenides IV 891.22–899.2. I will not discuss the Proclus argument in my paper, because it is equally plausible that the Neoplatonists imported their own interpretive idiosyncrasies, and there is little reason to take their word on Plato to be decisive or authoritative.

  10. 10.

    Gerson (1999) writes, “The locution τὸ νόημα νοεῖ understandably compels some translators to render νόημα ‘thought’. Nevertheless, thoughts do not think any more than do concepts. Minimally, the locution may be understood as indicating merely that there must be some object of thought or something that a concept must be of” (66).

  11. 11.

    The issue that confronts us in the text behind B3 is that the invalidity of inferring extra-mental objects from thoughts was well-attested before Plato in the texts of Gorgias of Leontini, who asserts that we cannot infer from the mere thought of a chariot being driven over the sea that there is actually such a chariot (DK 82B3). See the discussion in Caston (2002). We can avoid attributing an invalid inference to Parmenides by reading νόημα as a content and taking ‘something that is’ not as a straightforward existential claim, but as a reference to the Forms. It can be taken to assert that there are no empty concepts; for everything of which there is a genuine concept, there is a corresponding Form. The trouble, which is alluded to by Parmenides at 130a–e, is that the extent of the Forms is unclear. Socrates denies that there can be Forms of natural kinds, mixtures, and things like mud or hair. Nevertheless, we do seem to have thoughts of human, and of water, for example. If there are no Forms of these things, how, then, can we have the thoughts? The answer will require an account of concept-formation in Plato, which is beyond the scope of my paper. However, we might simply consider our concepts of things that lack Forms as lacking the important kind of unity that they should have in order to be useful by any measure (i.e. the unity that makes them objective and shareable). I discuss this further in Sect. 4.

  12. 12.

    Another way of putting this is, per Cherniss (1944, 216–6 n. 128), “[Forms are] the objective correlates of the mental concepts…”.

  13. 13.

    Helmig (2007, 324) claims that “This object of thought, which is identified with the Form, is a unity because it is unified by thought.” This strikes me as an implausible reading of Parmenides’ final question in (b). The oneness clearly belongs to the extra-mental object of the thought. Helmig’s reading treats the oneness of the Form as a feature of the mind rather than as an inherent feature of the Form, which I disagree with. Forms have an inherent unity independent of thought.

  14. 14.

    See, for instance, Allen (1983).

  15. 15.

    See also Gill and Ryan (1996, 39), Miller (1986, 54–55), and Rickless (2007, 75).

  16. 16.

    As other commenters have remarked, ἀνόητα is ambiguous and can mean ‘non-thinking things’, ‘unintelligent’ or ‘silly’. Since here, it is in opposition to νοεῖν, with Cornford (1939) and Helmig (2007) I take it to have the sense of ‘non-thinking’. Allen (1983), pp. 156–157 claims that ἀνόητα can be understood as passive: “thoughts in things that do not think are unthought or unthinkable.” and later claims that the two possibilities in C3 should read: “if Ideas are thoughts, other things that partake of characters either all think, or do not think and are unthought or unthinkable”. Allen does not explicitly state this, but I am assuming that the reasoning here is that if something has a thought (in the passive sense) in it, then it is a thinking thing. But this seems to me to be asymmetric—if the Form is a thought in the passive sense, then the thing participating in it should also be a thought in the passive sense. Otherwise, it sinks back into an active reading.

  17. 17.

    See Helmig (2012, 14) for discussion and a more complete list.

  18. 18.

    One recent attempt can be found in Helmig (2012). Helmig’s core project is, rather than to carve out a Platonic account of concepthood, to argue that for Plato, concepts are formed by knowledge of the Forms, so that concepts are always understood in relation to Forms, as the contents of Forms. At pages 16–23, Helmig prefaces his project by setting some criteria for concepthood, but his approach to building this list of criteria is imported from contemporary assumptions about concepts. This approach is understandable, because in the absence of any explicit evidence in Plato for what concepts are, such a study is doomed to failure from the start. However, my view is that we can aim to be more optimistic about the possibility of discovering a Platonic account of concepthood.

  19. 19.

    I do not think that there is motivation to take the νοήματα in 132b–c as abilities or as Fregean senses. In our contemporary vocabulary, the view here looks like it amounts to the notion of a concept as a mental representation of some kind, as described above.

  20. 20.

    I intend for (1)–(5) to constitute necessary and jointly sufficient criteria for concepthood.

  21. 21.

    Translation by White (2007).

  22. 22.

    Six of them are found at 231c9–e6. The seventh is stated at the end of the dialogue at 268c–d.

  23. 23.

    Taylor (2006) argues that this represents a shift in Plato’s thought, from the view of philosophy as the Socratic practice represented in the earlier dialogues to a view of philosophy as a comprehensive knowledge of reality. The failure to distinguish between sophistry and philosophy in this dialogue is a deliberate way of describing Socrates’ approach to doing philosophy as sophistry. Brown’s response is that this reading too readily accepts the starting assumption that sophistry is a τέχνη.

  24. 24.

    This is not to claim that it is explicitly denied anywhere in the corpus that sophistry has a Form, but I do believe that it is implied in the Gorgias, as cited above.


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I thank Kelly Arenson, Zach Blaesi, Beatriz Bossi, Doug Campbell, Victor Caston, Matt Evans, Jerry Green, Jim Hankinson, Natalie Hannan, Alex Mourelatos, Rachel O’Keefe, and Galen Strawson for helpful comments and discussions, as well as the audiences at the Pacific APA 2019, the NYU-Columbia Graduate Philosophy Conference, and the UT-Austin Dissertation seminar, who helped make this paper better.

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Correspondence to Sosseh Assaturian.

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Assaturian, S. What the forms are not: Plato on conceptualism in Parmenides 132b–c. Philos Stud 177, 353–368 (2020). https://doi.org/10.1007/s11098-019-01396-9

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  • Ancient philosophy
  • Plato
  • Metaphysics
  • Theory of forms
  • Concepts
  • Conceptualism