Forms and Physics in Plato's Timaeus Iain K. Laidley Brown University Department of Philosophy May 15, 2018

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Forms and Physics in Plato’s Timaeus Iain K. Laidley Brown University Department of Philosophy May 15, 2018

This dissertation by Iain K. Laidley is accepted in its present form by the department of Philosophy as satisfying the dissertation requirements for the degree of Doctor of Philosophy.

Date______Mary Louise Gill, Advisor

Recommended to the Graduate Council

Date______Justin Broackes, Reader

Date______Colin Guthrie King, Reader

Approved by the Graduate Council

Date______Andrew G. Campbell, Dean of the Graduate School

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Iain Laidley AOS: Ancient Philosophy AOC: Metaphysics, Early Modern Philosophy

Languages (spoken): English Languages (read): French, Ancient Greek

Education: Ph.D., Brown University (current) Philosophy Expected defense date: May 2018 Dissertation: Forms and Physics in Plato’s Timaeus I give a systematic account of Plato’s late Theory of Forms, the theory as it appears in his Timaeus. I argue that Forms are geometrical or mathematical objects; the only Forms are those that can be characterized in terms of numbers or ratios. Committee: Mary Louise Gill (chair), Justin Broackes, Colin King M.A., Carleton University (2012) Philosophy with Highest Honors Thesis: The Problem of Parmenides (Supervisor: Annie Larivée)

B.A., Simon Fraser University (2010) Humanities

Primary instructor, Brown: PHIL 0350/CLAS 0150 Ancient Philosophy Fall 2017 PHIL 0350/CLAS 0150 Ancient Philosophy Fall 2016

Talks: North American Workshop in Platonic Philosophy (2017): Plato’s Unified Theory of Representation COVE Conference (2011): The Unity of the Virtues in Parmenides

Teaching Assistant, Brown: PHIL 0360 Early Modern Philosophy Spring 2015 PHIL 1660 Metaphysics Fall 2014 PHIL 0060 Modern Science Human Values Spring 2014 PHIL 0350 Ancient Philosophy Fall 2013

Teaching Assistant, Carleton: PHIL 2005 Greek Philosophy and the Western Tradition Fall 2011-Spring 2012 (Instructor: Annie Larivée) PHIL 1600 History of Philosophy Fall 2010-Spring 2011 (Instructor: Iva Apostolova)

Guest Lectures: PHIL 1660 Metaphysics (Brown): ‘Impossible Worlds’ (Instructor: Nina Emery) PHIL 1600 History of Philosophy (Carleton): ‘Aristotle’, ‘Hume’ (Instructor: Iva Apostolova)

Awards: Open Graduate Program Fellowship, Brown University (2015-present)

Ontario Graduate Scholarship (2012) declined Presidential Medal Runner-up, Carleton University (2012) Excellence in Teaching Award, Carleton University (2012) Departmental Scholarship, Carleton University (2010-2012) Full Entrance Scholarship, Simon Fraser University (2006)

Service: Department Representative, Sheridan Center for Teaching and Learning (2016-present) Organizer, Summer Immersion Program in Philosophy at Brown (2017) Graduate Mentor, Summer Immersion Program in Philosophy at Brown (2015-16) Graduate Student President, Department of Philosophy (2014-16) Organizer, Mark Shapiro Graduate Conference (2015)

PREFACE AND ACKNOLWEDGEMENTS

Timaeus’ kosmos is a work of craft. We know this because it’s beautiful and structured, displaying regularity and order. What follows, too, is strictly speaking also a work of some technē; tragically, our only evidence of this is (unreliable, partial) testimony.

This dissertation has benefited from the patient and repeated contributions of any number of people, all of whom at one point or another had to overcome my stubbornness and attachment to some part of the view or another. They include the members of the Ancient Philosophy Reading Group, the long-suffering members of Brown’s dissertation workshop, and an (incredulous) audience at the North American Workshop in Platonic Philosophy at Hamline. The middle chapters especially benefitted from Justin Broackes’ careful reading and his drawing out of interesting connections (and difficult objections).

By far the greatest bulk of the labor, though, was performed by Mary Louise Gill, who read draft after draft (after draft) of ill-conceived material and sorted, if not the gold from the stone, at least the wheat from the chaff. Her patient (and persistent) commentary is responsible for most of what is intelligible of what follows. What isn’t is purely mine.

Finally, my cats, Juno and Sobe, were no help at all.

TABLE OF CONTENTS Introduction ...... 1 Chapter 1: The Theory of Forms before the Timaeus ...... 4 Parmenides, without the problems...... 6 The Scope of the Theory of Forms ...... 16 Chapter 2: Before there was anything ...... 27 Discordant and Disorderly Motion ...... 28 Forms in the precosmos ...... 35 An interlude on the nature of precosmic motion ...... 40 Precosmic teleology ...... 45 On the possibility of material explanation ...... 47 Possibility and Matter ...... 50 A note on cosmic motion ...... 54 Platonic Explanation: What Simmias should have said to Socrates ...... 55 Chapter 3: Plato’s Unified Theory of Representation ...... 57 A note on imitation and representation ...... 59 Statues in the Sophist ...... 61 Good names and bad: the semantics of the Cratylus ...... 65 The Wax Block and Memory ...... 76 Mirrors, shadows, and eidōla ...... 85 Some concluding remarks on the underlying theory of representation ...... 88 Chapter 4: The Geometry of Forms ...... 92 The argument from representation ...... 93 Interlude I: The Living Thing and the World of the Forms ...... 106 Taking Self-Predication Seriously ...... 110 The Likeness Regress: Parmenides Returns ...... 112 Interlude II: Representation and change ...... 115 Rationalist physics ...... 117 Timaeus’ physics ...... 122

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Conclusion: on geometrical paradigmatism and natural philosophy ...... 138 Works Cited ...... 142

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INTRODUCTION In the Phaedrus, Socrates suggests that proper philosophical methodology consists in both being able to collect apparently disparate kinds together and to divide them. On collecting, he says:

[Collection] consists in seeing together things that are scattered about everywhere and collecting them into one kind, so that by defining each thing we can make clear the subject of any instruction we wish to give (265d, Nehamas and Woodruff trans.).

One part of the philosopher’s job is to recognize commonality and to discern one thing where we might have initially thought that there were many. We can see this at work in the Meno: when

Socrates asks for a definition of virtue, he criticizes Meno for giving him not a definition – a single thing – but instead a ‘swarm’ of examples (72b). But we must be cautious in our collection to discern only those kinds that actually are and not to conflate them with others. Coining one of his most famous images, Socrates says:

[Division] is to be able to cut up each kind according to its species along its natural joints, and to try not to splinter any part, as a bad butcher might do (265e, Nehamas and Woodruff trans.).

When we think ourselves to be discerning a single thing, we must make sure that it is indeed one: that we haven’t confused justice for courage (or, in more contemporary language, we must make sure we’re talking about green and not grue).

In what follows, I will argue, roughly, that Timaeus successfully philosophizes in the

Phaedrus sense: he discerns the kinds – posits Forms – where they belong and nowhere else.

These Forms will not, I argue, be the Forms that we recognize from Socrates’ investigation into

virtue: they will not (primarily) be Justice and Courage and Moderation.1 Instead, these Forms are what I’ll call geometrical: they are mathematical entities that are posited as analyses of fundamental physical magnitudes.2 And they are the only Forms that Timaeus requires in his natural philosophy.

We’ll find that positing exclusively geometrical Forms, given certain auxiliary assumptions, leaves us with an explanatory problem.3 If Forms have their own features, and all the Forms are geometrical, how is it that we’re meant to explain all of those obviously non- geometrical parts of our experience? The old Socratic Forms like Justice don’t seem particularly triangular. And furthermore, how could a Form – an entity outside of time and space – be hot or red or large in the same way that a fire, an apple, and an elephant are, respectively? I’ll argue that we can discharge both of these explanatory burdens by introducing the Receptacle, the ‘third kind’, into our ontology (Tim. 49a). It is by the addition of the Receptacle’s explanatory powers that we can get from purely Formal, geometrical Heat to heat as we experience it in coffee or on a summer day.

Any Theory of Forms must answer at least three questions: 1) what is the relationship between Forms and the sensible world such that the Forms can do explanatory work in the sensible world; 2) what are the Forms, anyway; 3) what Forms are there? The above answers the third question. But I will also be arguing for answers to the first two. The participation relation – the relation that obtains between the Forms and the sensible world such that the Forms can explain sensible things – is a representation relation in the Timaeus, in a strict sense that I will

1 Though we will see that in principle such Forms can be analyzed in terms of the kinds that Timaeus posits: cf. Tim. 42b-d, for instance.

2 So, for instance, consider the case of fire, analyzed as several sorts of tetrahedra at 56a.

3 Our chief assumption, one for which I’ll argue at length, is a strong version of Self-Predication: the claim that Forms have their own proper features in the same way as the sensible things that participate in them do. That is, Beauty is beautiful in the exact same way – though perhaps to a different degree – that Helen is.

clarify in the third chapter. And as such, I’ll argue, Forms are models or paradigms: they are

(roughly) perfect instances of their own proper features. Taken together, then, I will argue for geometrical paradigmatism about the Forms.

In chapter one, I take up the three questions in the previous paragraph at greater length and sketch the possible responses we might have to them. In chapter two, we turn to the Timaeus and note that the Receptacle seems to play an independent explanatory role, one whose powers cannot be reduced to those of the Forms or to the Demiurge. In the third chapter, looking to the

Sophist, Cratylus, and Theaetetus, I argue that Plato has a notion of representation well-suited to standing as the participation relation that is remarkably consistent throughout the dialogues and is used to explain common features between disparate sorts of things. And finally, in chapter four, I bring the material of the previous chapters together in order to muster the argument for geometrical paradigmatism.

Surely anyone with any sense at all will always call upon a god before setting out on any venture, whatever its importance. In our case, we are about to make speeches about the universe – whether it has an origin or even if it does not – and so if we’re not to go completely astray we have no choice but to call upon the gods and goddesses, and pray that they above all will approve of all we have to say, and that in consequence we will, too (27c-d, Zeyl trans.).

CHAPTER 1: THE THEORY OF FORMS BEFORE THE TIMAEUS

It seems to me that if some other thing is beautiful besides the Beautiful itself, it will be beautiful on account of nothing other than because it partakes of that Beautiful’ (Phaedo 100c4-6).

Socrates, on the last day of his life, affirms his commitment to the Theory of the Forms. He has engaged in dialectic trying to characterize these Forms, eschewing the explanations of natural science. And he has, at least as a character in Plato’s dialogues, been remarkably dogged in this pursuit; we see it, or versions thereof, espoused throughout the corpus. It’s at work in his extended quotation of Diotima in the Symposium, in which she says of Beauty:

First, it always is and neither comes to be nor passes away, neither waxes nor wanes. Second, it is not beautiful this way and ugly that way, nor beautiful at one time and ugly at another, nor beautiful in relation to one thing and ugly in relation to another; nor is it beautiful here but ugly there, as it would be if it were beautiful for some people and ugly for others. Nor will the beautiful appear to him in the guise of a face or hands or anything else that belongs to the body. It will not appear to him as one idea or one kind of knowledge. It is not anywhere in another thing, as in an animal, or in earth, or in heaven, or in anything else, but itself by itself with itself, it is always one in form; and all the other beautiful things share in that, in such a way that when those others come to be or pass away, this does not become the least bit smaller or greater nor suffer any change (Sym. 211a2-b4).

True Beauty, Diotima says, is not a fleeting or fragile thing that depends on bodies or thoughts, on beautiful people and beautiful things. True Beauty is nowhere at all and eternal, grounding every beautiful thing around us.

Socrates also affirms this theory as a young man. He asks of Zeno:

Tell me this: Do you think there to be some form, itself by itself, of Likeness, and to this also some other opposite, which is Unlikeness; and don’t you and I and all

the others which we call ‘many’ partake in these two? And do the things that partake of Likeness come to be like in this way and to the extent that they partake, and the things that partake of Unlikeness come to be unlike, and things that partake of both come to be both? (Parm. 128e6-129a6)

Here too he plays a familiar tune. Likeness and Unlikeness are those things in virtue of which all other things are like and unlike; they, like Beauty, are what explain Helen’s resemblance to her family. And these Forms, in the Parmenides as much as in the Symposium, are themselves by themselves. They are, somehow or another, distinct from the things that they explain.

Though the Socrates of Plato’s dialogues makes use of this sort of explanatory model throughout his life, it is not at all obvious the extent to which he really endorses one consistent theory. More specifically, there seem to be three questions on which he isn’t always fully consistent:

1) Participation: What is the nature of participation, the relation that ties together the world

of the Forms and the world in which we reside?

2) Nature: Closely related to (1), what are the Forms?

3) Scope: How many Forms are there and for what sorts of properties?

In this chapter, I’ll survey the possible answers to these questions on the basis of the Phaedo,

Symposium, Republic, and Parmenides. We need not decide the matter and unearth The Theory of Forms as it stands in Plato’s Middle Period. For our purposes we need only see what the conceptual terrain looks like as we move towards the late dialogues.4 I will contend in later chapters that Plato in the Timaeus endorses a theory that answers our three questions as follows:

1) Participation is a representation relation.

2) Correspondingly, Forms are models or paradigms.

4 Indeed, Socrates expresses agnosticism about the Participation question in the Phaedo, saying that he will not insist on the precise nature of the relationship between Forms and the sensible world at 100d.

3) What few Forms there are can be characterized mathematically.

What any of this means might yet be mysterious and will remain so for at least another chapter.

Before we can understand this theory and why Plato might have settled on it, we need to understand what other options were available to him (and, more briefly, their corresponding flaws). Let us start, then, with the dialogue in which we are most transparently presented with a set of (somewhat undesirable) theories of Forms: the Parmenides.

PARMENIDES, WITHOUT THE PROBLEMS

In the Parmenides, a teenage Socrates encounters Parmenides and his student, Zeno. We arrive

(after some narrative framing) in medias res, with Zeno having just finished reading out his famous book. Socrates, naturally, raises a challenge in response. Zeno, he claims, has shown that things in our world have incompatible properties – they’re like and unlike, equal and unequal, and so on (129d). But this is unimpressive: the world in which we live is (apparently) obviously the seat of these sorts of contradictions. What would amaze Socrates is if this were true of

Likeness and Unlikeness, the Many and the One, Rest and Motion: ‘the Forms, themselves by themselves’ (ibid.). The visible things, he says are ‘entwined in multifarious ways’ (129e); the

Forms themselves are, he thinks, not.

Here, then, the Forms are introduced for a specific purpose. Zeno’s strategy is to assume that there are a plurality of things in the world – the contrary of Parmenidean monism – and show that if this is the case then those things must instantiate contrary properties. Socrates is unimpressed by the argument as it applies to the sensible world, preferring instead to take up

Zeno’s challenge in the world of the Forms: Likeness, he thinks, isn’t unlike and the One isn’t many. He rejects monism, then, on the basis of the plurality of the Forms.

Parmenides intervenes here and forces Socrates to be more specific. Grant, for the sake of argument, that Likeness and One and Rest exist by themselves, separate from our world. This raises a whole host of questions, the questions in which we’re interested here. How are they related to the things in our world that are like and one and at rest? And what are these separate things, anyway? Socrates and Parmenides work together to work out some possible answers to these questions. Those will be our focus.5

After hearing Socrates’ opening speech in response to Zeno, the speech that we saw on pages four and five, Parmenides asks Socrates several clarificatory questions:

But tell me this: is it your view that, as you say, there are certain forms from which these other things, by getting a share of them, derive their names — 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? (Parm. 130e-131a, Gill and Ryan trans.)

Answering ‘yes’, Socrates commits himself to three claims: there are Forms; they explain the names of particulars and their natures; they do that explaining by way of the getting a share of relation. For now, we can understand getting a share of loosely; Forms are the sorts of things that can inhere in something else.6

Carrying on, Parmenides proposes, and Socrates agrees, that there are only two ways to get a share of something: getting a share of part of that thing or getting a share of the whole of that thing (131a). He then reduces both options to an absurdity, in arguments that some

5 This recounting of the plot of the Parmenides elides an important passage for our purposes. From 130b-e, Parmenides asks what Forms there are, aside from One and Rest and Likeness. Are there Forms of Good and Justice and Beauty? Fire? Water? Mud? Hair? Socrates’ answer to this line of questioning about the scope of the Forms is equivocal and unconfident. We will take it up below when we consider our third question, where it is obviously germane.

6 I return to an alternative reading of getting-a-share-of in my discussion of Forms as Thoughts below.

commentators have found suspect.7 First: the beautiful and just things cannot get a share of the whole, because then the Form will be separate from itself (131b); it will be wholly in more than one place.8 Socrates objects that a day can be in more than one place at the same time without being separate from itself. There is nothing paradoxical about it being the same day in New

Haven and in Providence. After asking for some clarification, Parmenides replaces the day with a sail, and argues that if we were to place a sail over several people, it is not the whole sail that covers each, but only a part.9 As such, the day analogy will not do; if, as Parmenides claims, the day is relevantly like the sail, and the sail is not wholly in different places but only partially, then the day doesn’t in fact show that a whole can be simultaneously in several places. If sensibles take on Forms as parts, they can’t take on whole Forms on pain of Forms being separate from themselves.

This leaves Socrates on the second horn of the dilemma, holding that just things have only part of Justice as a part. But this too results in absurdity. Take the case of the Form of the

Small. Parmenides says:

Well, suppose one of us is going to have a part of the small. The small will be larger than that part of it, since the part is a part of it: so the small itself will be larger! And that to which the part subtracted is added will be smaller, not larger, than it was before. (131d-e)

The objection comes in two parts. For one, it seems as if the Small will be the largest small thing; every other small thing would have to take on a part of the Small, a part that will

7 Cf. Crombie 1963, Panagiotou 1987.

8 This, of course, makes it an Aristotelian universal. And some (cf. Gill 1996: 27 for instance) think that this means that we have an easy answer to the part/whole dilemma: Aristotle’s. We need not worry about whether Parmenides’ objections are good ones here; our only goal is to clarify the options available to Plato when he writes the Timaeus.

9 This might be an illicit move. We could take day as a calendar day (i.e. April 30th, 2018) or as daylight. A sail is a poor analogy for the first but might be a suitable substitution for the second. See Gill (2012) for more on this.

necessarily be smaller than the whole. But whether or not we think that Forms are strictly perfect instances of their proper features, it seems to strike Parmenides as surprising that the Small should be larger than every sensible small thing. Furthermore, when someone adds a part to something, the resulting whole is larger. Precisely the opposite happens here. By the addition of a part, a sum is made smaller. This, both to Parmenides and to Socrates, seems an absurdity.

We’ve belabored the part/whole dilemma despite being uninterested in its soundness. Our purpose here is to tease out its assumptions and we have ample material with which to do that.

The dilemma relies on at least the following claim: Forms must be the sorts of things that can be parts of the just and the beautiful things in our world. They must, that is, be stuffs (or, if we take the route that Socrates and Parmenides do not fully explore, universals).10

Denyer finds a ‘stuff’ account of Forms in the Phaedo:

Consider the contrast between my ring and gold, the element of which it is made. My ring has parts, a top and a bottom, a left and a right. There are no such parts to gold. My ring is therefore composite and gold is incomposite, just as particulars and forms are respectively said to be (Phaedo 78c7-8) (1983: 316).

He carries on, claiming that once we accept that gold is incomposite and rings composite, more claims from the Phaedo follow. The ring is divisible and the gold indivisible (Phd. 80b2-4); the ring was generated and can be destroyed and gold cannot (80b4, 79d2); the ring can change, and gold ‘is always the same way in the same respects, and never admits of any change in any fashion whatsoever’ (78d5-7).11

10 I mean this (roughly) in Denyer’s (1983) sense: chemical elements like gold. The nature of gold is indivisible, as Socrates seems to want to insist that the Forms are. But despite that, many things are made out of gold.

11 Denyer goes further than claiming merely that this is an available view; he takes it to be the view (315). I have reservations on this point. But the truth of the ‘stuff’ view of Forms is irrelevant for our purposes; we need only see that it is available in the Phaedo and elsewhere.

Denyer’s discussion is helpful in elaborating what Socrates might have in mind in his exchange with Parmenides about parts and wholes. Perhaps he understands Forms as Aristotelian universals. But there is evidence external to the Parmenides that he might be meaning to talk about Forms as stuffs like chemical elements; their natures are indivisible, but they can nonetheless be divided into parts and distributed to sensible objects like rings. We have, then, two possible answers to the Nature question: stuffs or universals.

In response to Parmenides’ raising the specter of the Third Man,12 Socrates proposes a solution that doesn’t require that Forms have their own proper features,13 an assumption upon which the Third Man relies:

But, Parmenides, maybe each of these Forms is a thought…and properly occurs only in minds (132b).

Socrates suggests that Forms are mental objects: they are thoughts (though whose thoughts is left unspecified). And just like my thought of a tiger isn’t liable to bite me, the thought Justice need not be just – or at least not in the same way that the kallipolis is.

This passage at least initially appears to offer a novel answer to the Nature question. But its primary interest, for our purposes, is that Parmenides’ response to it makes use of an assumption about participation: that it follows from the fact that some sensible object partakes of some Form that, somehow, that Form becomes a part of that sensible object. Though this isn’t

12 We need not know much about the Third Man for our purposes; it raises no new answers to the questions we’re considering. There is a vast literature on the topic that we can thus avoid. The modern debate starts with Vlastos (1954) and Geach (1956). See Gill (2012: 35 fn. 43) for a brief overview and 35-39 for a helpful discussion of the topic. Issues related to this debate – particularly, the question of whether and in what way Forms have their own proper features – will feature prominently in chapter four.

13 A Form’s proper features are the features it has in virtue of being the Form that it is: i.e. Justice, just; Likeness, like; Beauty, beautiful. A Form’s ideal features are the features it has in virtue of being a Form (like, for instance, being non-spatiotemporal).

his primary objection, Parmenides thinks that idealism follows from Socrates’ proposal. The argument goes as follows:

1) Assume that all Forms are thoughts, i.e., mental objects.

2) Assume that Helen partakes of Beauty iff Helen has Beauty as a part.

3) Helen is beautiful.

4) If Helen is beautiful, then Helen partakes of Beauty.

5) So, Helen has Beauty as a part.

6) Beauty is a thought.

7) So, Helen has a thought as a part.

8) Generalizing: if all Forms are thoughts, then ‘each thing is composed of thoughts’ (132c).

The only way that we can get the result that Helen – and everyone else – is made out of thoughts is that this is a question of parthood. Distinguish two ways in which we might take a share of something. On the one hand, we might take a share of a piece of cake and have it on the plate in front of us. Despite having a share of it, we wouldn’t say that that cake is (or is yet!) a piece of us. We might also get a share, though, by taking a part of something and making it a part of us: by, say, eating the piece of cake. If Parmenides is looking to get the result that all things are composed of thoughts if Forms are thoughts and all things partake of the Forms, he has to have the second sort of parthood in mind when he’s talking about participation in this passage. This, then, seems like an answer to the Participation question: one way that sensible things might partake of the Forms is by taking them on, somehow or another, as parts.

The next proposal, though, provides novel answers both to the Nature and the

Participation questions:

SOC: Parmenides, what appears most likely to hold is this: these Forms are just like paradigms set in nature, and the others are like them and are likenesses [of

them], and this partaking of the Forms is for the other things nothing other than to being modeled on them. (132c12-d4)

Forms are paradigms or models that are somehow part of nature.14 But this is more than merely being perfect instances of their own proper features. The difference is subtler: they are not in several places at the same time and thus not vulnerable to a version of the part/whole dilemma.

Naturally, then, the sensibles are meant to be copies of these Forms and stand in some sort of representation relation to them. Socrates does not say more about what this relation entails and this, for now, stands as our theory.15 Forms are paradigms; participation is representation.

To get a rough grasp on what this theory entails, though, we must look to Parmenides’ objection to it. His response is highly compressed and leaves quite a lot implicit; I reconstruct

132d-133a below, with additions in order to make the argument valid and marking from where they must have been inferred:

1) All beautiful things partake of the Form of Beauty [Assumption].

2) If x partakes of y, then x is a likeness of y (132d1-3).

3) If x is a likeness of y, then x is like y (132d3-4).

4) If x is like y, then y is like x (132d5-7).

5) Beautiful things are like the Form of Beauty, and the Form of Beauty is like the beautiful

things. [1-4]

6) All like things partake of the Form of Likeness. [Assumption]

7) The Form of Likeness is like the Form of Beauty and the beautiful things. [2-6]

8) The Form of Likeness cannot partake of itself. [Assumption]

14 I do not take this claim to mean that they are part of the empirical world, only that they are uncreated and part of the fabric of reality.

15 Chapter 3 pursues this question in some detail.

9) The Forms of Likeness and Beauty and the beautiful things partake of some Form

Likeness2 (132e6-133a3).

Assume for the sake of argument that there is at least one beautiful thing. Since we’re theorists of the Forms, that beautiful thing, Helen, partakes of Beauty. Participation is representation, so

Helen’s beauty is a representation of Beauty. If Helen’s beauty is a representation of beauty, then her beauty must somehow resemble Beauty. Resemblance is a symmetric relation, so this entails that Beauty resembles Helen’s beauty, too. Once we grant this symmetry, we posit a Form to explain it, a Form of Likeness. Beauty and the beautiful things partake of likeness in virtue of their being like each other. But partaking is being modeled on, which we find entails being like, so Likeness itself is like Beauty and the beautiful things. This fact (allegedly) can’t be explained by Likeness, or so the argument assumes;16 a regress looms.

We learn a little bit more about participation in Parmenides’ (and presumably Socrates’) view here. The most substantive inference is that representation apparently entails resemblance.

Put another way, being a copy of something entails resembling somehow or other.17 And this is further evidence that, if we think that Forms are paradigms or models, they must have their own proper feature in the same way that the sensible things in our world do: otherwise, we do not get the resemblance relation that this argument requires.

In the chapters that follow, I’ll suggest that the sort of theory proposed here – one on which the answer to the Participation question is ‘representation’ and the answer to the Nature

16 There are, I think, very good reasons internal to a representationalist theory to think that Likeness can’t explain its own being like something else. I consider these in chapter four. For now, we need not worry about the soundness of the objection.

17 This might seem like an obvious inference at first glance. See chapter three for an extensive discussion.

question is ‘paradigms’ – is resurrected in the Timaeus.18 And this is because the language of this theory is all over that later dialogue.19 Consider just one passage:

…of all the things that have come to be, our universe is the most beautiful, and of the causes the craftsman is the most excellent. This, then, is how it [the universe] has come to be: it is a work of craft, modeled after that which is changeless and is grasped by a rational account, that is, by wisdom (29a, trans. Zeyl).

In this passage, we see that the sensible world is a copy of a model, just as Socrates proposes in the Parmenides. The Forms are paradigms and participation is representation (indeed, with a craftsman doing the representing). But this, of course, isn’t evidence that Plato had such a view available to him before writing the Timaeus; it is just an especially clear echo of Socrates’ representationalist account.

The next clearest articulations of the sort of theory Socrates here proposes is in the

Phaedrus:

Justice and self-control do not shine out through their images down here, and neither do the other objects of the soul’s admiration; the senses are so murky that only a few people are able to make out, with difficulty, the original of the likenesses they encounter here (250b, trans. Nehamas and Woodruff).

Here we have all the characteristic talk of a representationalist theory of Forms in the context of a myth about the divine journey of the soul. Justice and self-control have images down in the world in which we live: just and self-controlled things, presumably. Because we’re better attuned to beauty than to justice, though, we’re better at noticing its images; we find them more attractive. Just as a sculptor or a painter might capture the look of a person better or worse, the

18 Obviously, this requires that I think that the Likeness Regress can be overcome. I provide my answer in some detail in chapter four. But, roughly, I take it that we can deny the question that prompts the eighth premise: that there must be some Form that explains Likeness’ being like anything at all. This is because, if Forms are models and the things that partake of them copies, there is simply no question, in terms of models, as to why Likeness is like. It’s the original like thing. It simply is like. Consider the analogous question: why, in terms of models and copies, does Socrates (the living breathing being) have a snub nose? This questioner is confused: there is no answer to this question because Socrates is not a copy but a model.

19 See chapter four for an exhaustive list.

artistic idiom is deployed to describe the relation between Form and sensible. Here in the

Phaedrus then we can see both that Forms are models and sensibles copies and that the relation between them is one very much like artistic representation.

We might also look to the Republic for another instance of a representationalist theory of the Forms. Consider the famous discussion of craftsmen and poets in Book X. After distinguishing the Forms of Bed and Table, Socrates says:

And don’t we also customarily say that their makers [the makers of sensible beds and tables] look towards the appropriate Form in making the beds or tables we use, and similarly in the other cases? (596b, trans. Reeve)

Socrates proposes a picture on which there is a Form of Bed (and Table and Chair and so on).

And what happens when the carpenter is trying to make a bed is that she ‘looks towards the

Form’. This ‘looking’ (blepein) language is, incidentally, precisely the language that Timaeus will use in his discussion of the divine craftsman, the Demiurge. And a natural reading of this passage – though, admittedly, not one that the text forces upon us – is that the carpenter is copying the Form of the Bed, that the Form of the Bed stands to her as the sensible bed stands to the painter (who merely imitates the carpenter’s work).20

Before moving on to the third question, fraught with peril as it is, let us take stock of the possible answers we’ve entertained to the first two. Participation, it seems, has two prominent candidate answers: participation could be closely related to having as a part or it could be representational.21 And we also saw some candidate answers to the Nature question: Forms could be stuffs, universals, mental objects, or paradigms. We need not take a stance here on what the

20 Read this way, the passage sounds rather like Diotima’s ascent at Symposium 211a-d and Phaedo 74a-c, both of which rely on the similarity of Form and sensible.

21 There is a third option, what we might call a ‘presence’ view on which x partakes of y just in case y is with x, somehow. Rickless (2007) finds this at Euthydemus 301a1-8. The view isn’t a serious contender in the Parmenides nor is it particularly well worked-out; we’ll pass it over, here.

Theory of Forms circa Republic, Phaedo, and Symposium holds.22 All we need is a grasp on what options are available – and their rough character – by the time Plato composes the Timaeus.23

THE SCOPE OF THE THEORY OF FORMS

On to our third question: how many Forms are there and for what sorts of properties? Parmenides asks Socrates (recast in direct speech for convenience):

PARM: Tell me. Have you yourself distinguished as separate, in the way you mention, certain Forms themselves, and also as separate the things that partake of them? And do you think that Likeness itself is something, separate from the likeness we have? And One and Many and all the things you heard Zeno read about a while ago? SOC: I do indeed. PARM: And what about these? Is there a Form, itself by itself, of Just, and Beautiful, and Good, and everything of that sort? SOC: Yes. PARM: What about a Form of Human being, separate from us and all those like us? Is there a Form itself of Human Being, or Fire, or Water? SOC: Parmenides, I’ve often found myself in doubt whether I should talk about those in the same way as the others or differently. PARM: And what about these, Socrates? Things that might seem absurd, like hair and mud and dirt, or anything else totally undignified and worthless? Are you doubtful whether or not you should say that a Form is separate for each of these, too, which in turn is other than anything we touch with our hands? SOC: Not at all. On the contrary, these things are in fact just what we see. Surely it’s too outlandish to think that there is a Form for them. Not that the thought that the same thing might hold in all cases hasn’t troubled me from time to time. Then, when I get bogged down in that, I hurry away, afraid that I may fall into some pit of nonsense and come to harm…(130b-d, Gill and Ryan trans.).

22 Though one could and many have. Consider Fine (1993), Rickless (2007), Crombie (1963), Grube (1935), and Taylor (1926) among others.

23 Of course, some – Owen (1953) prominently among them – might want to claim that the Timaeus is in fact prior to the Parmenides, and thus it is part of the cluster of dialogues we’re considering. This view has not won much support; I think Cherniss (1956) has it roughly right when he defends the traditional late dating of the dialogue.

Parmenides proceeds to scold Socrates, claiming that he has avoided this hard question because he is still young and insufficiently philosophical. And he has a real point: Socrates articulates no reason to think that we should on the one hand posit as ‘separate’ Forms of Justice and the Good, and perhaps of Human and Water, but not of Mud and Dirt and Hair.

This, naturally, leads us precisely into the ‘pit of nonsense’ that Socrates tries to avoid.

Consider one possibility, what we can call the Wide Scope view. J. A. Smith articulates it thus:

‘there are just as many Ideas [Forms] as, and no more than, there are groups-of-particulars- called-by-a-common-name’ (1917: 70). For any name we can apply to a group: table, chair, barbarian, not-a-mammal, there is a corresponding Form. And Smith immediately infers what makes this view unpalatable: there are thus Forms for ‘artefacta, negatives, and relatives’ (ibid.).

That is, we don’t just have a Form for each color, but also a Form for not-Red and not-Green and so on. And we might take this as philosophically somewhat offensive: surely, all that it is to be not-Red is to be some other color or no color at all. That simply exhausts the property without having to introduce some further (seemingly epiphenomenal) Form.

The Wide Scope view has been generally quite popular.24 And despite the philosophical misgivings we might have about it, there is substantial textual support for such a view. Consider, for instance, a passage from the Parmenides:

I suppose that this is what leads you to believe that there is one Form in each case. Whenever you think that many things are large, you perhaps think that there is a certain Form, the same in your view of all of them; hence you believe that largeness is one (132a1-4, Cherniss trans.)

24 Fine (1980: 197) cites Ross (1951), Nehamas (1973), Cohen and Matthews (1968) as examples. We may also include Rickless (2007), who holds that ‘[f]or any property F and any plurality of F things, there is a Form of F-ness by virtue of partaking of which each member of the plurality is F’ (16). So has Frede (XX)

On Cherniss’ translation of the passage – a question we’ll return to in a moment – the first sentence seems to encourage Socrates to posit a Form for each predicate, pushing him towards a

Wide Scope account. But we should look carefully at the Greek, here. The first line reads: ‘Οἶμαί

σε ἐκ τοῦ τοιοῦδε ἓν ἕκαστον εἶδος οἴεσθαι εἶναι’. Cherniss has us take the claim to be that there is one Form. But instead of taking the einai to be existential, we could take it attributively, hooking it up to the hen as a predicate (as Gill and Ryan do): ‘I suppose you think each Form is one on the following ground’. Given the context of the passage – we’ve just gotten to the other side of the part/whole dilemma in which we worry about the unity of Forms – the latter reading seems more apt, especially given how the passage ends, on the claim that Largeness is single.

Less equivocal evidence appears in the Republic. In Book X, Socrates says:

As you know, we customarily hypothesize a single Form in connection with each of the many things to which we apply the same name (596a, Reeve trans.).25

The natural reading – one about which we will soon raise some questions – holds that this doesn’t merely imply but straightforwardly states a Wide Scope view. If we posit a Form whenever something has the same name – tauton onoma – as something else, then there must be

Forms for every general term, no matter how artificial. My cats have in common not being dogs; so there must be a Form of not-Dog. Similarly, they’re both smaller than I am. By the same logic: there is a Form of Smaller-than-Iain (-but-bigger-than-a-breadbox). We might well think, then, that there are good grounds, at least in the Republic, for thinking that Socrates endorses a

Wide Scope view.

Even aside from the philosophical reasons that might motivate us to limit the scope of the

Theory of Forms, there are some textual grounds on which we might reconsider it.26 Consider, for instance, a passage from the Statesman:

25 εἶδος γάρ πού τι ἓν ἕκαστον εἰώθαμεν τίθεσθαι περὶ ἕκαστα τὰ πολλά, οἷς ταὐτὸν ὄνομα ἐπιφέρομεν.

…it’s as if someone tried to divide the human race into two and made the cut in the way that most people here carve things up, taking the Greek race away as one, separate from all the rest, and to all the other races together, which are unlimited in number, which don’t mix with one another, and don’t share the same language – calling this collection by the single appellation ‘barbarian’. Because of this single appellation, they expect it to be a single family or class too….But I imagine the division would be done better, more by real classes and more into two, if one cut by means of…male and female, and only split off the Lydians or the Phrygians or anyone else and ranged them against all the rest when one was at a loss as to how to split in such a way that each of the halves split off was simultaneously a real class and a part (262c-263a, Rowe trans.).

Here the Eleatic Stranger seems to recognize precisely what was troubling us (and Smith) about the passage in Republic X. ‘Barbarian’, though not obviously a negative general term on its surface, is precisely that: it simply picks out all the non-Greeks. And the Stranger notes as much.

He further points out that it isn’t particularly explanatory to take the barbarians to be a single kind: the only thing they have in common is what they’re not, lacking any common language or culture. They are not, he argues, a single genus or class. ‘Barbarian’ does not pick out a real kind; there is not, we should think, an associated Form. So, contra our first reading of Republic

X, Plato might have the resources to limit the scope of his theory.

This passage from the Statesman leads Fine to pursue another reading of Republic X, one that doesn’t require of us that we posit negative Forms. Smith proposes an alternative translation, on the grounds that the standard reading requires that the relative clause, starting with the hois just after the comma, be general in a way that the Greek doesn’t seem entirely to support: ‘for we are, as you know, in the habit of assuming [as a rule of procedure] that the Idea which corresponds to a group of particulars, each to each, is always one, in which case [or, and in that case] we call the group of particulars by a common name’ (70). Much Cherniss’ evidence in the

26 The discussion here will follow Smith (1917) and Fine (1980) closely.

Parmenides, then, 596a could be read not as a positing of some Form for each possible group of sensibles, but as asserting the oneness of those Forms that we have already posited for a genuine group.

Fine proposes a different solution that focuses on the tauton onoma at the end of the line.27 She suggests that we understand onoma not to be the unrestricted, general ‘term’ or

‘word’, but instead a special restricted sense on which some word is a name only if it ‘denotes a real property or kind’ (214).28 On this view, ‘barbarian’ isn’t really a name at all; it doesn’t denote a genuine kind, as the Eleatic Stranger argued. And if a word doesn’t denote a genuine kind – a kind that cuts nature at the joints – then there is no associated Form. If we restrict our reading of 596a in this way, we get her 1d (ibid.):

Whenever a group of particulars are property-named “F”, some one property, the F, is predicated of them.29

Though this doesn’t itself fix the scope of the theory of Forms, it does give us some wiggle room by undermining the primary textual evidence for the broad scope view. That is: it is still a question, if Fine’s (or Smith’s) reading of 596a is correct, just what Forms there are. The question of whether something is aptly named just reduces to the question of whether there is a

Form for the property predicated of it.

If we are not forced to a wide scope view, the sort of view that Parmenides seems to be pushing upon Socrates at the start of the Parmenides, it’s worth seeing what other options are available to us. Fine (1993), building on her 1980, gives us two more options: the realist and

27 Smith (71) notes a similar solution but doesn’t pursue it at length, preferring instead to focus on the relative clause.

28 Fine’s argument for understanding onoma this way doesn’t matter much for our purposes, but she takes it that a reading of the Cratylus (esp. 387d6ff) that she defends in Fine (1977) can give us the result she’s making use of here.

29 ‘Property-named’ is just her technical sense of onoma: something is property-named just in case it has a genuine property predicated of it.

semantic conceptions of Forms (21). A realist about Forms holds that they are posited ‘for various explanatory purposes. On this view, not every meaningful predicate denotes a universal, since not every meaningful predicate denotes an explanatory property’ (22). Take, as she does,

Goodman’s ‘grue’, which ‘applies to all things examined before t just in case they are green but to other things just in case they are blue’ (1965: 74). A natural way of glossing what’s suspicious about this property is that it doesn’t explain much of anything at all: blue and green do the trick just fine. The realist, presumably, will disqualify the Form of Grue on these grounds.

The semantic conception, though broader than the realist, is not as permissive as the traditional wide scope theory. Forms, on this view, just are meanings (1993: 22); they’re discovered not by pursuing explanations, but ‘by asking what general terms are meaningful

(ibid.). This, of course, pushes back the question: what makes some general term meaningful?

Fine proposes two possible accounts: (i) some general term is meaningful just in case competent speakers of the language ‘understand it or can easily be brought to understand it’ or (ii) some general term is meaningful just in case there are some entities picked out by that general term

(and we answer that further question with reference to the linguistic intuitions of ordinary speakers) (ibid.).

We can illuminate the contrast between the semantic and realist views by thinking about how we might get at Forms for each camp. The realist – someone like Armstrong (1978), for instance – would have us get at Forms by doing natural science. Whatever properties the natural scientist needs in order to have her theories explain the world are the properties a theory of

Forms ought to countenance. The semantic theorist does not require that natural science should so limit our ontology. Imagine that we discover that we can do science without positing macro- level animals like dogs: the predicate ‘dog’ doesn’t do any explanatory work. The realist says:

‘well, there’s no Form of Dog, then!’ The semantic theorist, though, maintains that there is such a Form; even though science doesn’t require one, it is still an easily recognizable (and useful) term in our language.

Sometimes, Plato’s Socrates seems very much like a realist.30 Consider the Euthyphro. In

Socrates’ interrogation of the titular character, he scolds him for giving him examples of piety rather than a general account:

Bear in mind then that I did not bid you tell me one or two of the many pious actions but that Form itself that makes all pious actions pious [τὸ εἶδος ᾧ πάντα τὰ ὅσια ὅσιά ἐστιν], for you agreed that all impious actions are impious and all pious actions pious through one Form, or don’t you remember? (6d, Grube trans.)

Socrates uses the instrumental dative to refer to the Forms, here: it is by the Form of Piety that pious things are pious and impious ones impious. This isn’t asking Euthyphro about the meaning of the term ‘piety’ or pursuing a semantic question; Socrates and Euthyphro have agreed that there is some entity that explains the facts about piety and impiety, and Euthyphro’s job – he’s the expert in piety, after all! – is to help Socrates to find it.

The Euthyphro is by no means an isolated incident of realism. We can see it too in the

Meno:

The same is true in the case of the virtues. Even if they are many and various, all of them have one and the same Form which makes them virtues [δι’ ὃ εἰσὶν ἀρεταί], and it is right to look to this when one is asked to make clear what virtue is (72c- d, Grube trans.).

Socrates doesn’t use the instrumental dative here. Instead, he uses the preposition dia to capture roughly the same meaning: it is by some one Form that all virtuous things are virtuous. And when we are in pursuit of accounts and explanations, he adds, we would do well to look to this

30 And indeed, my view is that Timaeus defends an odd sort of realism.

Form. If Forms play this role – if they are the things that make pious things pious and virtuous things virtuous – then Socrates is a realist in Fine’s sense.

Indeed, even in places where Socrates is being epistemically modest about the status of the Theory of Forms, he seems to endorse what looks like a realist conception. He says:

I simply, naively and perhaps foolishly cling to this, that nothing else makes it [any beautiful thing] beautiful [ὅτι οὐκ ἄλλο τι ποιεῖ αὐτὸ καλὸν] other than the presence of, or sharing in, or however you may describe its relationship to that Beautiful we mentioned, for I will not insist on the precise nature of the relationship, but that all beautiful things are beautiful by the Beautiful [ὅτι τῷ καλῷ πάντα τὰ καλὰ [γίγνεται] καλά]. That, I think, is the safest answer I can give myself or anyone else (Phaedo 100d, Grube trans.).

In the Phaedo passage, Socrates is happy to say that he doesn’t really know what relation obtains between the Forms and the sensible world. But he does know that it is Beauty that makes for beautiful things; Beauty is the explanation of certain real-world facts.

The evidence for a semantic conception is thinner and depends upon some controversial interpretations of certain passages. Consider just two for our purposes. First, after Parmenides has finished presenting his objections to Socrates, he suggests that Socrates should still pursue a theory of Forms, even if it isn’t one of the ones that they have been discussing:

…if someone, having an eye on all the difficulties we have just brought up and others of the same sort, won’t allow that there are Forms for things and won’t mark off a Form for each one, he won’t have anywhere to turn his thought, since he doesn’t allow that for each thing there is a character that is always the same. In this way he will destroy the power of dialectic entirely (135b-c, Gill and Ryan trans.).

As translated by Gill and Ryan, this passage doesn’t seem particularly germane to the semantic/realist debate. However, Cornford interprets the closing line differently. What Gill and

Ryan translate ‘In this way he will destroy the power of dialectic entirely’ reads in the Greek:

οὕτως τὴν τοῦ διαλέγεσθαι δύναμιν παντάπασι διαφθερεῖ. At issue is how to translate the

articular infinitive tou dialegesthai. While Gill and Ryan take it as the technical term for dialectic, having the claim amount to ‘philosophy is impossible without Forms’, Cornford would prefer it be taken in its broadest possible sense: meaningful discussion is impossible without

Forms (1939: 100);31 without them, there is nothing onto which we can fix reference. But surely, such an argument goes, a realist conception of Forms wouldn’t get us this result. Assume that our scientific theories, whatever their verisimilitude, are broadly false. The realist, as a consequence, wouldn’t really know what Forms to posit; she doesn’t know what the properties are that we need in our final and complete scientific explanations. And this seems roughly to capture our situation: no one thinks we have a final and complete fundamental physics. That said, we seem perfectly able to converse nonetheless; there are entities onto which we can fix reference. So,

Forms must have something to do with meanings, not with explanations; we haven’t discovered the properties for which the realist would have us posit Forms but are still able to have meaningful discussions.32

A similar argument – again, on Cornford’s (1935) view – occurs in the Theaetetus. From

181-183, Socrates tries to refute the radical Heraclitean, again on the grounds that language wouldn’t be meaningful if Heracliteanism were true.

We were most anxious to prove that all things are in motion, in order to make that answer come out correct; but what has really emerged is that, if all things are in motion, every answer, on whatever subject, is equally correct, both ‘it is thus’ and ‘it is not thus’ – or if you like ‘becomes’, as we don’t want to use any expressions which will bring our friends to a standstill (183a, trans. Levett and Burnyeat).

31 It doesn’t much matter which translation of tou dialegesthai is correct for our purposes. Again, we are just countenancing all the possible theories.

32 I am suspicious of this argument. The realist could well say that there’s an indirect reason we couldn’t talk: nothing would be true of anything, so everything we’d say would be nonsense or false. We need not pursue this further; we’re just setting out the options.

Cornford glosses this passage thus. If all things are changing in every way, then language ‘can have no fixed meaning’ (1935: 99); the reference of our terms will continually change, and we will thus be rendered unable to communicate. We need Forms, knowable entities, that can be the subjects of stable truths. Here too, Cornford might contend, we need some close relationship between meanings and Forms. Forms, after all, are meant to fix the contents of language. And realism, a semantic theorist might argue, doesn’t guarantee a link between language and the

Forms.

So, we’ve seen two alternatives to the standard wide scope theory of Forms: a realism on which we use the Forms to ground our scientific (or natural philosophical) explanations, or a semantic conception on which Forms are the meanings of general terms. I’ve expressed some reservations about the semantic conception; it seems plausible that realism can countenance the close relationship between language and explanatory Forms however it is we choose to translate the tou dialegesthai of the Parmenides.33

The theory I’ll defend in chapter four chooses versions of the answers we’ve countenanced here:

1) Participation: it’s representation.

2) Nature: Forms are models or paradigms.

3) Scope: A strange sort of (mathematical) realism.

I won’t defend these choices in this chapter; we will save that for later. However, we’re now in a better position to appreciate the significance of these answers by way of the contrasts:

33 There are questions on which this taxonomy is silent. So, for instance, are there Forms for properties like being five-foot-six? The realist conception and the semantic conception can each answer either way, here. If 5’6 plays an indispensable role in our explanatory theories, then there’s a Form on the realist view. If 5’6 is a meaningful general term – and it probably is – then the semantic theorist should say that there is such a thing. The view I defend in chapter four will probably entail that there’s no such Form.

participation could well be taking on as a part, Forms could well be stuffs, and the scope of the theory could be very (very!) wide. But, as I’ll argue in what follows, none of this is the case:

Timaeus ends up endorsing a representationalist Theory of Forms, what I will call a geometrical paradigmatism.

CHAPTER 2: BEFORE THERE WAS ANYTHING

The distinctive core of the Theory of Forms, as Socrates deploys it, goes as follows. Forms, non- spatiotemporal objects that anchor the properties of sensible things, explain. And there is no other explanation for these phenomena — or at least, no other explanation that is as good.34

Perhaps a sculpture’s beauty could be explained causally, with reference to its sculptor and her skill. But this story, Socrates thinks, must bottom out in the Forms if it’s to have any explanatory power at all.

It will be my concern in this chapter to show that Plato modifies this account of explanation. A version of this view is not altogether uncommon. Many people think that the

Timaeus provides the sorts of teleological explanations that Socrates expected in his youth to receive from Anaxagoras (Phaedo 97b-98b).35 And he does; the initial ordering of the kosmos is teleologically organized, grounded in the intentions and goals of the Demiurge. He set things up as he did because that was best, just as he expected Anaxagoras’ Nous to do. But this does not fully capture the distinctive explanatory structure of the Timaeus, a structure that is not exhausted by teleology or by Forms. Timaeus offers explanations that bottom out in the nature of matter. This is not to say that Plato abandons the Forms or somehow deflates them.36 But they do

34 We can see this in the Phaedo passage with which we started the previous chapter: 100c4-6. There, Socrates says that it is on account of nothing other than Beauty that any beautiful thing is beautiful.

35 This includes Johansen (2004), Zeyl (2000, 2009).

36 To see this, we need look no further than the start of Timaeus’ speech. He claims that one must distinguish (diaireteon) ‘what always is and does not have becoming, and what always is coming to be, but never is’ (27d5- 28a1). This is of course the common distinction between Forms and particulars.

not anchor every explanation, and not just because they are the objects to which the Demiurge looks.

The first part of this chapter will be concerned with establishing the negative thesis: that there is at least one property in the Timaeus that is not explained with reference to Forms or ends.37 To do this, we will look to a set of passages in Timaeus’ speech that refer to a time before the Demiurge constructed the kosmos.38 We will take up the set of issues that Vlastos (1939) raises: whether there are genuine properties in the precosmos, and what explains them if there are. I will argue that we should take the precosmos literally, and, more controversially, that none of the standard explanations — Forms or souls, for example — will explain fully the state of affairs that obtains there, both its obtaining and its nature. In the second part of the chapter, I’ll argue that the best explanation for those phenomena obtaining is one that does not bottom out in the Forms or the Demiurge. There are genuine material explanations.

DISCORDANT AND DISORDERLY MOTION

I will make the following simple argument in this section: Before the Demiurge arranged the pre- existing material into a proper kosmos, there were properties. He did not find unmoving, inert stuff — or indeed nothing at all — before he set to work, but instead a lively, if disorganized, not-quite-world. These properties did not obtain in virtue of some explanatory relation with the

37 By ‘ends’ here I mean specific sorts of ends: the intentions or goals of agents, specifically the Demiurge or some souls.

38 These passages are mired in a famous controversy about whether Plato really thought that there was a time before time. See Sorabji (1983: 268-272) for an overview of the possible answers to this problem. I will argue below that we should take the Timaeus as an honest cosmogony. But I don’t think that, were it merely an image, that would fundamentally change the arguments here. The precosmos would no longer literally exist at a time prior to the kosmos, but presumably it would be in some way prior, explanatorily. Otherwise, it’s not at all obvious what is accomplished by talking about it as if it were temporally prior.

Forms, nor in virtue of the Demiurge’s ends. So, there must be some other explanation available for such properties.39

Let us start with the passages in which Timaeus discusses the precosmic world. Here, I will quote and summarize them, with minimal commentary, appropriate to our (here) modest goal. At 28c6-29b1 Timaeus considers the question of whether the Demiurge looked to a generated or ungenerated model in the fashioning of the universe. He argues:

In relation to which of the two models did the builder make the kosmos? It was either in relation to the one that is in accordance with itself and unchanging or in relation to the one that was in a state of becoming.40 If in fact on the one hand this world is beautiful and the Demiurge good, it is clear that he looked to the eternal one; if however we say something blasphemous, he looked to the one that came to be. It is clear to everyone that he looked to the eternal one; for the kosmos is the most beautiful of the things that have come to be, and it had the best of the causes. Thus coming to be it was made in relation to the model comprehended by reason and wisdom and that holds in accordance with itself.

Two things existed before the Demiurge made the kosmos: a stable unchanging model and one constantly becoming. If the kosmos is beautiful, then the Demiurge must have looked towards the stable model.41 The kosmos is in fact beautiful, and thus its model was the unchanging one.

39 This argument has a suppressed premise: that there must be an explanation of such properties. I have no knock- down argument for this premise, but consider an alternative view, the no-explanation view. This view holds that there is no explanation (in the metaphysical sense, so no grounds or causes) for these precosmic properties. The best way to make sense of such a claim is to say that those properties obtain in virtue of themselves alone (what would it mean, after all, to say that they obtain in virtue of nothing at all, other than to say nothing further?). This is not so different from the view I defend below at all; the explanation in either case bottoms out in matter. This would not be an unhappy result for me.

40 Zeyl takes to gegonos as ‘the one that came to be’; Cornford: ‘that which has come to be’; Taylor: ‘come to be’. I prefer ‘become’. I do this because it’s not the case that Plato thinks that the alternative model to which the Demiurge could have looked came to be in the sense that there was a time such that it didn’t exist. The distinction he makes, just before our passage, is the standard distinction between things that are stable and unchanging and those that are always becoming, or in flux. This is a technical use of to gegonos, and not faithfully rendered by ‘come to be’.

41 Presumably, this is because being structured is an important part of being beautiful. Put simply: the world cannot both be a mess and beautiful, on Timaeus’ view. Plato seems to think there’s a link between structure, stability, and during Diotima’s speech in the Symposium, 211a-d: what makes the Form of Beauty more beautiful than any beautiful thing is partially its eternity. Something similar is defended at Philebus 64d-e, where Socrates says that

Timaeus claims, in setting up this argument, that the Demiurge had a genuine choice. Something exists prior to the kosmos that is always in a state of becoming and is not part of the world of the

Forms. That thing, whatever it is, is constantly changing. Something featureless cannot change; things change with respect to having or lacking certain features. So, there is a precosmos that is constantly undergoing some sort of process of becoming, one that is distinct enough from the world of the Forms that the Demiurge was faced with a genuine choice between paradigms, and it has at least two properties: it has a property with respect to which it can change, and it changes.

Not long after, we get the following short passage.

For the god wanted everything to be good and nothing to be bad so far as possible [kata dunamin], thus taking everything that was visible, not at rest but moving faultily and with disorder, he led it to order from disorder, thinking of this that it is entirely better. (30a2-6)

There are two things we should notice in this passage. It confirms that Timaeus’ Demiurge did not find an inert world ripe for the shaping. Instead, he found matter (or at least: visible stuff) that was in constant unpredictable motion. He orders it in his act of cosmogony, gives it a taxis that it otherwise lacks. He neither creates the matter nor does he breathe life into it; he structures the disorganized, moving matter that antedates his involvement with the kosmos. Second, note the qualification in the first clause: the Demiurge only makes things so good as he can. As is common in the first part of Timaeus’ speech, the Demiurge’s goodness is cited as a reason that something obtains. But despite his good intentions, his materials — the precosmic soup — limit him. They have dispositions that frustrate his efforts to make a perfect kosmos.

At 53a, we are given a more detailed account of precosmic motion.

‘any kind of mixture that does not in some way or other possess measure or the nature of proportion will necessarily corrupt its ingredients and most of all itself’.

That is how at that time the four kinds were being shaken by the receiver, which was itself agitating like a shaking machine, separating the kinds most unlike each other furthest apart and pushing those most like each other closest together into the same region. This, of course, explains how these different kinds came to occupy different regions of space, even before the universe was set in order and constituted from them. Indeed, it is a fact that before this took place the four kinds all lacked proportion and measure, and at the time the ordering of the universe was undertaken, fire, water, earth, and air initially possessed certain traces42 of what they are now. They were indeed in the condition one would expect thoroughly god-forsaken things to be in. So, finding them in this natural condition, the first thing the god then did was to mould them, using forms and numbers. (53a2-b5, Zeyl trans. with modifications)

This passage elaborates on the themes that we saw previously in detail. The precosmic matter — by this point identified with the Receptacle — moves distinctively, separating out its parts from one another, such that (for example) the heavy ones sink to the bottom and the light ones rise to the top. Timaeus cites this motion as an explanation for the arrangement of the universe before it was properly ordered. The disorderly motion takes on some definite character, then.43 And the structure of this shaking motion is a clue to the existence of further precosmic properties.

Whereas the previous passages have suggested that basic matter has locomotive properties, here

Timaeus suggests that there were, before the kosmos, traces of the classical elements. They’re disproportionate and poorly structured; but deficient or not, they are closely related to the elements themselves, those that the Demiurge works up out of fundamental triangles later in the dialogue.

Taking up the question of the elements further, Timaeus says:

42 The word Zeyl translates as ‘trace’ is ichnos, which has as its base meaning ‘track’ or ‘footstep’.

43 That character seems inconsistent with the previous descriptions, though; whereas before, we were told that the motion was without order — ἀτάκτως — now we find that there is some intrinsic structure to the material precosmos, independent of the Demiurge’s intervention. The shaking sorts the precosmic materials such that like is near like. This is at least prima facie evidence that there is some difference between the precosmic kinds that is not mere motion, on which motion acts in sorting it.

To repeat what was said at the outset, the things we see were in a condition of disorderliness when the god introduced as much proportionality into them and in as many ways — making each thing proportional (συμμετρίας) both to itself and to other things — as was possible for making them be commensurable and proportionate (ἀνάλογα καὶ σύμμετρα). For at the time they had no proportionality at all, except by chance (τύχῃ), nor did any of them qualify at all (παράπαν...ἀξιόλογον ἦν οὐδέν) for the names we now use to name them, names like fire, water, and so on. (69b2-8, Zeyl trans.)

Timaeus hits upon familiar themes: the precosmos is somehow disorderly and it lacks proportion.

But he does not repeat the claim about the elements from 53b; instead of suggesting that there were precosmic traces or tracks of the elements, he appears to hold that there were, strictly speaking, no instances of fire or water at all. This impression, though, is not quite correct. The word Zeyl translates as “qualify”, ἀξιόλογος, appends the adjective ‘worthy’ to logos. “Qualify” doesn’t quite capture the sense: “worth being called”, “worthy of the name” do better. This seems to do roughly the same metaphorical work as ἴχνος does; it doesn’t suggest that there are no such entities, but instead that they’re deficiently fire and water and the rest.44

So far, we have very good reason to think that the precosmos is somehow disorderly and in motion. Looking to the final passage of this section, though, we can see clearly that the sense in which the precosmos is disorderly is that it moves in a disorderly way. Speaking of the body of the world, Timaeus says:

In fact, he [the Demiurge] awarded it the movement suited to its body — that one of the seven motions which is especially associated with understanding and intelligence. And so he set it turning continuously in the same place, spinning around upon itself. All the other six motions he took away, and made its movement free of their wanderings (34a1-5).

The kosmos didn’t merely shake before the Demiurge intervened; it moved to the left and to the right, up and down, forward and back. And as part of his process of setting the kosmos into taxis,

44 We will return to this point in the next section and take it up in more detail.

of ordering the precosmic soup into a proper universe, he took all six of those motions away from the body of the kosmos, causing the whole thing to spin in place.45 This passage is explicit: there is motion in the precosmos, and that motion is at least partially constitutive of the disorder spoken of in the other passages. Here too, then, there is a precosmic property. The precosmos moves; moving is a property; thus, there is at least one property in the precosmos.46

This is not uncontroversial. Lee (1966) has argued that despite appearances, the precosmos doesn’t move. Distinguish between ‘substantial’ and ‘insubstantial’ images. A substantial image is an image that has ‘some independent physical identity of their own, a kind of image that can survive the destruction of the original it represents’ (1966: 353). Statues, paintings, and so on all are perfectly capable of enduring longer than their subjects. Insubstantial images, on the other hand, ‘depend for their existence on a continuing relation to their original’

(ibid.). Shadows do not exist without the relevant bodies and the sun. Such insubstantial images do not, he claims, have any independent existences of their own, but are entirely derivative. He argues that due to their derivativeness, such images do not themselves have properties (362). My shadow isn’t, allegedly, six feet long. If the universe is merely an insubstantial image, then it is false, strictly speaking, to say that it is moving.

Insubstantial images do not give us reason to reject my first claim. First, even granting that the universe lacks properties, we cannot avoid something’s being in motion. On Lee’s view, this would be the Receptacle — we are perfectly correct to predicate properties of it. So, this

45 Obviously, things still move in those six ways; my cursor moves to the right as I type this note. But this is a claim about the kosmos as a whole. The whole thing, taken as a set, moved right and up and forwards (into what space where, one wonders) before being set into order.

46 The precosmos is also disorderly, deficient, and instantiates any number of further negative properties. I have chosen motion as our focus because one might deny that negative properties are properties at all. Perhaps being disorderly is just not instantiating being orderly. If that were the case, then this would not require further explanation. It also has some property with respect to which it changes, as we saw earlier. All we need to be true is that there is one property: any others we can find are, for this section, not relevant.

might change the terms in which I cast my argument, but it does not pose a significant problem.

Second, as Gill (1987: 41-42) argues, the text of the Timaeus does not support the distinction between substantial and insubstantial images. We can apparently say that the image both resembles and shares the name of the Forms (52a5). But on Lee’s view, this can’t be right; what’s doing the resembling and name-sharing, really, is the Receptacle. Unless Timaeus is speaking loosely in this important passage, then the text doesn’t support Lee’s reading. Finally,

Lee defends an untenable error theory. My shadow is six feet long, give or take; this is not a property of the sidewalk, barring some further extraordinarily pressing theoretical considerations.

Such considerations are not forthcoming.

Another objector might choose to take precosmic motion as a metaphor. There is a tradition, as Vlastos (1939) points out, of interpreting the disorderly motion of the Timaeus as a myth, or in a way that does not entail that there could be such a thing.47 He provides several arguments against specific versions of the view, but for our purposes a general response will do.

The account of the precosmos seems to do some explanatory work, work that it could not do were it merely a metaphor.48 Timaeus frequently expresses the thought that the Demiurge is somehow limited, prevented from achieving his ends. We can see this, for example, when he says that he wants the kosmos to be like the paradigm kata dunamin at 38c, or for everything to be good and nothing bad kata dunamin at 30a.49 The Demiurge cannot realize his intentions; he is frustrated by the materials with which he is working. And this is a key part of Timaeus’ story.

This is not a perfect world — it is not perfectly good and beautiful, or at least not so good and

47 Vlastos cites, among others, Taylor (1926) Robin (1935), Grube (1935), and Cornford (1937).

48 ‘For what?’, we might ask, if not for something that is in some way — temporally or otherwise — prior to the kosmos.

49 More on these qualifiers below.

beautiful as the Forms. Tradeoffs must be made. So, for example, the hips and arms are surrounded by excess flesh for protection; but those parts of us that are endowed with intelligence cannot ‘accommodate the combination of thick bone and massive flesh with keen and responsive sensation’ (75b), in order that they can, in fact, be responsive to sensory stimulation. Were the world perfect, no such compromise would have to be made. And this fact requires explanation. And the only way to discharge this explanatory obligation is to refer to the properties of the precosmos, taking the discordant and disorderly motion seriously.50

FORMS IN THE PRECOSMOS

There is something, prior to the arrangement of the kosmos, that requires explanation: motion.

The next thing to do, then, is to see what explanations might be available to us in the Timaeus.

The first and most obvious option is to suggest something in the spirit of Phaedo 100c: in some way or another, the Forms do the relevant explanatory work. Proclus defends a version of this view. Commenting on Timaeus 30a, one of the passages in which the Demiurge moves the world from precosmic disorder into taxis, Proclus says:

But it [i.e. the underlying thing, the matter] is that which already partakes of the Forms and has some traces and reflections of them, moving faultily and in disorder. For the image-like and undifferentiated presences of the Forms produce in it diverse motions. (Proclus Comm. on Tim. vol 1, 118a2-5)51

50 It seems to me that, of the reasons Vlastos cites to be skeptical about precosmic motion — that the Timaeus is a myth, the testimony of the Academy, that motion couldn’t predate the creation of time or the soul — the last appears to be the most compelling. But it also begs the question against anyone who thinks that there can be motion without Forms or souls; that is precisely what is at issue in this chapter.

51 ἀλλ' ἔστι τὸ ἢδη μετασχὸν τῶν εἰδῶν καὶ ἲχνη τινὰ ἔχον αὐτῶν καὶ ἐμφάσεις πλημμελῶς καὶ ἀτάκτως κινούμενον· αἱ γάρ εἰδωλικαὶ τῶν εἰδῶν καὶ ἀδιάρθωτοι παρουσίαι διαφόρους αὐτῷ κινήσεις ἐμποιοῦσιν...

Proclus thinks that there is some precosmic relationship between Forms and particulars and that that relation explains precosmic motion. He describes the precosmic properties as traces, tracks, or footprints (ἴχνη), as reflections (ἐμφάσεις), and as image-like presences (εἰδωλικαί

παρουσίαι). These are all words that describe deficient, fleeting sorts of being. The Forms are present in the way an image would be, or like a reflection. The sensible world is a deficient or fleeting image; reflections and tracks are the sorts of things that tend to be destroyed soon after being generated. Proclus thinks that the sensible world is a reflection; the Forms come into a brief, contingent relation with the world, and the world bears momentary traces of them. So, on this view, the Forms still explain the precosmic properties; they just do so in a different, less stable, way than they do in the fully-formed kosmos. Thus, it is by a different relation that Forms explain the cosmic and precosmic worlds.52

As I understand this account, it introduces a different relation between the world of the

Forms and the sensible world than the one that we see in the rest of the Timaeus. This relation is less structured and somehow weaker than participation -- or at least, it is not the representation relation as we find it in its paradigmatic instances in the first part of Timaeus’ account.53 But, properly understood, we’ll find that the Form, on its own, will not be doing all of the relevant explanatory work: it might well explain the nature of precosmic motion, but it won’t successfully explain its existence.

52 Most plausible is that this is by some weaker sort of the representation relation, one that is not truth- and proportion-preserving and does not require some agent to do the representing. See the next two chapters for more on this.

53 I will argue in the next chapter that being a representation in the Timaeus is a high bar; representation without the Demiurge won’t be able to meet it. And if the Demiurge is involved, then this account reduces to a teleological account anyway.

Timaeus gives us an analysis of motion. Though we should note that Timaeus seems to take himself to be explaining cosmic motion, it could offer an explanation of precosmic motion as well. He says:

Now as for motion and rest, in what way and under what conditions they obtain, unless there is agreement on the matter, we will have many obstacles to face in our subsequent course of reasoning. Although we have already said something about them, we need to say this as well: there will be no motion in a state of equilibrium [ὁμαλότητι]. For it is difficult, or rather impossible, for something to be moved without something to set it in motion, or something to set a thing in motion without something to be moved by it. When either is absent, there is no motion, but [when they are present] it is quite impossible for them to be in a state of equilibrium. And so let us always presume that rest is found in a state of equilibrium and to attribute motion to inequilibrium. The latter, moreover, is caused by inequality, the origin of which we have already discussed (57d8-58a2, Zeyl trans. with minor modifications).

Motion occurs wherever equilibrium doesn’t, which itself is caused by inequality. There are a couple of ways we might take this claim. For one, as Gill (2012: 230) has it, this passage minimally entails that ‘change is always relational, involving both a changer (agent) and a changed (patient), and that without some sort of nonuniformity or inequality between the agent and patient the patient would remain in a state of rest’. She goes on to argue that we can understand this nonuniformity or inequality as a sort of difference. As such, any explanation of motion on her view can be understood in terms of – reduced to, in fact – oneness, sameness, and difference (234). Put in the language of separate Forms that I prefer: Motion or Change is not a

Form at all: the One, the Same, and the Different will do.

Gill’s account draws extensively on the Sophist and is well-suited to that dialectical context. However, the back-reference at the end of the Timaeus passage leads us to expect something more of a natural philosopher’s account in our attempt to explain how it is that lack of uniformity (‘inequilibrium’) results in inequality. We might take it to be a reference to 52e, as

Zeyl does, where Timaeus says, of the Receptacle, that ‘it sways irregularly in every direction as it is shaken by [‘powers neither similar nor evenly balanced’], and being set in motion it in turn shakes them’ (52e3-4). If this is what causes us to depart from a state of ὁμαλότης, then the

Receptacle is moved by the powers that are manifested in it, and it in return moves them

(presumably those things that bear those powers, the elemental triangles). The explanation of motion in the kosmos, taking the passage this way, is that the elemental triangles have certain powers and tendencies — to cut each other up, relative weights — and this causes them to move the whole Receptacle. And in turn, when the Receptacle is moved, it moves them in turn. So, motion is constant.

This tells us that and how the elements move the Receptacle and the Receptacle the elements, but it does not tell us why, other than to say that the elements move because of their powers. The explanation of inequality appeals simply to the power of the elemental triangles to move – the very power that we are trying to explain in the first place. This passage is an explanation of a sort, then. It tells us what the nature of the motion is, or, more precisely, it provides us with the background we need in order to explain the nature of motion once we know more about the elemental triangles and their characteristic motions. But it doesn’t tell us why that motion obtains in the first place; the tendency for matter to move is in fact appealed to in the explanation itself.

Returning to Gill’s account, the Timaeus looks initially as if it gives simply a version of her dialectician’s account that is applied to the natural case: we still need the Same, the Different, and the One. And the objects that are same and different and one are further specified since we’re doing physics: they’re the fundamental physical magnitudes. Those too are Formally

explained. But these explanations only tell us about the nature of motion. They cannot explain why there is precosmic motion at all.

To see our options here, it’s helpful to look to the comparatively simpler case of precosmic fire. It, as we’ve already seen, is not in fact fire – it’s not ‘worthy of the name’ (69b).

But for the sake of analogy, let’s imagine that it is. We can explain both its nature and why it exists at all with the resources available to us in the precosmos. It is warm, it cuts, and so on because of its geometrical features and their relation to the geometrical features of the rest of the elements.54 This is its nature. But it obtains precisely because of the ever-shifting and shaking nature of the Receptacle – sometimes, some part of the Receptacle takes on the right shape, and then fire’s namesake shows up. That is, at Timaeus says at 69b, fire sometimes comes into existence in the precosmos by chance. It is this second sort of explanation we lack in the case of motion: it just seems brute (or, as I’ll argue, a function of the nature of matter itself) that there’s motion at all.

Alternatively, take the case of cosmic fire. Here too we can answer both of our explanatory demands. On the one hand, cosmic fire has the nature that it does because Fire has that nature, and the Demiurge tied them together.55 On the other, fire obtains in the kosmos at all because the Demiurge willed it and executed this intention: he created it. The defender of the

Forms-first view on which the Forms play a precosmic explanatory role, then, might be able to say that the Forms explain the nature of precosmic motion. But this doesn’t stop the explanatory gap; we must also answer the question as to what explains that there is motion at all. And no answer analogous to the precosmic or cosmic fire cases is forthcoming. Reducing motion to, say,

54 If we think that Forms explain natures in the precosmos, then they will play a role in grounding the geometrical features here.

55 Depending upon our view about the role of the Forms in the precosmos, then, this might be the same explanation that we got there.

Inequality or Inequilibrium merely pushes the question back: there must still be an explanation as to why those conditions obtain, a question independent from what natures those conditions have.

And the available options seem to be two: either the Demiurge did it and this is a teleological explanation, or the Receptacle plays a role in grounding these properties.56 The second option is my view. We will take up the first below.

AN INTERLUDE ON THE NATURE OF PRECOSMIC MOTION

All that’s required for our discussion to continue is that (a) there’s a difference between the

‘nature’ question and the ‘existence’ question for motion and (b) that the Forms don’t answer at least one of those questions. I’ve argued that the Forms don’t seem to answer the existence question in the Timaeus and that we must then move on to wondering whether the Demiurge can.

But we might take up a further worry as to whether the Forms can explain the nature of precosmic motion. If the Forms are going to explain precosmic natures, then there needs to be some relation by which they do so. I’ll argue below that it doesn’t seem as if that relation can be the very same relation that obtains in the kosmos – it must somehow be inferior. I’ll then propose that the there is a reading available to us, at least, on which the text is consistent with the Forms not playing any explanatory role at all, even of natures. On this view, the precosmic world resembles the world imagined in the Greatest Difficulty of the Parmenides. It allows that there is a relation between Form and sensible world without that relation being explanatory. To emphasize: this needn’t be the case in order for the argument to continue; all that must obtain is what we’ve already seen, that Forms don’t in the Timaeus explain the obtaining of motion.

56 It can do this despite being a property-free base (50c). This is because it is not, in fact, fully without properties: it may lack any particular morphē, as we hear at 50c, but it can do explanatory work simply by being extended and in motion.

First, it’s worth noting that there are indeed some textual reasons to think that the Forms do explain the nature of precosmic motion, though I don’t ultimately think them decisive.

Consider, for instance, that Timaeus refers to the Forms as the father of the world at 50d. There, we find a threefold analogy on which the Receptacle is the mother, the Forms the father, and the offspring the nature between them [τὴν μεταξὺ τούτων φύσιν], whether kosmos or prescosmos.

All of the other relevant instances of πατήρ — one, near the start of the dialogue, refers to literal human fathers — seem to refer to the Demiurge. We have heard that he is the ‘father of all’ at

28c3-4, the father of the things that came to be (37c6), and the father of the lesser gods (41a7) prior to this point. There are two questions to ask, then. Is this in fact an inconsistency (i.e. can both be father in some sense)? And if it is, how are we meant to resolve it?

I am inclined to say that 50d is not inconsistent with 29c, 37c, and 41a. This is because the father plays two conceptual roles in the generation of the offspring for the Greeks. On the one hand, as we see frequently in Aristotle (for example, Physics 194b31), the father is the efficient cause of the offspring, the primary source of change. The Demiurge is clearly just this sort of cause; he brings the world from disorderliness to order. But the other contribution the father makes to reproduction is the form. So, Aristotle notes this dual role at Generation of Animals

(729a9-10), saying: ‘what the male contributes to generation is the form and the efficient cause, while the female contributes the material’. The passing on of the form is often mustered to explain the resemblance between generations. Once we make this observation, it is clear that if

Plato endorses roughly the Aristotelian view, he can maintain that both Demiurge and Form are father. The Demiurge is the father in the efficient sense; he brings about change. The Forms — particularly, the Form of the Living Thing — is what the offspring comes to resemble. But until that resemblance obtains — that is, until the kosmos is properly en-Formed — the Forms need

not play the role of the father. So, the two claims are consistent. But further, the claim that the

Forms are father is simply not true until the Demiurge has started his work; the Forms are father to the extent that (a) the world resembles them in certain respects and (b) it resembles them because it stands in some relation to them. As such, this passage is not free-standing evidence for the existence of an explanatory role for the Forms, or for Motion, in the precosmos; because of

(b), in fact, it is only evidence for such a role if we already have reason to think that there is one.57

There is another passage that might tell in favor of the view that the Forms explain precosmic natures. Timaeus says, claiming that he is stating ‘the truth’:

Since that for which an image has come to be is not at all intrinsic to the image, which is invariably borne along to picture something else, it stands to reason that the image should therefore come to be in something else, somehow clinging to being, or else be nothing at all (52b-c, Zeyl trans.).

This passage comes soon after the introduction of the third kind and might well be taken to be about the precosmos. And if it’s about the precosmos, then the Forms must do something: the images are still images, and if they’re images then they must be related somehow to the models of which they’re copies. But we’re not yet clear on what that relation is meant to be. It is not, at least the strong sense of the representation relation that we’ll discuss in the next two chapters; it lacks certain key features.58

57 After all, as we have seen at 69b, it is by chance that fire and the rest resemble the Forms. Consider an analogy upon which we will dwell next chapter. Imagine that you come upon a perfect copy of your face on a cliff on a deserted island. And for the sake of the case, imagine that we know that that face was carved by the slow process of erosion, a process that started long before you were born. It wouldn’t be wrong to say that that cliff looked like you – that’s what it is to be a perfect copy of your face, after all. But though your features are part of the explanation of the resemblance, they are no part of the explanation of the features of the cliff-face. Those features came about by freak accident. The picture under consideration here is that though precosmic motion might well resemble its Formal namesake without that namesake playing any role in explaining its nature.

58 I will assert this rather than argue for it here. See chapter three and the first half of chapter four on this point. But notice that, as in the previous footnote, this passage is fully consistent with the cliff-face picture.

We know, at the very least, that there is some similarity between the Forms and the precosmic particulars. And we know this on the basis of the latter being an image of the former.

But what precisely this similarity consists in is yet unclear. The taxonomy of kinds just prior provides a more detailed description of the situation, a description that helps us to see how it is this all might be possible. The first kind, the Forms, is eternal and unchanging, the object of reasoning rather than sense perception; the third kind, space, ‘provides a fixed state for all things that come to be’; but the second kind ‘shares the name’ of the first and has come to be (52a).

Forms in the precosmos share names with the precosmic particulars and resemble them.

We might expect that name-sharing is somehow shorthand for a firm explanatory relation; we call the pious things pious and the just things just because they bear some relation to

Piety and Justice. This, after all, is what is claimed in the Phaedo: other things acquire their names by partaking of the Forms (102b). But given the tension here – given that at 69b we hear that the precosmic particulars aren’t in fact worthy of their names – we might want to seek another extra-textual analogy. Here, then, consider Parmenides’ Greatest Difficulty.

And so all the characters that are what they are in relation to each other have their being in relation to themselves but not in relation to things that belong to us. And whether one posits the latter as likenesses or in some other way, it is by partaking of them that we come to be called by their various names. These things that belong to us, although they have the same names as the forms, are in their turn what they are in relation to themselves but not in relation to the forms; and all the things named in this way are of themselves but not of the forms. (133c-d)

By this point in the dialogue, Parmenides has successfully severed the explanatory link between

Form and particular by showing that none of Socrates’ theories of participation will do. His last argument is meant to show, then, that we need some account of participation in order to make sense of the world as it is. He imagines a world in which Forms are in some way related to particulars: there is a symmetric sharing of names. Yet what explains the properties in the

sensible world (and indeed the world of the Forms) is not this name-sharing, but instead intraworld relations: the things that belong to us — i.e. sensible property instances — are what they are in relation to themselves. To take the example Parmenides proceeds to give, sensible masters are defined in terms of sensible slaves, not in terms of some Form, Master. The Form and the property instance, then, share a feature: they share the name ‘master’. But despite this, there is no explanatory link between the two; any other features they might happen to have in common will be nothing but the product of chance. There is resemblance of a sort in this world, but no asymmetry by which we can ground it.

The Greatest Difficulty can help us to illuminate the (un)explanatory structure of the precosmos. The picture is the following. The Demiurge has not yet intervened, so there is no stable and asymmetric relation between Form and particular, yet.59 But there are clearly intraworld relations at this point: the Forms have all of the properties that they are ever going to have, and there is no reason to think that the sensible world lacks causal structure, even if it lacks formal structure. What explains, then, that a certain part of the precosmos instantiates a certain shape is the causal history of the world. But this does not entail that there is no symmetric (read: unexplanatory) relation between sensible and Form. If the precosmic world moves in a chancy way and comes to take on one shape or another, it is inevitable that, given enough time, it will come to have a tetrahedral portion and thus be fiery. This is what it would mean, I expect, to have fire not worthy of the name.60 When this happens, there will be a relation between Fire and its sensible instantiation. But importantly, this relation is necessarily (on the view I am considering) mere resemblance; they instantiate the same proportions, but that’s it.

59 Asymmetry is a necessary condition on explanation; if some x explains y, y cannot explain x in the same way. (To see this, consider causal or grounding relations.)

60 Cutting in favor of the name-sharing relation from the Greatest Difficulty being reproduced here is the fact that we do refer to precosmic fire as fire, unworthily.

Proclus suggests in his commentary that the sensible world already partakes in the world of the Forms. And perhaps this is right; perhaps the precosmic sensibles do in fact, by some weaker imaging relation, partake of the Forms. But that the relation is an imaging relation does not, strictly speaking, entail that the features of the Forms explain the features of the precosmic sensibles. There are clear similarities between the situation envisaged at 52a-c and Parmenides’

Greatest Difficulty. We need not think that Forms explain precosmic natures on the basis of the text we’ve seen. Or at least: there is a reading available that doesn’t require this. That said: nothing in what follows, logically speaking, requires that natures go unexplained by Forms.

PRECOSMIC TELEOLOGY

Let us return to the main argument and consider the possibility of precosmic teleology. All clear cases of teleological explanations in the Timaeus involve the Demiurge’s intentions. The world became ordered in the first place because ‘the god wanted [βουληθεὶς] everything to be good and nothing to be bad’ (30a2-3); his desires explain the existence of any stable order at all. In the same way, the Demiurge sets up celestial orbits as he does in order that we might learn about the rotation of the same and the similar (39b7-8). Given that the precosmos is the world before the

Demiurge’s intentions become relevant, it’s clear that he cannot be the source of any teleological explanation for the precosmic properties. But not everyone thinks this obvious. Johansen explains precosmic motion as the Demiurge preparing his materials like any good craftsman (96-

7). The argument given for it is speculative: it takes the Demiurge’s craftsmanship very seriously and holds, on the strength of that analogy, that the best explanation of motion is the characteristic activity of a craftsman with his raw materials. But even granting this argument, it’s not at all obvious what the link is between the Demiurge’s preparations and the disorderly motion; how is

it that causing the precosmic soup to move in some disordered way, specifically, would make it more amenable to shaping? Further, the precosmic world is described as ‘god-forsaken’ (53b).

The world is not, on Johansen’s view, ever in fact forsaken by the Demiurge. Even prior to the creation of the kosmos, he is involved with its shaping.

Another option for the person tempted by teleology is that we posit a telos internal to the matter. Here, though, we have to distinguish between any old end – something that the precosmic materials clearly have, as they tend towards each other (53a) – and an end that explain complex structure. For one, if we admit of structuring natural ends, it is not at all clear why it is that

Timaeus posits a Demiurge at all; the initial arrangement of the world could be explained in terms of the natural ends of the pre-existing materials, without the intervention of a Demiurge.

Furthermore, if matter has extremely robust natural ends that aim at its becoming structured, it’s not at all clear why it is that the precosmos is in such poor condition when the Demiurge decides to shape it. If what’s best for the precosmic material is for it to form a kosmos,61 and Timaeus mentions nothing in his account to prevent matter from realizing such an end, we should expect that matter should not be completely lacking in proportion and measure prior to the Demiurge.

Cornford (1937: 205) presents yet another possibility, arguing that the motion is caused by an as-of-yet immature world soul, since, by 34c, soul rules and directs body.62 Imperfection then is still coherent, as the world soul does not yet tend to structure and organization, and the

Demiurge is still a necessary part of the account. But, as with Johansen’s preparation account, there is simply no textual evidence that either matter is ensouled or that there is a world soul before the intervention of the Demiurge. Cornford’s view is simply an inference: if there is

61 The Demiurge wants everything to be good so far as is possible, and presumably that means he has the ‘interests’ of matter in mind as well when he arranges the world.

62 Stronger evidence for the claim that motion requires a soul can be found at Laws 891e-892c, for example.

motion, it must be caused by something ensouled. But the Timaeus provides us with more evidence for denying the principle than for endorsing it; nowhere in the Timaeus is it stated, and much of the dialogue seems in fact to ignore it actively. Plutarch’s hypothesis, a cousin to

Cornford’s, that what causes the disorderly motion of the Timaeus is an evil soul, does not rest on any evidence from the dialogue at all (it is instead on the basis of an odd reading of Statesman

269d); it would be surprising, to say the least, if Plato’s cosmogony required an evil world soul that had been tamed by the Demiurge, to find it unmentioned in the Timaeus. None of this is to say that such a reading is impossible. It could be the case that matter moves, even prior to the intervention of the Demiurge, because matter is fundamentally ensouled. But I see no reason, other than the Laws, to posit precosmic soul as an explanation. And in the face of the total absence of evidence inside the Timaeus for this view, it doesn’t seem like one we should endorse except if there are no alternatives.63

The best argument for teleological explanations of precosmic motion is simply that there are no other possibilities. This, in each account, justifies our moving beyond the text to philosophical speculation that is at least generally coherent with Timaeus’ cosmogony. The way forward, then, is to provide a coherent alternative that doesn’t require us to posit extra-textual ontological principles. Such an alternative is available: that the nature of matter explains the motion of the Receptacle.

ON THE POSSIBILITY OF MATERIAL EXPLANATION

63 For a more detailed engagement with teleologists about precosmic motion, consider Jelinek (2011), who engages with Silverman (1992) in addition to those people whom I here mention.

The parallels between Socrates’ intellectual autobiography in the Phaedo and the broader explanatory paradigm in the Timaeus are close. One might think that the ‘helping causes’ of the

Timaeus (46c) are the necessary conditions of the Phaedo. Given that the necessary conditions that Socrates in the Phaedo discusses are matter, and Socrates of the Phaedo thinks that these are no explanation at all,64 it’s not at all obvious how it is that the Timaeus is meant to present a different view.65

After giving an account of how it is that reflection works in terms of the properties of fire, the eyes, and the reflective surface — notably with no reference to the goodness of that arrangement — Timaeus goes on to give the following argument:

Now all of the above are among the auxiliary causes employed in the service of the god as he does his utmost to bring to completion the character of what is most excellent. But because they make things cold or hot, compact or disperse them, and produce all sorts of similar effects, most people regard them not as auxiliary causes, but as the actual causes of all things. Things like these, however, are totally incapable of possessing any reason or understanding about anything. We must pronounce the soul to be the only thing there is that properly possesses understanding. The soul is an invisible thing, whereas fire, water, earth, and air have all come to be as visible bodies. So anyone who is a lover of understanding and knowledge must of necessity pursue as primary causes those that belong to intelligent nature, and as secondary all those belonging to things that are moved

64 It is, after all, by nothing else than Beauty that beautiful things are beautiful at Phaedo 100.

65 Johansen puts the point as follows:

As many scholars have pointed out, Socrates finds in Timaeus someone who can teach him about causes. Timaeus explains to Socrates how the universe was composed in the best possible way. In that sense, the Timaeus is the fulfilment of the teleological project that Socrates envisaged and abandoned in the Phaedo. One passage in the Timaeus, in particular, provides a link with the Phaedo: 46c-d. Here Timaeus says that most people take processes such as heating and cooling, dilating and condensing to be causes when in fact they are only sunaitia, ‘co-causes’ (plural of sunaition). Scholars have generally, and rightly, I think, taken this to echo the Phaedo (103).

It is important to note that Johansen does not straightforwardly endorse this view, and he goes on to provide some reasons not merely to identify the sunaitia with the Phaedo’s necessary conditions. Auxiliary causes might well be an echo of sunaitia without themselves being sunaitia. In the following I give at least a brief argument for thinking that they aren’t quite the same thing.

by others and that set still others in motion by necessity...we must describe both types of causes, distinguishing those which possess understanding and thus fashion what is beautiful and good, from those which, when deserted by intelligence, produce only haphazard and disorderly effects every time. (46c7-e6)

Material processes are not the primary cause of anything in this passage, for they are unreasoning, and only reasoning things have the capacity to be primary causes. This initially looks like trouble for anyone who wants explanations to bottom out in matter. But looking more closely, we’ll see that this is not the case. The claim that only reasoning things can be primary causes should cause us some puzzlement. If we understand ‘primary cause’ to mean

‘fundamental cause’, the cause ‘further back’ than which we are unable to go, this seems to entail that for every event — or whatever the relata of causation are — there is some teleological fact that terminates the chain of causes. But this seems to be in direct contradiction to the evidence that we examined in section one. There are lots of things that have happened, prior to the arrangement of the kosmos, and those things are caused. This looks grossly inconsistent.

Luckily for us, the passage provides us with a clear second option that avoids inconsistency. Notice that Timaeus closes the section I’ve quoted by claiming that the sunaitia

‘produce only haphazard and disorderly effects every time’. Here, Timaeus uses a word that we remarked on earlier, ἄτακτον (disordered), to describe the sorts of things produced by the sunaitia when it acts without the guidance of intellect. It goes without saying that there were disordered things in the precosmos; everything, before the introduction of structure by the

Demiurge, was in such a state. So, as we noted above, it’s clear that the sunaitia do have some causal or explanatory power. The primary causes are the grounds of those things — or those features of things, perhaps — that are καλόν or ἀγαθόν; the sunaitia are the grounds of everything else. There seems to me no good way to interpret the text such that the material causes are mere necessary conditions.

POSSIBILITY AND MATTER

We have seen that there are good exegetical reasons to think that neither Forms nor ends of any sort can fully account for the precosmic world. Let us start in on an alternative explanation for precosmic motion before taking up the corresponding cosmic question.

The explanation for the Demiurge’s limitations will shed some light on our primary question. As such, we’ll start by reviewing appeals to possibility in the Timaeus. What follows is a ponderous list, but it’s important to note just how frequently and in how many contexts pleas to possibility occur in Timaeus’ cosmogony.66 At 30a, Timaeus says that the Demiurge, due to his being unbegrudging, wants everything to be good and nothing bad so far as possible. This comes immediately after the note that the Demiurge wants everything to be like him παραπλήσιος, approximately or nearly. Given that we are to think that the Demiurge is entirely good, we should not think that this approximation is a matter of his desires being deficient, but instead that approximation is the best that he could achieve. At 32b, we are told that the Demiurge can work up the elements to bear the proper ratio to each other only so far as this is possible; they instantiate the right mathematical structure only imperfectly. After time is created, we hear that the reason for this is that the Demiurge wants the visible world to be as much like the paradigm as possible (38b), so he makes the kosmos a moving image of eternity. Having assigned the task of the creation of mortals to the lesser gods, the Demiurge has them govern us so far as is possible given our deficient natures at 42e. And at 46c, we hear that the discussion to this point has been regarding the sunaitia that the Demiurge has used to complete and make excellent the kosmos, so far as this is possible. Once the elements are introduced, we are reminded that the

66 I will not note the Greek of most of these sentences, but unless I mention otherwise, they are variations of kata dunamin.

Demiurge made them — just as he made everything else — as perfect and excellent as possible

(53b). We get this claim repeated at 69b. It is clear that the Demiurge is thoroughly limited in his capacity to make a good world, a world like the Living Thing itself, and Timaeus makes sure to remind us of this fact frequently.

There are appeals to possibility in the Timaeus that do not bear on the Demiurge or the minor gods. Take the discussion of human virtue near the end of the dialogue. At 89d-e, referring to the constitution of the human body and soul, we hear that things have been arranged such that we are as well-suited as possible for leading a good human life. But if we fail to live up to our promise and cultivate our mortal parts, we will not fail to be as mortal as possible (90b); that is, we can fall short of being imperfect, in virtue of having immortal and divine souls. But by engaging in mathematics and philosophy, we can come to resemble the immortal as much as is possible (90c). Our biology fixes our ability both to achieve and to fall short of virtue; it is impossible for us to be completely virtuous or vicious because of it.

The ointment analogy at 50e also illuminates Timaeus’ notion of possibility. When someone tries to make a fragrant ointment, she must first create an odorless base to receive the smells. This can’t be done completely; all sensible objects are sensible, after all. So, the base is only odorless so far as possible. The sculptor works similarly: she doesn’t want clay that is lumpy and misshapen, but instead clay that lacks definite structure. Both the perfumer and the sculptor are limited by the bounds of possibility. The reason that I can’t be fully virtuous and divine is that I am partially bodily and mortal; were my nature some other way, I could achieve virtue. But there are heights of virtue unavailable to me. Similarly, the perfumer cannot make a perfect perfume because she cannot make a perfect base. There is no sensible thing entirely

without odor. Skill, no doubt, constrains mortal craftsmen (and the lesser divinities). But it is not the only limitation. The materials further impede the craftsman.

There is no principled difference between more familiar craftsmen and Timaeus’

Demiurge. The Demiurge, as we’re told over and over and over again, cannot make a perfect world despite his best intentions. But he lacks no skill or art. He may not, as Broadie emphasizes,67 be a familiar God of Genesis who makes the world from nothing at all. Perhaps creation ex nihilo is beyond his powers. His skills are in no way in question.68 His materials must be the source of the deficiency, either his model or that out of which he makes his copy. The

Forms can’t be the imperfection; the Living Thing is regularly described as superlatively complete and perfect and beautiful. The limits of possibility, then, are in the sensible world itself.

It is impossible for the Demiurge to make a perfect world because his materials are imperfect. But we yet lack an analysis of possibility in Plato. (What, that is, plays the role for him that possible world semantics tends to play for us?) The possibility of virtue and vice provides an illuminating case. I can’t be perfectly virtuous because virtue consists in my soul imitating the movement of the world soul, and I’m a mere mortal whose orbits will break down and be knocked off-kilter, even if I am lucky enough to get them close to divinity. My mortal nature, my phusis, forecloses the possibility of full virtue. Conversely, I can’t be fully vicious because despite my best efforts my nature is partially divine. My soul will, no matter how badly I damage it with food and drink and sex, still have orbits. Pure vice and virtue are impossible because they’re inconsistent with my nature. The Demiurge settles for second-rate eternity in his work of craft for the same reason. The Living Thing is properly eternal and changeless; it can be

67 Broadie 2012: 11.

68 This is not quite true. The reason that the lesser gods make humanity is that, were the Demiurge to make us, we would rival the lesser gods themselves. But this limit on his ability is not a lack of the capacity to make good things; he in fact is incapable of making worse things.

because it’s non-spatiotemporal. The kosmos though came to be (necessarily) and it changes.

Full-blooded eternity is inconsistent with its nature as a material being, and consequently it can’t be eternal. So, the natures of the objects in question ground the possibility and impossibility of virtue and eternity.69

The nature of the materials with which he works makes it impossible for the Demiurge to design a fully eternal kosmos just as it makes it impossible for me to be fully virtuous (which, I admit, is a particularly convenient excuse). The latter fact — that I necessarily have a mortal part to my nature — is grounded in some Form, the Form of Human. But the Receptacle – the imperfect material with which the Demiurge is working – prevents me from reaching full virtue.

The Receptacle must have a nature, though, even if it lacks a morphē at 50c, if it is to ground possibility claims in the way that possibility claims seem generally to be analyzed in the

Timaeus. The explanation for my imperfection looks to be an explanation that bottoms out in terms of the materials.

Perhaps this demand for an explanation is a mistaken one; somehow, we have asked an incoherent question. We might have asked a question with a false presupposition, like asking whether my table is content with its lot in life. (Neither ‘yes’ nor ‘no’ will do; my table is not the sort of thing with a lot in life.) But the question ‘Why does matter move?’ doesn’t seem like it makes any presuppositional mistakes; it is conceptually possible that there is an explanation for such a thing (indeed, this is what Proclus takes himself to be giving when he cites the Forms).

We might also be asking a question that the theory makes no claims to answer. I’m asking a bad question if I ask of a chemist, when she tells me about the periodic table of the elements, what

69 Put precisely: it is possible for x to be F just in case it is consistent with x’s nature to be F. It is impossible for x to be F just in case it inconsistent with x’s nature to be F. This analysis of possibility has certain problems — defining consistency without a prior account of possibility is a notorious problem for ersatzists about possible worlds, for example — but these aren’t special problems for Plato or me.

elements constitute beauty. Chemistry, she’ll respond, has no bearing on that. But asking why it is that matter moves is not similarly outside the domain of our theory. Timaeus is providing a physics, an account of the natural world. A physics not only has but must have a theory of matter; we don’t step outside the domain of Timaeus’ theory by asking about it. We aren’t asking any incoherent questions of the typical sort.

Someone else might instead want to resist this inference by denying that it follows from the Receptacle’s nature having no further grounds that the Receptacle’s nature is explanatorily fundamental. As I am using the word ‘fundamental’, this is a trivial inference. What I mean to say when I call the Receptacle fundamental is that (a) the Receptacle explains something and (b) the Receptacle is not itself explained by something else.70 If we understand explanation metaphysically, this isn’t an idiosyncratic account.71 And it’s clear the Receptacle meets both conditions. It explains why it is that it is impossible for the Demiurge to perform certain actions

(by explaining certain higher-level properties, like its being in motion); it has no further explanation (it is a nature ungrounded by a Form). If the Receptacle does this work, there are fundamentally material explanations.

A NOTE ON COSMIC MOTION

The Receptacle explains why precosmic motion obtains, at the very least. And the obtaining of this motion explains imperfections in the kosmos and the limits of possibility. Grant, for the sake of argument, that the story above about precosmic explanations is roughly right, and that the the

Receptacle explains why precosmic motion obtains. Perhaps the Forms don’t explain precosmic

70 Take ‘explained’ here in a metaphysical sense: ‘stands in an explanatory relation’ (causing, grounding…).

71 Consider, for example, Schaffer (2009).

motion. But this wouldn’t be an enormous revision of the Theory of Forms; Socrates wasn’t theorizing about a not-quite-world all throughout Plato’s corpus. The more exciting result would be that the Forms don’t explain cosmic motion, either.

As before, we should distinguish the existence question from the nature question. In the precosmos, I argued that the best the Form-first theorist could hope for is that the Forms explain the nature of precosmic motion, though not motion’s obtaining. Some Form would fix the facts about what kinds of inequalities entail what sorts of motions, on the basis of the passages we saw above. But in the precosmos, the explanation for ‘inequilibrium’ and inequality was simply the shaking of the Receptacle. Timaeus appeals to the existence of some motion to explain its nature.

Motion’s obtaining, at the very least, was explained elsewhere. If we endorse this view, then we should think that nothing (significant) has changed in the kosmos. The major difference between the kosmos and the precosmos is that the fully-crafted universe is orderly. And it is by tying the world securely to the Forms that the Demiurge introduces order. But though this might entail there being less motion in virtue of the kosmos being closer to a state of equilibrium, it doesn’t show that the Forms are responsible for cosmic motion. The motion that was already there is being redirected and better ordered. If we assume that Forms explain precosmic motion’s nature and not existence, then we get the same result for our world.

PLATONIC EXPLANATION: WHAT SIMMIAS SHOULD HAVE SAID TO SOCRATES

In a famous passage in the Phaedo, Socrates suggests that giving material, mechanistic explanations is like citing as reasons that he is sitting in jail his bones and sinews (Phaedo 98c).

They might be a necessary background condition, but they have no independent explanatory force; they do not bring about his sitting. That role is played by teleology: he sits because of

certain principles of justice. In a sense, after having reviewed the Timaeus we should still agree with Socrates. It is true that his material constitution is a necessary condition for his sitting. But that is not all that it is. His bones and his sinews may not ground his sitting, but they ground that he is the sort of thing that sits. Had he accomplished the (probably hypothetical) end of philosophy and succeeded in separating his soul from his body, there would be no question of his sitting. Souls, as the Stoics will later emphasize, cannot be shackled. His bones and sinews are necessary conditions because they explain a certain capacity that Socrates has. Socrates was right that they don’t explain why he’s sitting, but they answer a close-by question. This, of course, is what Simmias should have said to Socrates. And it’s what Timaeus seems to defend.

Let me review where we’ve been before I begin to draw out what I take to be the most interesting metaphysical implication of Plato countenancing fundamental material explanations.

In the first section, we reviewed the primary passages in the Timaeus in which a state of the world before it was anything at all is mentioned and noted that there seems at least to be motion in that world. With Vlastos, we noted that this motion cries out for explanation, but argued in the sections that followed that none of the options that have been proposed — generally, variations of appeals to Forms and to the Demiurge’s ends — seem to work. More specifically, they cannot fully answer the explanatory demands: at best, they are able to explain the nature of precosmic motion; they cannot explain its obtaining. Taking all of this on board, I argued that, on the basis of the appeals to possibility, we should think that it is the nature of matter that explains Vlastos’ discordant and disorderly motion in the precosmos, and that there is very good reason to think that the very same thing does the explanatory work in the kosmos itself. So, there are some explanations for Plato, circa the Timaeus, that bottom out at matter.72

72 Marwan Rashed has defended a view not too distant from this one in, for example, ‘Plato’s Five Worlds Hypothesis’ (2013).

CHAPTER 3: PLATO’S UNIFIED THEORY OF REPRESENTATION

Plato famously suggests that this world is nothing but an image of another one. Speaking of our cosmos, Timaeus says:

This, then, is how it came to be: it is a work of craft, modeled after that which is changeless and is grasped by a rational account, that is, by wisdom (29a6-7).

The world is like the Forms in the same way that a bust is like its subject or a photograph like the photographed: the sensible universe is a representation of the eternal Forms. Put another way: the participation relation, the relation between Form and sensible (token) property-instance, is a representation relation.73

The question of what makes for a representation relation is of course a thorny one, at least partially because it makes its appearance in a surprising number of distinct areas of philosophical inquiry. So, it’s very plausible that the representation relation obtains between artistic works and the world; this would be aesthetic representations.74 It also plausibly obtains

73 We can see this theory proposed in its most transparent guise in the Parmenides. In the first part of the dialogue, Socrates tries to answer the question ‘what is the relationship between the Forms and the sensible objects?’. One of his proposals is that Forms are patterns — paradeigmata — set in nature, and the other things are likenesses; ‘this partaking of the Forms is, for the other things, simply being modeled on them’ (132d1-4). On this theory, it is sometimes said that Forms are perfect, self-predicative particulars, as opposed to universals. For more on the question of whether Forms are universals or are paradigms (or something yet further), consider Fine (1993) and Harte (2008), who argue for the former, or Johansen (2008) for the latter. Views on this question are also laid out briefly in chapter one. The paradigmatist view comes with a number of well-known problems, among them that it seems to entail that Form and sensible share features; not only is Justice just, but Largeness is large and Heat hot. This has led some people who are otherwise inclined to endorse a Forms-as-paradigms theory to suggest that there are ways of sharing features that are in some sense non-literal. So, see Meinwald (1991) for an example of a theory on which Largeness is large, but not in the same way that an elephant is large.

74 Consider Goodman (1968) for the classic 20th-century account of the relation under this guise.

between language and the world.75 Minds, too, look like they represent the world, or at least the objects of experience.76 It would be very surprising, the natural thought goes, if there was really one notion underlying all of these relations. What makes a bust a bust of Socrates is going to involve some isomorphisms between Socrates’ head and the marble. But words, for example, don’t seem like they look like or sound like their referents; they aren’t isomorphic in the same way. We might rightly despair of having a single and unified theory of the representation relation.

In what follows, though, I’ll argue that Plato does not shrink from the challenge, and in fact offers what looks to be an underlying account of representation, one that holds that the same relation underlies the aesthetic, linguistic, and mental cases. Representation obtains, on Plato’s view, just in case (1) some representing agent looks towards a model while generating a copy,

(2) the copy depends on the model, (3) the model and copy share features because of (1) and

(2),77 and (4) the features shared serve to individuate (though not always uniquely) the copy as a copy of its particular model.78 This theory is the best way to make sense of some otherwise very strange claims made in the Cratylus — that letters naturally have something in common with the properties they are best suited to picking out — and the Theaetetus — that memories are only

75 Yablo’s (2014) Aboutness is an account of this sort. This might be the right way to talk about the picture theory of language in Wittgenstein’s Tractatus, too.

76 Jackson (1997).

77 This condition is stronger and more controversial than it might appear. It’s not consistent with Crombie’s (1963) account, for instance: ‘Helen’s beauty…was analogous to but not identical with true beauty…’ (279). Helen’s beauty is of course not identical to Beauty, but it is identical to Beauty’s beauty on my view.

78 The question of what, in general, representation is in Plato is not so far as I can tell regularly discussed. The question that most often has inspired work on this issue is how it is that we are meant to make sense of Plato’s psychological views about perception and judgment. So, we can find discussions of this more specific notion of representation — say, about the comparison between aesthetic and mental representation — in Moss (2006 and 2008), Barney (1992), Lorenz (2005). Those concerned about Plato’s theory of poetry, found in the tenth book of the Republic, also occasionally make more general claims about representation. See, for example, Ferrari (1989), Nehamas (1982) and Moss (2007).

ever formed intentionally. Further, it helps to settle questions about the late Theory of Forms, as it appears in the Timaeus. If the participation relation really is representation, then we should think that Plato is committed to the literal existence of a Demiurge, a creator god, and that Forms literally have the properties that they explain in sensible objects.

The first text to take up is the Sophist, in which Socrates outlines a theory of aesthetic representation by taking up the case of sculpture. Next, I’ll consider the Cratylus, containing what has generally been taken to be an unbelievable theory of meaning, reference, and linguistic representation, one on which letters are naturally suited to making up words that pick out certain properties in virtue of the letters themselves having those properties. The letter rho, we’ll find, is a suitable part for words to do with the concept of motion. This is a difficult and complicated text, but is perhaps the most surprising application of the underlying theory. The last of the primary texts will be the discussion of mental representation in the Theaetetus, in which the best explanation of Socrates proposing a view on which memories must necessarily be intentionally formed is that he is committed to the underlying theory that we saw in the other two dialogues.

A NOTE ON IMITATION AND REPRESENTATION

Plato, it is often said, is a notorious skeptic about the value of imitation and imitations. This is because imitation is associated with seductive falsehood. What’s wrong with the poets and imitative artists in Republic III is that they’re wrong about the nature of the gods and heroes; they are making an empirical mistake, so to speak, and are a benighted but not totally valueless tribe. But by the time we arrive in Book X, Socrates’ prescriptions are much harsher. The poets aren’t just misguided, and they’re not just doing their jobs badly; the entire project of poetry is

doomed, and the poets must be banished from the city.79 Imitation, then, often looks like the sincerest form of falsehood.

But as with so many appearances in Plato, this one is deceptive. Some imitations are truth-preserving. As I noted in the opening paragraphs, the contemporary philosophical notion of

‘representation’ isn’t just restricted to the aesthetic domain. Though we do have representational

(and perhaps non-representational) art, mind and language are also said to represent the world and democratically-elected politicians to represent their constituents. These notions of representation – and indeed, the aesthetic notion of representation that stands in contrast to non- representational art – have a built-in truth criterion. When I look out the window of my office, I should represent trees and brick buildings; if I represent a bubbling caldera, I’m not representing what’s outside at all. I am, that is, failing to represent. If I am trying to talk about a state of affairs in which a feline is sitting on a rug and I say ‘the dog is on the mat’, I am failing to represent the world properly in language. If representation is a category of imitations – and as we’ll see soon in the Sophist, Plato clearly thinks this – then some imitations aren’t associated with falsehoods, but instead preserve truths.

Plato, I will argue, admits of imitations that are truth-preserving in the same way that these ways of representing are; the Wax Block in the Theaetetus, image-making in the Sophist, and name-making in the Cratylus are all concerned with duplicating important features of the objects that they are imitating. In what follows, I’ll not be tracking a single Greek word in

Plato’s lexicon, but instead the notion of a truth-preserving imitation.80 There are, as we’ll see, other kinds of images made in Plato, images that aren’t intended to communicate truths (or

79 For more on this, see Philip (1961).

80 The claim that Plato doesn’t have a consistent philosophical vocabulary of images in the Republic era is not unique or original to me. Noboru Notomi, comparing the treatment of these questions in the Republic and the Sophist, calls the Republic treatment ‘comparatively primitive’, and suggests that there is a ‘more subtle division of image-making’ in the Sophist (2011: 325).

communicate truths only by concealing something else). But, contrary to what the Republic leads us to expect, there are images that are, by Plato’s lights, philosophically important. These are the kind that faithfully preserve the features of their model.

STATUES IN THE SOPHIST

In a paper on mimēsis in the Sophist, J. A. Philip writes:

This class is then divided into two sub-classes, eikastikē and phantastikē. Eikastike is the art or craft that creates eikones, replicas or true likenesses of their paradeigma-exemplar (235d-e). It is not in the Sophistes apparent what the eikones are. In the Cratylus (432b) the eikōn is a portrait, but in the Sophistēs a two-dimensional portrait could not be classified under eikastikē, nor are there any replicas made by a craft, and not at two removes from the Forms, that could be classed as eikones in the present sense. Eikastikē would appear to be a class without members, serving only the purpose of symmetry. The eikōn of the Timaeus and its paradigm-exemplar has a very different significance, not relevant here (1961: 459).

Philip is correct, so far as it goes, both that the word eikōn refers to a portrait in the Craytlus and that it, as we’ll see, in no way qualifies as an eikōn in the Sophist sense. But there are reasons to be skeptical of the other major claims in this passage. It is true that, if we are narrowly searching for the word eikōn, it does not appear that there are any clear objects of the craft eikastikē in the corpus (other than in the Timaeus). But, as we’ll see, that does not entail that there are no images that meet the criteria that the Eleatic Strange sets out; we should just think that they are not consistently named eikōnes.

The Sophist is primarily concerned with an investigation of sophistry, and what distinguishes that practice from statesmanship and philosophy. It does this by employing what is called the method of division; the Eleatic Stranger identifies a genus to which the sophist seems

to belong and divides it until he finds that specific species, such as the sophist. Among the sophist’s arts, Theaetetus and the Eleatic Stranger discover, is imitating people who in fact know what they’re talking about, when the sophist himself does not know (233c1-2). This leads the

Eleatic Stranger to ask what sort of imitator the sophist is.

As Philip notes, the Eleatic Stranger and Theaetetus consider the difference between two kinds of mimetic arts: likeness-making (eikastikē), and semblance-making (phantastikē) (Soph.

235d1-236b8). The Eleatic Stranger characterizes the first as follows:

I see in this one art, likeness-making. Likeness making is most of all whenever someone works up an imitation, one that is in accordance with the proportions of the model in length and width and depth, and further assigns to each part the appropriate color (235d6-e2).

Theaetetus wonders whether or not this really distinguishes those imitators interested in generating likenesses and those that produce mere semblances. After all, isn’t it distinctive of imitators that they try to create close copies of their models? The Stranger clarifies:

Certainly not those who mold or draw somewhere any of the large works. For if they assigned the true proportion of the limbs, you see, the upper parts would appear smaller than they should, and the lower parts would appear greater, on account of the first being seen from afar, and the second being seen by us from up close (235e5-36a2).

The sort of people who engage in this kind of craftsmanship are those that make mere semblances, we soon find. The distinction, then, seems to be this: people who make proper images actually reproduce the proportions of the model to which they’re looking. The hands stand to the feet just as the model’s hands and feet stand to each other, and measurement would bear this out. The semblance-maker, though, creates a product that only apparently instantiates these properties. The head of a large statue, when it is viewed from below, must in fact be disproportionately large if it is to appear proportionate. The distance between the statue’s base

and its top causes the top to seem smaller than it really is. Though the effect is less pronounced than size, color too seems less vivid when seen from further away. If we were to paint a mural on the side of a skyscraper, meant to be viewed from well below, and one of the people in our mural is meant to appear to have pale blue eyes, then we ought to use a more intense shade of blue to achieve the desired effect. Here too the sculptor interested in his sculptures appearing beautiful is a semblance-maker.81

It’s important to note that it is not just the sharing of particular features — proportions, colors — that determines whether some object is or is not a representation of some other.

Someone makes a likeness when she works something up such that it shares certain features with something else. That is, it inextricably involves an intentional action, a building up. Were I to come across my visage carved into a cliff face by the sea, I’d be wrong to call it a representation of my face, no matter how striking it was; it might well look like me, but that’s not enough. Put another way: the Stranger’s view requires that someone makes the representation, or does the representing. I was not the sea’s model when it carved my face into the cliff, so I am not represented there. My features are not responsible for its features. So artistic representation requires that there is some intentional act, some actor, linking model and copy. Both the first and the third condition are present on the surface of the passage.

The Eleatic Stranger is helpfully clear on the question of what features must be shared between copy and model: shape and color are the two properties that the Stranger discusses in this passage. And this should come as no great surprise; the sculptor works with materials whose

81 Soon after (239d-40c), Theaetetus and the Stranger return to the topic, and try to define “copy” [eidōlon], with evident difficulty. Theaetetus first tries to answer in terms of a swarm of examples: water, mirrors. The Stranger rightly points out that this is no answer at all, and Theaetetus proposes that a copy is something made like a true thing (240a8), resembling it (10). The proposal seems to be that eidōlon is a generic, more so than eikōn and phantasma. Notice that in the earlier passage, at 236, the Stranger asks, referring to the distinction between eikones and phantasmata: ‘can’t the first sort of image [eidōlon] be called a likeness [eikōn]’ (236a)? This suggests that eikastikē and phantastikē are categories of eidōlopoion.

most salient features are extension and color. A bust of Socrates is not worse because it is not wise nor convicted of a crime in 399 BCE.82 With enough of these features added, it might no longer be a bust at all; it would just be a ‘second’ Socrates, in the sense of Cratylus 432b. Given that we are talking about the sorts of properties that can be captured by a sculptor, the central question is whether these properties are the kind that would best be able to individuate the subject of a statue. And the bust of Socrates case seems instructive here. It is precisely the

(unattractive) proportions of his face that make the bust of Socrates distinctive; they serve to individuate him so well as any set of features that are merely spatial can. Further, failing to instantiate them properly and making a mere semblance will decrease the bust’s capacity to individuate; if we have made his eyes too large relative to his nose, we will find that Socrates is still ugly, but in a very different way.83

Let us take up the question of whether busts depend on their models. First, it is clear that there is some causal dependence between the subject and the bust. One of the causes, of course, is the sculptor. But Socrates’ face stands in the causal history of the bust of Socrates. There is some question as to how precisely to cash this out. It might be that the fact that the bust of

Socrates has a snub nose depends on the fact that Socrates has a snub nose, or we might think that the fact that the bust is a bust of Socrates depends on the existence (in some way) of

Socrates. Most plausible is the first option, that the individuating features of the representation

82 We’ll see this point developed further in the discussion of the Cratylus. Nehamas (1975) notes that ‘[i]f our two similar objects share every characteristic, then we shall no longer be confronted by a copy, portrait, or image and its original’ (113). Instead, we’ll have two Cratyluses; we’ll have a clone or a duplicate.

83 It is clear that a sculpture cannot entirely distinguish its subject from the rest of the world simply in virtue of instantiating the right proportions and colors. A litany of counterexamples immediately come to mind. Were Socrates to have an identical twin, his face would not be unique. So even capturing his visage for a bust perfectly wouldn’t do; it could always be his twin. I invite the reader to hold on to this concern until the discussion of the Cratylus, where we can make a profitable comparison to the aptness of a name. In short, we’ll find that some copy represents to the extent that it marks off its model; this is not a binary condition.

depend on the features of the represented, and it doesn’t further commit us to a discussion of representations of fictional characters.

The Sophist, then, seems to propose a fairly straightforward theory of representation. It holds that in the case of representation in the visual arts, someone represents aptly just in case she preserves the proportions of her model (that is, just in case her model and her copy share a salient set of features), because those proportions reliably distinguish her model from other possible models (the salient set of features is the set by which we distinguish these sorts of things from each other). It is also, if you’re a fully orthodox Platonist who is convinced that painting is not a genuine art, not hugely surprising. It is the natural view; of course aesthetic representation, in the most basic sorts of arts, has something to do with resemblance or the sharing of features.

But, strikingly, it has the very same structure as the theory of representation that appears to underlie Socrates’ theory of linguistic representation in the Cratylus and mental representation in the Theaetetus.

GOOD NAMES AND BAD: THE SEMANTICS OF THE CRATYLUS

Socrates provides a theory of meaning that makes central use of the notion of representation in the Cratylus. The first discussion of imitations and representations occurs at 430a12-b1: names are imitations (mimēmata) of things, just as paintings are. To borrow a phrase from Sedley

(2003), names are vocal imitations. This is already a surprising claim: names, maybe, could be descriptions; we regularly name children after virtues that we hope will eventually be descriptions (Sophia, for example). But that is not the same as them being imitations, of them somehow being like the things that they pick out. Sophia might be wise, but the word ‘sophia’

never will be; it’s not even the sort of thing that could be wise. Socrates, though, draws out what might seem like an inapt analogy with paintings:

...in paintings also [it is possible to] assign all the fitting colors and shapes, and also not all, but to leave one out, and to add one, and to have some greater and bigger...Someone who assigns everything produces beautiful drawings [grammata]84 and likenesses, while the one adding or taking away works up drawings or likenesses, but they’re ugly (Crat. 431c4-14).

In a painting, Socrates says here, it is possible to add too much, to embellish it such that it no longer captures its model. It is also possible to do the opposite, and to take features away. Either way, we have represented, but badly.85 Socrates makes a surprising claim here, then: it is possible to represent badly in words by adding or subtracting too much.

Carrying on, Socrates elaborates:

What about the person who imitates the being [ousia] of a thing through syllables and letters? Isn’t it the case that by the same account, if you produce all of the fitting things, the representation will be fine — this is a name — but if you leave out or add small things occasionally, it will be an image, but not a fine one? With the result that there will be beautiful reproductions of names and ugly ones? (431d2-8)

Words, then, are meant to be imitations of something’s being in language, in syllables and letters.

As representations they have the same features as paintings or sculptures: when coining a name, you must not add too much or too little, at risk of making one that represents badly. But this is puzzling: it is not at all obvious how we can add too much to words, or indeed how they could be imitations. What then, are we to make of the claim that they’re vocal imitations of something’s being? Taking up the phrase in reverse order, I’ll start by arguing that we should understand

84 There is a clear pun here: γράμματα could just as well be ‘letters’ or something written rather than drawn.

85 The Eleatic Stranger at Statesman 277a-c says something similar, suggesting that the myth he has just given is insufficient because they’ve both added too much in certain places and been too quick in others, like sculptors and painters sometimes do.

being here as being a matter of individuation; we imitate something’s being in this case if we reproduce the properties by which it can be individuated. The next trick is making sense of the way in which names are said to imitate. I’ll argue that Socrates seems to think that letters have distinctive capacities to represent certain features of the world, capacities that are actualized only when they are arranged into words. Letters have those capacities in virtue of in fact having the feature they have the capacity to represent.

First, it is necessary to take up some of the Cratylus’ famous etymologies. We can see names marking their objects off by their ousia in the examination of successful and unsuccessful

— or at least, less successful — naming, discussed at 392d and taking up Hector, a prince of

Troy and soldier, and his infant son Astyanax as examples. Astyanax has an alternative name in

Homer: ‘Skamandrios’. ‘Astyanax’ roughly means ‘ruler of the city’; ‘Skamandrios’, means

‘man from the river Skamandros’, near Troy. Socrates suggests that the Trojan men called him

‘Astyanax’ and the women ‘Skamandrios’, and further that the men were wiser than the women

(392d5-6), and thus that the more correct — orthoteron — name was Astyanax (d8). No further explanation is offered for why it is that Astyanax is a better name than Skamandrios, except a quote from Homer, saying of Hector: ‘He alone defended their city and long walls’ (392e1).

This, along with the meanings of ‘Astyanax’ and ‘Skamandrios’, is meant to explain the aptness of the name.

Note that the claim at issue is a comparative claim: that ‘Astyanax’ is better than

‘Skamandrios’. What grounds this claim can’t be merely that it is true of Astyanax that he is the ruler of the city, for it is no less true that the son of Hector is a man from near the Skamandros.

The most plausible explanation is that ‘Astyanax’ picks out the son of Hector more successfully from everyone else than ‘Skamandrios’ does; there are very few people of whom it’s true that

they are the rulers of Troy, whereas there are many men born near the Skamandros that could truly be called ‘Skamandrios’. Only some of Hector’s relatives share this former feature with his son. On this count, ‘Astyanax’ is the better name.

Socrates’ immediately subsequent reflection on the name ‘Hector’ supports this reading.

Socrates, in response to the quote from Homer that Hector alone defends the city, points out that

‘Hector’ means, roughly, ‘possessor’, and that the lord of the city is more or less the same thing as the possessor of the city (393a4-b4), and Socrates suggests that this represents some sort of confusion about how naming works. The only way the analysis of Hector’s name is at all relevant is as a counterexample to the claim that ‘Astyanax’ is the best name for the son of

Hector; it does not distinguish Hector’s son from Hector himself successfully. Both names, after all, denote a sort of rulership. ‘Astyanax’ is a better name than ‘Skamandrios’ for Hector’s son, but not the ideal name.

Let us consider another case and see if the same sort of principle is at work: Socrates’ analysis of the name ‘Zeus’ at 396a1-b3. Socrates claims that ‘Zeus’ can be subdivided into two names: the poetic accusative, zēna (life), and preposition dia86 (‘on account of’, when taken with the accusative). And when we take these two portions of the name together, we get ‘the

(masculine) thing that is the cause of life’. Socrates judges this name to be ‘entirely fine’ or pangkalōs, because ‘no one is more the cause of life [estin aitios mallon tou zēn], whether for us or for anything else, than the ruler and king of all things’ (396a7-9).87 The superlative here is good evidence for the principle that seemed to be at work in the case of Astyanax’s alternative name. The reason that ‘Zeus’ is not just a good name but is entirely fine — that is, I take, the

86 The capitalized ‘Dia’ means ‘Zeus’, in the attic accusative.

87 This is Socrates’ claim, not mine; I intend to take no particular stance on the accuracy of his reading of Hesiod and Homer.

right name — is that no one else is picked out by the description ‘the cause of life’. We saw that the comparative was used in the Astyanax/Skamandrios case, and Socrates expressed some consequent reservations about the aptness of ‘Astyanax’, despite Homer’s praise. But here, there is no such qualification: Zeus’ name is straightforwardly apt. The best explanation of this is that the analysis of Zeus’ name relies on the same principle as the comparison between Astyanax and

Skamandrios. What determines the aptness of a proper name is its capacity to mark off its bearer from the rest of the world.88 The same account can be given (and indeed is given in the Cratylus) for words in general; we can split them up into parts and then provide descriptive etymologies.89

Names are meant to be vocal imitations of something’s being. We have made sense of the latter part of the definition — names are about something’s ousia to the extent that they mark their object off from the rest of the world — but it is not totally clear that names like ‘Zeus’ and

‘Astyanax’ are vocal imitations. When we imitate, we try to somehow take on the character of the thing we are imitating. Socrates has, earlier in the Cratylus, used painting as an example of imitation. And we can see immediately why this might be. When we paint a picture, even if it’s abstract, we try to capture certain aspects of our subjects. Even in a painting like Guernica — which obviously does not try to capture the spatial aspects of its subject faithfully — puts on display certain emotional and psychological features of the horrors of war. Our imitations, then, are meant to have something in common with their object, whether emotional valence or simple look. But ‘Hector’ and ‘Astyanax’ are not, in any obvious way, like Guernica. Guernica is an

88 This is not, I think, a particularly controversial view. Take, for example, Crivelli (2008). Here he briefly defends the claim that language has two fundamental features on Plato’s view: ‘communication and truth’ (225), echoing Kretzmann (1971) and Ackrill (1994). He cashes out ‘truth’ as the capacity to distinguish something from everything else by its ousia: ‘we use names to “separate being” in that we isolate certain specific beings from others as topics of discussion’ (ibid.). He also maintains that names imitate, whether sounds or shapes or essences. He notes 388b10-11: that it is by using names ‘we teach one another and we separate objects according to how they are’.

89 So, Socrates splits phronēsis, wisdom, up into either ‘the understanding of motion and of flow [phoras…kai rou noēsis]’ (411d4), or ‘to take enjoyment in motion [onēsin hupolabein phoras]’ (d5).

imitation, but these names seem instead like descriptions. So, how are we to make sense of the mimetic aspect of the theory?

Imitation, it seems will be a matter of the properties of the letters of which it is composed.

We will see what this means, in detail, momentarily. I will suggest, after clarifying the theory, that the implausibility that it wears on its face is best explained by trying to make a theory of atomic linguistic representation fit what I claim to be the central point of Plato’s general theory of representation: that model and copy must literally share properties. At 434a2-4, Socrates asks:

If indeed a name will be like a thing, is it not necessary that the elements/letters naturally be like the things, out of which someone put together the first names?

Cratylus quickly assents, agreeing that paintings wouldn’t imitate people if their components did not also resemble the components of people. (Pigments, that is, must resemble skin tones.) Given that this is the case, we cannot get at a complete understanding of Socrates’ theory of linguistic representation without looking at the strange and difficult passages in which he reflects on the properties of individual letters.

As Socrates seems to suggest in the passage quoted above, he takes it that letters have particular natures, with respect to which they can be like or unlike things in the world. Consider as an example the letter rho. Rho, Socrates says, seems to be a tool that is just like all motion

(426c1-2), because the tongue when pronouncing rho is in this least at rest and most shaking

(426e5-6). So, a word that is dominated by rhos should be a word that represents motion somehow, as the rho itself by nature picks out moving things. Socrates gives examples of such apt words, like rhein — to flow — and trechein, to run. The relevant nature isn’t some sort of brute relation between letter and world; it is not as if the name-givers, by fiat, attached rho to motion. If we take the uttering of rho to be more fundamental than the symbol rho — as Socrates seems to do in the Cratylus — then what grounds the aptness of rho for motion is simply that the

uttering of rho, of all the letters, most moves. That is, the letter shares a salient property with the thing that it is best suited to represent. And it is by being composed of letters that have the right relations to the descriptions in the etymologies that we come to have words representing. Once we know that wisdom (here, phronēsis) is, say, delighting in motion, we can judge whether or not it is aptly named by investigating whether our word for wisdom could represent the concepts

‘motion’ and ‘delight’. We answer this question by looking to the primary elements, from which words inherit their capacities to represent: the letters of which they’re composed. And there we’ll find that Greek is better off than English; phora better represents motion than motion does. It is in virtue of sharing features then, in virtue of an imitative relation, that words represent.

There is a wrinkle here that is important to note. Letters taken alone represent no more than colors on a painter’s palette. As Barney (2001: pp. 88-90 esp.) notes, letters merely have the capacity to represent; rho itself doesn’t represent motion, even though it moves, having motion’s characteristic property in common with it. That is, letters merely resemble; they do not yet rise to the level of representation until they have been arranged into a word. Put another way: letters aren’t about anything, not in the same way words are. Take an analogy. Usain Bolt, when he runs the 100-meter dash, is not about motion. Saying he’s about anything sounds like a conceptual mistake. But we could well imagine a photograph of Usain Bolt, a snapshot of the very dash which wasn’t about anything at all and was titled About Motion. What explains the difference in the Bolt case is that the photograph is an intentional object in a way that Usain Bolt himself is not; it was made in order to represent, with reference to some model. In the same way, letters in the Cratylus aren’t works of the right sort of craft. They’re not made, or at least not

made because they have certain features. Rho does not represent motion; it has a capacity to do so that must be actualized.90

There is some concern as to how seriously we ought to take Socrates’ theory here. The atomic theory seems pretty implausible on its face.91 And Socrates seems to disclaim it before he even gives it. In framing his discussion, he says that he will do what little of this that he is able

(425b9-10), and merely the best that he can (426c5-6). He takes his epistemic situation with regard to the aptness of names to be parallel to the one he has in relation to the gods: he in no way knows the truth of the matter (425c2-3). Given this, the objection goes, should we take such a theory to play such a central role in the view of linguistic representation that Socrates seems to propose in the Cratylus?

Though it is hard to imagine what further evidence, besides Socrates’ proclaimed modesty, could decide the issue, it is best to think that Socrates commits himself to the principle, but perhaps not the details, of the theory he here professes. Perhaps it isn’t the case that Socrates means to propose as a final analysis of linguistic representation that rho is best suited for motion- words. But that’s neither here nor there; we are only interested in the broad-strokes view about what makes for a good representation. Claims about the intrinsic natures of letters might be what satisfy the principle for which we’re looking, but they’re not the principle itself. What matters then is that there is some property that letters have by nature such that they are better or worse

90 Letters of the Philebus may well have this feature; they might be works of craft. If they individuate somehow as well, then they might, there, count as representational.

91 I can find few people who disagree with this assessment; the question that divides people is how seriously we ought to think Plato takes this theory. A fairly moderate view is taken by Kahn (1973: 167), who says that though the theory might well seem ‘silly’, Plato ‘may simply have been motivated by the desire to construct a model language that was as natural as possible, in order to make clear the implications’. That is, Plato may not be committed to the mimetic part of the account, and that we should take it that this is just some sort of toy theory. Williams (1982: 92), less modestly, argues that we should take the Cratylus in fact to be a refutation of a mimetic theory. I myself am more sympathetic to Barney (2001: 91), and think that Socrates dissembling about it should merely tell us that ‘some account of this general kind [i.e. a mimetic account] is necessary’.

suited for separating some things off from the world, in virtue of the letters sharing that property with the things themselves.

The view that Plato puts in Socrates’ mouth here is not a popular one. And it’s unpopular for some very good reasons. Not only is it a bizarre view in its general, foundational claims, but it fails to capture some very obvious phenomena. A theory that suggests that in order for words to mean anything at all, their letters have to share some features with the referents of the words that they compose can only make sense of languages that generate words compositionally.

Languages where a single sign picks out a single concept can’t be analyzed into their parts and etymologized. Imagine a written language in which each symbol corresponds one-to-one with a concept. That language will all not just be inferior to Greek — an unlikely enough consequence

— but will entirely fail to represent complex concepts, as it will be representing such concepts with a single sign or ‘letter’. As such, we couldn’t decompose it into parts and check their properties. Further and more simply: perhaps a verbal utterance could move. But it can’t be wise or thoughtful in the same way a person can. Why should Plato have proposed so strange a view?

Surely, he could conceive of languages fundamentally unlike his own; we can see him mention such languages at Statesman 262d, for example. Whether or not he believes the view is beside the point; the key question is what could motivate his putting the atomic view in Socrates’ mouth. What best grounds this theory on which there is a fact of the matter about the representational capacity of letters — things that do not encode some sort of meaning, but instead are fundamentally representational on this view — is that Plato has a pre-existing commitment to a particular theory of representation. And this theory simply must require of him that he thinks that representations and the things that they represent share the same properties.

Not only then is the Cratylus theory of letter-level representation an instance of this more

general theory — rho represents motion because it is the most agitated of the letters — it is good evidence that Plato has a more general view of the phenomenon of representation in mind, and so strongly in mind that he is willing to apply it to cases, where, at best, it is a round peg in a square hole.

Returning to the four conditions on representation, it is clear that the theory of meaning presented here meets all of them. We can set aside the question as to whether we must intend to represent when we choose our words and compose our sentences.92 The theory includes something much stronger on this point. Socrates posits original namegivers, ancient wise men who made the words as tools for this very purpose. That is, there is a representing agent in a much stronger sense than just the person uttering the word; there are, as it were, artists who designed the words. And they designed them with an eye towards the phenomena that we’re trying to describe when we talk; the words depend causally on specific features of the world. It is because of these first two conditions that words and their referents literally share features. When looking for a name for ‘wisdom’, seeing that wisdom is a matter of understanding motion, the namegivers made sure to put a rho in the word. So, motion’s motion and the namegiver’s intentions ground the spelling of the word phronēsis.

There is some question as to what the relevant properties are that model and copy are meant to share. It can’t be every property — no theory of meaning should hold that my name for my cat needs to have the tendency to bite me if it is to count as a name — but the theory of representation as it appears so far is very clear that it needs to be some set of properties. The

Cratylus discussion of word-level representation provides a possible answer to this question: the

92 There isn’t any textual evidence for this claim; our best reasons for thinking it are philosophical. (We don’t think our computer is talking to us when it displays an error message because, among other things, it isn’t engaged in some conscious act of representational word choice.)

properties the model and the copy must share are properties that distinguish the copy as a copy of that particular model. A representation of wisdom is apt, that is, just in case two conditions obtain: first, we must analyze wisdom into its constituent etymological parts; second, we must see whether the elements of our word for wisdom properly are able to represent the description in the etymology.93 It is the first step that fixes which features need copying, and the second that does the copying. A representation of my cat Juno must have the capacity to distinguish her from other cats I happen to know: a representation must be able to individuate. So, the four conditions constituting Plato’s underlying theory of representation obtain in this case, and two of them are extremely surprising: words share properties with their referents, and were designed in pre- history for that very purpose.

The theory of meaning that Socrates defends in the Cratylus then appears to be undergirded by a theory of representation, one which (notably) entails that linguistic representations just must share features with those things that they represent, and entails that words must be tools made for a certain purpose. This is surprising; when we say that language represents, we don’t usually mean it in the same way that we say that paintings or novels or statues represent. But here, I’ll argue, we don’t just have homonymy. The best explanation of the fundamental strangeness of the Cratylean theory of meaning is that there is an essentially unified account of representation, one that we saw in its most transparent form in the Sophist, and that we’ll see again in the Theaetetus.

93 We see a discussion of logoi along these lines at the end of the Theaetetus. Socrates and Theaetetus distinguish three kinds of accounts: ‘a kind of vocal image [eidōlon] of thought’ (208c4-5); a ‘way to the whole through the elements’ (208c6); ‘being able to tell some mark [sēmeion] by which the object you are asked about differs from all other things’ (208c7-8). Here, it seems as if the first kind, images of thought, is being analyzed in terms of the last two: a vocal image in thought — a word — is analyzed into its elements, letters, and also by its capacity properly to distinguish its referent from the world as a whole.

THE WAX BLOCK AND MEMORY

The Theaetetus, in general, is concerned with the nature of knowledge (151d4). Theaetetus proposes accounts, starting with an analysis of knowledge as perception (151e3), and Socrates examines them for their plausibility. The dialogue ends inconclusively, partially because the accounts given have some difficulty accounting for falsity. How is it, Socrates wonders, that we manage to be wrong? At 191c, Socrates proposes that we imagine that our souls have wax blocks in them in an attempt to explain the possibility of false judgment. These wax blocks are meant to model our memories, and I’ll argue that they’re representational in the same way as the Sophist’s statues and the Cratylus’ words. Socrates says:

We make impressions upon this of everything we wish to remember among the things we have seen or heard or thought of ourselves; we hold the wax under our perceptions and thoughts and take a stamp from them, in the way we take the imprints of signet rings. Whatever is impressed upon the wax we remember and know so long as the image remains in the wax; whatever is obliterated or cannot be impressed, we forget and do not know (191d5-e2).

We remember something, on this view, when we possess a certain mental representation. When recalling a particular painting, a particular tree, a particular face, reference is made to some impression that has been made on the soul of that particular. That impression can be more or less like the particular that it is meant to represent. Socrates explains how we can model people who learn poorly or have bad memories with the analogy, saying of the ‘shaggy-souled’ (194e) that they have ‘unclear’ impressions, because they are covered in earth or stone or grime. That is, the metaphor goes, the souls of those who learn badly or remember poorly are somehow occluded, prevented from properly receiving the impressions delivered to them by the senses. Others, however, have no such trouble; ‘in some men, the wax in the soul is deep and abundant, smooth and worked to the proper consistency; and when the things that come through the senses are

imprinted upon this ‘heart’ of the soul...the signs that are made in it are lasting, because they are clear and have sufficient depth’ (194c5-d2). What explains our different capacities to learn and to remember, then, is our soul’s receptivity to the deliverances of the senses.

The wax block is proposed in order to explain the possibility of false judgment. How is it, when Socrates sees Theaetetus, that he can mistake him for Theodorus? He says:

I know both you and Theodorus; I have your signs upon that block of wax, like the imprints of rings. Then I see you both in the distance, but cannot see you well enough; but I am in a hurry to refer the proper sign to the proper visual perception, and so get this fitted into the trace of itself, that recognition may take place. This I fail to do...I get them out of line, applying the visual perception of the one to the sign of the other (193b9-c7).

Socrates experiences the visual perception of Theodorus and Theaetetus, but not perfectly clearly; they are far away, and he is in a hurry. As a result, he ‘fits’ the perceptions into the wrong signs or traces and gets them mixed up. He judges, say, that the man on the left is

Theodorus and the one on the right Theaetetus, when the truth is the other way around. Judging falsely, then, is a failure of matching; it is to match a sense experience to a trace of memory to which it doesn’t belong.

Let us start by noting a highly unusual part of the theory, given the phenomenology of memory. Not all memories, it seems, are generated intentionally. So, I might be able to recall the names of all of the major characters in the television show Friends without ever having had any intention to commit them to memory (and indeed, having formed the intention of committing other things to memory and failed miserably). But this, at least here, is not Plato’s view; encoding a memory, on the view that Socrates seems to propose at 191d, is an intentional action.

So, to repeat 191d4-5: ‘we make impression upon this [the wax block] of everything we wish to remember (boulēthōmen mnēmoneusai)’. Socrates seems to think that memories do not merely

form unnoticed as a matter of course, as part of the regular operation of perception.94 We must have some sort of desire, and act to fulfill it, in order to create some memory.95

This is notable for two reasons. First, in both the Cratylus and the Sophist cases, the theory of representation on which Plato seems to rely is one on which representations necessarily involving someone to do the representing; there are no natural, non-agential, representations.

Here too there is not just an agent, but an agent intending to represent (de re).96 Second, this is a surprising thesis; it seems like a fundamental part of the phenomenology of memory formation that it’s at least sometimes involuntary. But it is clear how this might follow from the theory of representation as it has appeared so far: if Plato thinks that representations are necessarily the result of intentional action, and he thinks that memories are representational, then he is indeed committed to the view that memory formation is the result of intentional action. This is at least one possible explanation for why it is that he claims in the Theaetetus that memory formation —

94 Note that it would be much less surprising if recall required intention (though still surprising; the feeling of deja vu seems to be a case of unintentional recall). But that’s not what the theory says, or at least not only. It is explicit: encoding a memory requires our intending to do it.

95 While characterizing Aristotle’s account of memory, Lorenz notes that: ‘Committing something to memory, on [Aristotle’s] view, crucially involves forming and retaining some sort of representation of it, and remembering it involves retrieving that representation and employing it in a certain way’ (2006: 162). He carries on, in a footnote to this passage, ‘Aristotle adopts Plato’s picture with two significant modifications. First, the generation of imprints does not [in Aristotle] depend on what one wishes to remember, but occurs simply as a matter of the ordinary functioning of the animal’s cognitive apparatus…’ (162 n. 34). Two points are notable here. First, Lorenz too agrees that Plato’s theory of memory (alongside Aristotle’s) is representational (though he leaves it open precisely what representation means here, some of what Lorenz says from 160-62 seems to suggest that he takes Aristotle to have a view roughly like the one that I have been attributing to Plato); second, he notes that memory-formation is for Plato voluntary.

96 It is difficult to overemphasize how striking this claim is. In the standard contemporary stable of representation relations, the least likely one to require that someone intends to represent is the case of minds; no one, so far as I know, thinks that in order to represent the world in my head I need to mean to or to want to. It’s not as if I can turn it off just by losing the desire. Socrates, though, seems to think that this is a perfectly plausible account of memory; it is worth asking why that is.

at least, memory formation given a representationalist view of memory — is an intentional action.97

Memories and their objects share features, though what sorts of features depends on the kind of memory about which we’re talking. According to Socrates, this model is meant to apply not just in the visual case — the case that I will be discussing, primarily, for ease of analysis — but in the case of any memory, including non-sensory ones. We can see this in the very same line where he says that memory formation is intentional: we make impressions of everything among the things we’ve seen, we’ve heard, or we’ve thought of and wish to remember. So, though we will be talking about shapes, primarily, notice that the same arguments could be run for mental content or sound.

The key question for our purposes is to what extent the wax block is merely an analogy.

Preliminarily, note that the language of the analogy is transparently representational. Memories consist of signs or impressions or images on a wax block, impressions that are better or worse fits to particular things in the world. And when we make our judgments, we make them correctly just in case we fit the object of our perception to the correct sign. That is, in judging, what we are doing is evaluating whether some object looks more like one image or another.98 The language with which Socrates analyzes memory wears its representational nature on its face; memory is the sort of thing that is amenable to representational analysis, and the images here are invariably

97 It’s important to note that it is just memory that here is representational. Socrates does not here propose a representational theory of consciousness or of perceiving (though he could very easily have extended the analogy in such directions). Instead, he is specifically interested in memories. This is important for what follows, as the act of perceiving does not require some sort of agent intending to perceive in the Theaetetus, as we can see at 186c1-3: ‘there are some things which all creaturest, men and animals alike, are naturally able to perceive as soon as they are born; I mean, the experiences [pathēmata] which reach the soul through the body’. If representation requires an agent intending to represent, then Plato cannot have a representational theory of perception, except as an analogy or as a metaphor.

98 The language of visual representation is just a convenience. At 192d Socrates clearly extends the analogy to include the other senses (though there is some question as to how to make sense of ‘fitting impressions’ in the case of, say, smells).

representational. But for those that find this appeal to reading straightforwardly when it is available to us unconvincing, there are fortunately several other arguments available.

One way forward is to imagine a view that doesn’t hold that the wax block is representational; if no such view is particularly tenable, that’s a good reason to endorse a representationalist reading. It’s hard to imagine such a theory that still has the requisite explanatory power. The model posits, no matter how we read it, some relation between mind and world. If this is not a representation relation, then we have to have some account of what sort of relation it is. The person who is inclined to be skeptical of the account I’ve given above might answer that what we’re judging is whether there is a causal relation between the memory and the object. We would judge rightly, on this sort of view, if we correctly identified the cause of our memory, without making reference to any shared features between our memory and the stimulus, other, perhaps, than the times at which they occur. But if this is to be an account of judgment, then the relation should be epistemically transparent to us, and causal relations aren’t, at least not in the appropriate sense. We might think that we know that Theodorus caused our memory of

Theodorus because we recall that the memory of Theodorus was generated right after we first saw Theodorus, and tends to get better — though it is unclear what ‘better’ means on the bare causal account, incidentally — every time we see him. But this turns out to ground our knowledge of memories in further memories, immediately generating a regress. It is hard to know what other explanatory relation is to do the work here; it must somehow depend on the features shared between the relata. And this is the domain of representation.

Further, the prologue of the dialogue gives us some reason to think that memory and representation will be linked in what follows. The text opens with a discussion between Euclides

and Terpsion. When Terpsion asks to hear an account of the conversation between Socrates and

Theaetetus, Euclides replies:

Good Lord, no. Not from memory, anyway. But I made some notes of it at the time, as soon as I got home; then afterwards I recalled it at my leisure and wrote it out, and whenever I went to Athens, I used to ask Socrates about the points I couldn’t remember, and correct my version when I got home. The result is that I have got pretty well the whole discussion in writing (143d6-143a5).

He carries on, a few lines later:

You see, I have written it out like this: I have not made Socrates relate the conversation as he related it to me, but I wrote him as speaking directly to the persons with whom he said he had this conversation...I wanted, in the written version, to avoid the bother of having the bits of narrative in between the speeches — I mean, when Socrates, whenever he mentions his own part in the discussion, says ‘And I maintained’ or ‘I said’, or, of the person answering, ‘He agreed’ or ‘He would not admit this.’ That is why I have made him talk directly to them and have left out these formulae (143b5-c6).

The prologue, then, makes salient the very two issues that we have been discussing: memory, and the relation between a representation and its original. And, somewhat surprisingly, it seems to connect the two, thematically. What’s central, though, is the meditation at the very end of the second passage on what is similar between Socrates’ account and the Theaetetus as we have it.

Notice that Euclides was not present at the original conversation between Theodorus, Theaetetus, and Socrates. He is merely recording Socrates’ story, itself a narrative representation of ‘actual’ events. But unlike the Republic, the narrator has self-consciously chosen to modify what he is presenting to the audience, casting the entire thing in direct speech. By doing this, he has made a copy that is more like the model than the one he received; he is better representing the conversation between Theodorus, Theaetetus, and Socrates in virtue of making it have more in

common (by removing some extraneous parts).99 As is so often the case, the frame forecasts a theme from later in the dialogue, and does so in a way consistent with what I have so far said: it emphasizes the agent doing the representing, and, even more strikingly, what representations have in common with that on which they’re modeled.

The only compelling reasons that are available for taking the wax block less literally than the reading above are (misguided) philosophical ones. We might think that a theory on which memories and their objects have features in common is simply too implausible for us charitably to attribute it to Plato. But the force of this worry can be dampened if we’re careful about what it means to share features; specifically, we must clarify what sorts of features are being shared.

Consider the case of the dialogue itself. There is no question of making the dialogue a duplicate of the conversation; it is not in the same place in spacetime and it doesn’t have a volume or a pitch while being ‘spoken’ in a single voice by the slave who is reading it. But location, volume, and pitch aren’t the sort of properties that are relevant for a written representation. What Euclides cares about when he tells Terpsion how he modified what he heard is content; the words, here written, are the same words that were then spoken. There is nothing strange about a written and a spoken dialogue having in common that they express the same propositions; this is just what movie scripts do. And there is nothing much stranger about having one’s (visual) memory instantiate the same proportions as its object. It doesn’t instantiate them in flesh, of course. But our memories need not be fleshy to be memories. Perhaps, for example, the properties shared by my memory of my cat and my cat itself are proportions, just as in the statue and model case. This is not to say that Plato has here struck upon the correct theory of memory. But it is not so laughable a theory that we should think that no serious thinker could have come to it. Further, we

99 And indeed, this is also the sense in which he is improving it; he is checking with Socrates to see whether he has gotten right what each speaker says.

should notice that Socrates doesn’t end up endorsing the model he gives in the wax block; it is not as if we are forced to say that this is Plato’s theory of memory. Instead, all this passage commits Plato to thinking is a conditional: were memory representational, it would involve the sharing of features between model and copy.100 This amounts to endorsing the third condition on representation. The wax block then looks plausibly to be an instance of the general theory so far outlined on this point, barring some more compelling exegetical reason to take the analogy loosely.

The first three conditions hold: a memory is made by a representing agent who is looking to a model, and model and copy share features because the copy depends on the model. The final question about the Theaetetus, then, is whether the properties do individuating work.

Just as it was striking that Socrates emphasized the intentional aspect of memory formation, we should be surprised, when we stop to think about it, that the theory of false judgment, the reason that we were examining models of memory in the first place, is about recognition. When Theodorus and Theaetetus approaching from the distance is the case under discussion, this feels perfectly natural; it is what we would think of as a case of recognition. But again, we should pay close attention to what Socrates says; it is not just things seen or heard of which the wax block is meant to be an analysis, but also things thought. We don’t just have evidence for this in the lines that introduce the model, quoted above, but also in the counterexample Socrates ends up finally mustering against it: a mathematical case. Though there is some controversy over whether the representationalist model really is challenged by

100 In the case of memory, it is the sharing of features between some perceptual process and some memory imprint or trace, as we saw above.

mathematical knowledge, we should notice that Socrates at least seems to take the objection seriously; he thinks that his model ought to be able to account for mistakes of pure reasoning.101

At 195e, Socrates proposes that the wax block theorist can’t account for a particular sort of mathematical case. There is great uncertainty over how we ought to take the details of this counterexample, but let the following stand as a hopefully-uncontroversial reconstruction of the basic structure of the case. Imagine that someone knows both eleven and twelve; they are imprinted on his soul. And when he comes upon eleven or twelve in the world — what that means, for our purposes, doesn’t matter very much — he can match them up to his soul’s impressions. But when he encounters seven-plus-five, he makes what we would call a performance error: he identifies it with eleven. That is, he matches it with the wrong imprint.

And this matching is meant to explain his false (mathematical) judgment. Importantly, the performance error here is not analyzed as an error in pure abstract reasoning; or at least, the sort of reasoning that is the source of his mistake is recognitional. He cannot pick twelve from a lineup, as it were, after having witnessed seven-and-five commit a crime. He falls short in his capacity to individuate some number; it has the exact same structure, cognitively, as recognizing someone’s face. The properties that he fails to recognize then are those very properties that, appropriately noticed, would allow him to pick out the number.102 This is the final condition.

In describing the Wax Block, Socrates makes use of distinctly representational language: he speaks of traces and signs and images. These kinds of things depend on something else, some original, in their causal history. Just as the signet ring leaves a negative in the wax, traces — in other contexts, generally rendered ‘tracks’ — require some animal to leave them behind by

101 Ackrill (1966: 393-4), Bostock (1988: 180), Burnyeat (1990), and Gill (2012), for instance, all think that this is a bad objection to one degree or another.

102 These properties needn’t be essential, at least not at first. We might learn to pick out 7+5 as ‘24/2’. Though, necessarily, (7+5)=(24/2), being half of 24 is not essential to 12; it is, in a certain sense, accidental.

stepping in dirt or snow. Put another way: the properties of some original object, whether paw or ring, are isomorphic to some copy. They share shapes, in the basic case. Images might be more complex, but the basic point stands. Socrates here uses this language to propose a model of false judgment, and to show that our being mistaken about a representation relation obtaining between memory and world is how it is that we make false judgments at all. And this being mistaken just consists in failing to recognize that two things instantiate different properties, and instead taking them to be the same. Not only does the representationalist model depend on the sharing of features, but it further makes the surprising claim that memories are intentionally formed. The best explanation of this being an aspect of the theory, given the phenomenology of remembering, is that there is an underlying account of representation, one that requires that copies are intentionally made by some agent.103

MIRRORS, SHADOWS, AND EIDŌLA

No matter how well we might think that the texts considered above bear out the four conditions with which we started, there are several intuitive and textual considerations that could well still give us pause. Consider as emblematic of these concerns the case of reflection.104 Reflections – as in mirrors or in water – are the sorts of things we might want to call representational. But the theory as outlined above doesn’t allow for such a thing for several reasons: such reflections

103 It is not only in the Theaetetus that Socrates proposes a theory of memory like this one. At Philebus 39a, Socrates wonders whether memory is like a book; ‘if what is written is true, then we form a true judgment and a true account of the matter’ (39a4-5). But not only is there a writer in our souls, but our memory also relies on a painter, one who follows the scribe and creates images, eikones, in the soul. Those images painted that are of the past and present are just that: eikones, or representations. But interestingly, those painted about the future, those that are hopes or fears of things that do not and have not existed and thus have not in fact been experienced — i.e. those things that are groundless — are called phantasmata (40a9). That is, the images painted in the soul that reflect reality are contrasted with those that don’t, along the lines that we would expect. Consider Barney (1992) on these issues.

104 This is not the only case that might trouble us. However, it nicely brings together both the textual concerns and philosophical ones; it is thus a convenient case to discuss.

involve no representing agent; mirrors and other reflective surfaces notoriously do not preserve proportions and other geometrical or visual features. These two facts, taken together, entail that three of the four conditions do not obtain. But we still might want to call them images or representations.

And the problem gets much worse when we see that it seems that Socrates calls them as much in Republic VI. In the famous Divided Line he says:

[The world] is like a line divided into two unequal sections. Then divide each section — namely, that of the visible and that of the intelligible — in the same ratio as the line. In terms now of relative clarity and opacity, one subsection of the visible consists of images (eikones). And by images I mean, first, shadows, then reflections (phantasmata) in water and in all close-packed, smooth, and shiny materials, and everything of that sort, if you understand (509d6-510a3).

One category of things in the world is images, eikones. But the example that Socrates gives – the example he takes to be a paradigm case – is that of shadows and reflections.105 It seems, then, that Socrates has the same intuition that we noticed above: there are images, images we might want to call representational, that fail to meet the conditions on representation given above.106

There are two closely related answers available to us, here. The first thing to check is whether it is possible to date the dialogues differently. It is generally thought that the Sophist and the Theaetetus are later than the Republic, and thus seems an available hypothesis to say that

Plato’s views changed between the composition of the Republic and the material characterized here. And there are some arguments for dating the Cratylus as a rough contemporary of the

105 Shadows are no better-off than reflections, given the theory. Anyone who has ever walked outside at sunset knows that you and your shadow are very different shapes and sizes.

106 In the same way that the word ‘image’ and ‘imagination’ – the corresponding mental faculty – are related, Socrates posits an eikasia to correspond to the eikones.

Theaetetus as well.107 If we find both the developmentalist hypothesis and the re-dating of the

Cratylus plausible, then it is clearly open to us to say that Plato simply has not yet fixed a technical sense of ‘eikōn’ yet, and Republic VI simply reflects an earlier usage. Once he has considered these issues carefully, the story goes, he becomes consistent in the ways that the view here defended would predict. This is an option. But it would be better if the question were answerable without relying on such controversial premises.108

We can say close to the same thing without relying on any controversial dating. It might not be merely that Plato hasn’t hit on a technical sense of eikōn yet; instead, it’s entirely possible that he never hits upon a technical sense at all. As I mentioned in the early paragraphs of this chapter, we might want to distinguish between strict truth-preserving representations that are made by agents who are intending to represent and a laxer notion. Those people might be what the Eleatic Stranger calls in the Sophist eidolopoion, makers of eidōla (239d). Reflections in mirrors and in water, paintings that try to deceive the eye into thinking that they’re three- dimensional – those things would not, on this view, measure up to the high standard of truth- preserving fully-fledged representation. Nor would my face carved into a cliff face by the ocean.

But they could still be images, and they could still, perhaps, be representational.

Put another way: nothing here depends on there being one fixed and final sense of eikōn.

This chapter has not, in fact, traced that word throughout; the Cratylus passages make no use of

107 Roughly, though it’s true that the Cratylus employs what looks to be a traditional theory of Forms, a theory of the same sort as Phaedo or Republic, it seems to take up issues that interest Plato in his later work; we aren’t looking for an analysis of some one thing, like Justice or Beauty, but instead inquiring into the nature of language. In this, the Cratylus resembles the Phaedrus, which itself is generally taken to be written after the Republic. Further, there is some evidence that the version of the Cratylus that has come down to us was revised; there are manuscripts that contain earlier drafts of the dialogue. So, even if it was originally composed earlier, as the stylistic evidence suggests, the version that we have is plausibly a late, or at least later-than-the-Republic product. See Luce (1964) for a review of the available evidence and a survey of the arguments on this topic, though note that he comes down in favor of the earlier date. Dating the Cratylus alongside the Theaetetus is notably argued for by Warburg (1929) in ‘Zwei Fragen zum Kratylos’.

108 And recall the reference to Notomi (2011) above (fn. 80), who also thinks that the vocabulary of images in the Republic is, compared to the Sophist, primitive and not representative of Plato’s considered view.

it at all, and the Theaetetus passages use it interchangeably with eidōlon. What I hope to show here is that there is one surprisingly consistent concept at work in the three dialogues that we’ve primarily discussed, a concept that I’m calling representation (but which you can just as well take as incredibly-strict-representation as opposed to representation-taken-loosely). And in the next chapter, I’ll be arguing that this strict notion is the relation Plato employs as his participation relation in the Timaeus; the conditions that I’ve placed on that notion here will play important roles in the argument there. So long as we’re reasonably convinced that there is such a notion, and that that notion seems to be present in the texts that we’ve examined, then we’ve come far enough.

SOME CONCLUDING REMARKS ON THE UNDERLYING THEORY OF REPRESENTATION

I have argued that there is a surprisingly unified account of representation in Plato’s corpus, one that takes it that the relation that obtains between paintings and subjects, sculptures and models, literary creations and people, and thought and language and world are all the very same relation, distinguished only by what sort of properties are shared between model and copy. There is a representation relation in my strong sense just in case (1) some representing agent looks towards a model while generating a copy, (2) the copy depends on the model, (3) the model and copy share features because of (1) and (2), and (4) the features shared serve to individuate the copy as a copy of its particular model. The theory Plato defends, then, manages to unify what look to be disparate phenomena elegantly; it holds that representation in general is a distinguishing dependence relation that involves the sharing of properties, and that the set of properties shared determine which of the various kinds of representation each specific instance of the relation is.

Not only, though, have I suggested that Plato has a unified theory. I’ve further argued that this

theory solves otherwise intractable exegetical and philosophical problems; without a view of this kind, it is hard to see why it is that Plato, for instance, would think that memories must be formed intentionally.

Though a unified account of representation is interesting and philosophically useful in and of itself, it should be noted that Plato puts it to work beyond the domain of what we usually take to be representation. In the Timaeus, Plato considers the possibility that participation itself, the relation that obtains between Form and sensible quality, is a representation relation. The relation that obtains between Forms and the sensible world is, of course, the fundamental relation of Platonic metaphysics; this relation fixes all of the truths and is the ultimate explanation of every fact. Let me sketch, then, the outlines of a representation theory of participation, as understood in light of the above, and then remark briefly on its virtues.

A representation theory holds that Euthyphro is pious just in case he is at least partially a copy of Piety. That is, he shares a certain set of properties with the Form, the set that distinguishes the pious things from the impious. This set will be whatever the correct analysis of

Piety turns out to be. This set won’t include the ideal features of the Forms, the features Forms have in virtue of being Forms at all (being eternal, being unchanging, and so on). These features, after all, are not distinctive of Piety; they are distinctive of Forms. So Euthyphro needn’t be an abstract object in order to be pious. The relevant properties will, though, be the essence of Piety, if that’s what we’re looking for when we look for an account of a Form. The account defended here then does not just make good sense of some otherwise deeply puzzling passages, but can be extended to do important metaphysical work in dialogues that were not here taken up.

This sort of representation theory then has two further surprising and important implications. First, it is required by the account of representation we’ve found in the passages to

which we’ve looked that there is something doing the representing. In this case, then, something must set up the world such that Forms are the models and sensible particulars the copies.

Interestingly, precisely this claim is made in the Timaeus, if we take the dialogue as a literal cosmogony. The world, Timaeus claims ‘is a work of craft’ (29a), the product of a craftsman looking to ‘what is always changeless’ and using it as a model (28b). This dialogue, the only one that makes extensive use of image-language to characterize the participation relation, posits some craftsman to do the representing. The theory of representation I’ve characterized above entails that there is very good reason for this: otherwise, the world could not be a strict, truth- preserving representation at all, as it would lack a representing agent. We should, then, be literalists about this aspect of the Timaeus, and take it that the demiurge is no mere metaphor; he is a real agent.

Second, if this theory of representation is correct, it provides some strong evidence in favor of the view that Plato maintains Self Predication109 in the late dialogues, and, more importantly, that he should, or has good reason to. Piety must be pious, on a representation theory, because it is by being a copy of Piety’s piety that anything at all comes to be pious; the sensible particular, on this analysis, must have this property in common with the Form. As I argued above, this is clearly central to Plato’s theory of representation, so central that he goes through great trouble in the Cratylus to make it a part of his account. It is not some metaphorical sharing of properties — it is not that letters instantiate motion in one way and Achilles another.

Letters, and the words that they make up, move, just as Achilles does. Forms too, then, must on a representation theory have their proper feature in the exact same way that the particular properties instances which they ground do. And if the Timaeus is a late dialogue — contra Owen

109 This is the name given to the thesis that each Form has its own proper feature: that Justice is just, Piety pious, and Red red. It is, as Vlastos (1954) argues, a key premise in Parmenides’ Third Man, and has been an object of much discussion since.

(1953) and with Cherniss (1957) — then it is our latest extended discussion of Platonic metaphysics. This theory of representation, then, gives us good reason to think that Plato’s solution to the objections of the Parmenides is not to give up Self Predication, whatever his solution happens to be.110

The reading I’ve defended here, then, does not only suggest that Plato had an elegant and unified account of strict, truth-preserving representation, one that somehow managed to avoid being disjunctive and ad hoc. It does suggest these things; that Plato managed to defend such a view is itself a remarkable philosophical feat. But it further holds that he deployed this theory of representation in his late work to answer the central question of Platonic metaphysics: what is it, exactly, that ties our world to that of the Forms? Questions remain, of course. We might wonder how such a representation theory does deal with the objections of the Parmenides, if it does not

(and indeed cannot) use the strategy Lee pursued. It is my view that it can and does. But this must be answered elsewhere.

110 Some, like Edward Lee (1966) have tried to give an account of the Timaeus on which Forms and particulars do not literally share properties. I think, with Gill (1987), that there are clear problems with his account, and that it is not consistent with the text of the Timaeus itself. But it is not consistent with the passages in the Theaetetus, the Sophist, and the Cratylus either, among others. Whatever our account of the Timaeus happens to be at the end of the day, it must be consistent with Plato’s theory of representation.

CHAPTER 4: THE GEOMETRY OF FORMS

In this chapter, I hope to deliver on a long-awaited promissory note: to articulate and defend a

Theory of Forms with some surprising features. This Theory of Forms holds:

1) There are only Forms of mathematical or geometrical properties.

2) Forms are fundamental non-concrete objects.

3) Forms explain sensible property instances by being paradigms or models of those

property instances.

4) Forms themselves instantiate their proper features.

As noted in the first chapter, this is a way of answering our opening three questions: what the

Forms are, how they’re related to the sensible world, and how many there are. Given that the view I’ll defend here is a sort of realism, the scope is narrow. Further, we’ve committed ourselves to a version of paradigmatism, which is a combination of a claim about participation, that Forms and particulars are linked by a likeness or representation relation, and a claim about

Forms, that they’re perfect property instances. These two claims are strange bedfellows; they seem to suggest that the only property instances there could be are mathematical ones, and it’s abundantly obvious there are non-mathematical properties in the world.

That said, this is less surprising than it might initially appear. One of the fundamental features of the Timaeus, as I’ll argue below, is that it makes use of highly reductive explanatory paradigms. Apparently macro-level properties – like, for instance, willpower – are explained in virtue of the lower-level microphysical magnitudes (that is, the mathematically-structured

elements). All it is to be willpower is to instantiate certain physical properties that are, in principle, reducible to claims about ratios of geometrically-structured elements, instantiated in a matter-space hybrid with the fundamental tendency to move. These, I’ll argue, are the only explanatory principles we need in order to generate the physics and philosophical anthropology of the Timaeus.

I will start by giving two arguments that Forms must be mathematical, building upon the material from the two previous chapters. If the participation relation is a representation relation as I’ve analyzed it, then that straightforwardly entails that Forms and sensible particulars must share properties. And that in turn entails that the sorts of properties shared must be properties that can be instantiated by non-concrete objects. This, I’ll argue, gives us good reason to admit only of mathematical Forms.

We can get this same result the other way around, by starting with the physics and building up. I argued in the previous chapter that the Receptacle plays an explanatory role independent of the Forms: it, at minimum, explains motion (and probably also extension). Once we admit of a non-Formal explanation of motion, it will become apparent that we can do all the explanatory work the rest of the cosmogony requires of us with mathematical Forms; we won’t need Forms that can’t be analyzed down into ratios or numbers. If we think that Plato doesn’t introduce Forms that he doesn’t need, then this gives us further reason to believe my thesis.

THE ARGUMENT FROM REPRESENTATION

I argued, on the basis of passages in the Parmenides, Theaetetus, Cratylus, and Sophist that the representation relation has a number of consistent features in Plato. Most important for our

purposes here, though, is the feature-sharing condition: just as word and referent must in fact share salient features in order properly for the former to represent the latter in the Cratylus, I’ll argue that Form and sensible property instance must have some set of features in common. (Let us set aside what set until the end of this section.)

The argument from representation is very simple:

1) In order for x to be a representation of y, x must share salient features with y.

2) Token sensible properties are representations of Forms.

3) Token sensible properties share salient features with Forms.

I argued for the first premise in the third chapter, and I won’t relitigate the issue here. The central question for our purposes is related to the second premise: is the relation that obtains in the

Timaeus between Form and sensible property instance the same relation that I identified earlier?

If it is, then we have very good reason to endorse the property-sharing thesis, (3).

There is good direct and indirect evidence for (2). For one, the sensible world is frequently referred to as an image of the Forms throughout the Timaeus. The kosmos is an image of something at 29b2; it is an image of a paradigm at b3. He goes on, making similar claims at

29c2, 37d5, 37d7, 52c2, and 92c7. These are just the nouns. Timaeus claims that the sensible world is made in the image of something else – i.e. uses a verbal construction expressing the same thought – at 29c1, 39e4, 40a4, 48c2, and 50d2. I will take up specific claims in specific passages momentarily. However, it is hardly a novel observation to say that the Timaeus is chock-full of imagistic language, and its speaker uses it almost without exception to talk about the relationship between the Forms and the sensible world.111

111 With images, of course, come models. And the Timaeus contains lots of paradeigma talk as well. The world’s model is referred to at 28a7, 28b2, 28c6, 29b4, 31a4, 37c8, 38b8, 38c1, 39e7, 48e5, and 49a1.

As a matter of conceptual vocabulary, we are firmly in the language of paradigmatism.

This is clear if we compare the Timaeus as a whole to a wholly uncontroversial instance of this sort of theory in the Parmenides. At 132d, Socrates says:

…what seems to me most likely is thus: these Forms are just like paradigms [paradeigmata] set up in nature, and the other things are similar to them and are likenesses [eoikenai kai einai homoiomata], and partaking of the Forms for the others is nothing other than being made in their image [eikasthenai autois].

This is as clear an articulation of paradigmatism as we could hope to receive, and it is characterized, in many respects, exactly as the theory of the Timaeus is. The Forms are models or paradigms, standing in nature independently. The sensible things – the ‘others’, that is – bear a relation to them in the neighborhood of ‘being an image of’ (eoikenai, einai homoiomata, eikasthenai). The first two phrases express some sort of similarity relation; the last, eikasthenai, means at base ‘to be made an eikōn of something’. The theory, then, in its clearest instance, is expressed in terms of paradigms and images – just as we’d expect from paradigmatism.112

But merely sounding like the Parmenides passage and having a high concentration of image- and model-words does not at all guarantee that the Timaeus’ images are images in the strong sense I argued in chapter two. All of this is perfectly consistent with loose or metaphorical talk. Instead, I need to provide some reason to think that the theory of participation used by

Timaeus meets the conditions I’ve laid out on representation: Representation obtains just in case

(1) some representing agent looks towards a model while generating a copy, (2) the copy depends on the model, (3) the model and copy share features because of (1) and (2), and (4) the features shared serve to individuate (though not always uniquely) the copy as a copy of its particular model.

112 The Timaeus too makes extensive use of homoios language.

It’s worth pausing, though, and reflecting on what sort of argument might count as decisive here. In effect, the conclusion of this section is meant to be that the third condition on representation obtains in the Timaeus and that what has typically been called Self-Predication is true (as, if Self-Predication is true, we’re most of the way to a sort of paradigmatism). And the way I propose to get to that conclusion is by showing that the theory of representation at work in the Timaeus is the same as the theory that I have drawn out of the Cratylus, Sophist, and so on.

But this amounts to arguing that the conditions obtain, and the obtaining is the conclusion I am trying to establish. There is no chance of giving a non-circular decisive argument. Instead, I will try to show that there is good reason to think that each of the conditions obtains in the Timaeus.

It is very clearly true of Timaeus’ account that some agent is looking towards a model in making its copy.113 Timaeus asks, near the start of his long speech, what kind of model the

Demiurge used, an eternal or mortal one. In that context, he says:

…whenever the craftsman looks at what is always changeless and, using a thing of that kind as his model, reproduces its form and capacity, then, of necessity, all that he so completes is beautiful (28a-b).

Which of the two models did the maker use when he fashioned it [the kosmos]? Was it the one that does not change and stays the same, or the one that has come to be? Well, if this world of ours is beautiful and its craftsman good, then clearly he looked at the eternal model. But if what’s blasphemous to even say is the case, then he looked at the one that has come to be (29a).

In both of these cases, the discussion is framed in terms of looking. The Demiurge picks his model – precosmic soup or the Forms – and, keeping his eye on it, works up the sensible world such that the world resembles that model. Further, he’s engaged in a sort of creative act. Not, of course, an ex nihilo creation, but creating in the very same way that a sculptor turns a block of

113 We entertained the possibility briefly that the Demiurge might be a mythological device, a metaphor for something else, in chapter two. Given how much philosophical work he does in the dialogue, I suggested that such a reading seemed worse off than a literalist one.

marble into a bust. The Demiurge, after all, just is a craftsman. The first condition on representation is easily met.

The sensible world further depends on the model. There are two (importantly different) senses in which this is the case. There is, for one, the standard Theory-of-Forms sort of dependence. The Forms are those things upon which every sensible property instance depends for its character; the reason anything is a table is that it stands in relation to the Form of Table.

There is a clear sense in which the sensible world depends on the Forms. More specifically, the sensible world’s features depend on the features of the Forms. Consider a passage from early on in Timaeus’ account:

…let us lay it down that the universe resembles more closely than anything else that Living Thing of which all other living things are parts, both individually and by kinds. For that Living Thing comprehends within itself all intelligible living things, just as our world is made up of us and all other visible creatures. Since the god wanted nothing more than to make the world like the best of the intelligible things, complete in every way, he made it a single visible living thing, which contains within itself all the living things whose nature it is to share in its kind (30c-31a).

From the very beginning, we are led to believe that the Demiurge’s cosmogonic methodology consists in looking to the Forms and reproducing their characters and capacities in the sensible world. In each case, then, the features of the Forms stand in the causal history of the corresponding sensible features. Further, the latter counterfactually depend on the former. If the

Living Thing contained within it different living things than it does – if it contained no fishes, for instance – that difference would be reflected in the sensible kosmos. (This, ultimately, is no different from saying that the characteristics of the Forms stand in the causal history of the characteristics of the sensible world.)

Notice that not only does the copy depend on the model causally and synchronically, but it is further that dependence that explains the sharing of features between Form and sensible.

Consider the causal case and grant, for now, that the kosmos is like the Living Thing in at least the respect that they contain the same number of sorts of living things. This, after all, is what

30c-31a suggests. In the story I told above, two facts explain this similarity: (1) the Demiurge thinks it best that the Forms and the sensible world are as similar as possible and (2) as such he looks to the Forms and reproduces their characteristics in his work. We have, on the grounds of

30c-31a, evidence that if the Forms and the sensibles share features, they do so because the

Demiurge looks to the Forms and because the Forms stand in their causal history.114 This is

(conditional) evidence for the third condition on Platonic representation.

30c-31a is not a unique passage. Consider Timaeus’ account of the introduction of time to the kosmos.

Now when the Father who had begotten the universe observed it set in motion and alive, a thing that had come to be as a shrine for the everlasting gods, he was well pleased, and in his delight he thought of making it more like its model still. So, as the model was itself an everlasting Living Thing, he set himself to bringing this universe to completion in such a way that it, too, would have that character to the extent that was possible. Now it was the Living Thing’s nature to be eternal, but it isn’t possible to bestow eternity fully upon anything that is begotten. And so he began to think of making a moving image of eternity: at the same time as he brought order to the universe, he would make an eternal image, moving according to number, of eternity remaining in unity. This number, of course, is what we now call “time” (37c-d).

114 Another way to put the point is this. We all agree that somehow Forms and sensible objects stand in some sort of dependence relation: the sensibles depend on the Forms. But reasonable people might disagree as to what precisely the relata are – do Forms explain tables or do they explain the property of being a table, for instance? On a representation view, the copy depends on the model in a specific way: the copy’s features are a function of the model’s features. To see this, imagine if you were asked to explain a difficult representational case, like how it is that Guernica is meant to represent some specific scene from the Spanish Civil War, given that in the photorealistic sense, Guernica doesn’t at all look like a scene in any war in this (three-dimensional) world. In doing this, you might talk about the horror and the anguish on the subjects’ faces. This is meant to capture the horror and anguish of victims of a certain bombing. The model’s horror and anguish grounds the horror and anguish of the painting’s characters.

The explanation of time has much the same structure as the explanation of species at 30c.115 The

Demiurge noted that the Living Thing was eternal. He wanted to make the sensible world as much like the Living Thing as possible, so he made it as eternal as possible, so to speak.116 There is more to say about how it is, precisely, that the world can be pseudoeternal without being eternal – and I’ll say more below. But the structure of the explanation is clear. The Demiurge looked to the model, the copy depends on the model, and the copy and the model share features because of this looking and that dependence.117

I’ve been framing this argument as a conditional: if Form and sensible share features, this is why. And as I wrote above, arguing directly for the claim that the two worlds share features is troublingly close to circular. But despite that, it’s worth delving into the case of time to show that there is some good reason to think that Form and sensible do literally have features in common.

They aren’t mere approximations. This, of course, provides evidence for the argument from representation at the same time as making it redundant.

In the precosmos, the not-quite-world lacked days and nights and months and years (37e).

In a certain sense, time passed in the precosmos; as we know from the second chapter, things change. But the change lacked structure and consistency. There were some laws – like tended to like (53a) – but nothing cyclical or unified. The world of the Forms, of course, is totally unlike

115 With an important difference that we’ll come to soon: the species reproduced from the Living Thing were part of the Living Thing’s proper features, whereas its eternity is an ideal feature.

116 As mentioned briefly in chapter three, it is important to distinguish this view from an approximation view in Nehamas’ (1975) sense. On an approximation view, as he characterizes them, ‘a Form is never manifested in the sensible objects that participate in it…The imperfection of the sensible world consists in the imperfection of those very properties the possession of which makes it a copy of the world of the Forms’ (107-108). To use Crombie’s example that I cited there: an approximation theorist thinks that Helen’s beauty and Beauty’s beauty are somehow different. When I say that Forms and sensibles ‘literally share properties’, I mean to deny this: Helen’s beauty is not different in kind from Beauty’s. It is not merely analogical.

117 This point has been made in a funhouse mirror by David Keyt (1971) ‘The Mad Craftsman of the Timaeus’. Keyt thinks that the Demiurge is making a mistake in doing this.

this; it is maximally structured and unchanging. The Demiurge is faced with a problem: how to make an unstructured, constantly-changing mess into something perfectly stable. His solution is to keep the change – due to the nature of his materials, he can’t get rid of that anyway. Instead, he structures the change, makes it cyclical and time-governed. He introduces planets and stars and other astral bodies, bodies whose movements just are time.118 Their cyclical motions, those that constitute days, months, and years (39c), provide constancy in change. They provide an unchanging, constant, and predictable framework in which everything else is less so. This, according to Timaeus, is a way that the sensible kosmos can imitate Formal eternity.

Because of the limitations of the materials, this proves an interesting case for the argument from representation. The kosmos simply can’t be eternal in the same way that the

Forms are; the Forms are eternal in the sense that they exist in a constant present, outside of time, unchanging. Time, past and future included, is meant to help the sensible world achieve Formal constancy in a way that it otherwise couldn’t. The Demiurge accomplishes this end by introducing a feature of the Forms into a part of the world; he makes the orbits of the celestial objects regular, predictable, and unchanging (even their retrogressions are stable). The length of the day or of the year doesn’t change and provides stability in an unstable world. It’s true, then, that the kosmos is not identically eternal; but it’s (deficiently and partially but non- metaphorically) unchanging. The Living Thing and the kosmos are both unchanging, then, because the Demiurge looked to the former to make the latter and one depends on the other.

The difficult question for my reading of the Timaeus, I think, is the fourth condition on representation, that the features copied somehow individuate the copy as a copy of its model.

When making a bust of Socrates, we don’t try to capture his wit and his wisdom, at least not primarily. Instead, we’re trying to reproduce his distinctive facial features, his upturned nose and

118 …χρόνον ὄντα τὰς τούτων πλάνας (39d1).

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his protrusive eyes. If we try to make his eyes sparkle or his lips curl in order to capture his wit, note that it has to be his eyes and his lips; a witty-looking bust will not be a bust of Socrates, no matter how well it might visually portray his distinctive sense of humor, unless it fundamentally looks like Socrates. The sorts of properties that model and copy share are those that have the capacity to individuate in the given medium. (In order to make something sound like the song of a robin, you don’t paint it red.)

One appealing story about the relation between the sensible world and the Forms is that the individuating features of various Forms – which will turn out to be their essences – are instantiated by the kosmos such that we will know which Forms are instantiated where by their fruits; just things instantiate Justice, good ones Good, and so on. But this story, simple and appealing as it is, doesn’t quite fit the text. Take the case of time again. The reason that the

Demiurge makes the world a chronologically-governed one is that its model is eternal. But, importantly, it’s not at all obvious that that model is the Form of Time. Timaeus says that the model is the Living Thing, and it’s the Living Thing’s being everlasting that causes him to introduce time (37d). But being everlasting isn’t what’s distinctive about the Living Thing; every

Form has that property. The Demiurge isn’t reproducing a distinctive, individuating feature of the model, then. The appealingly clean first story can’t, as so often, be quite right.

It is first worth noting that, though they go unnamed, it is extremely likely that Forms other than the Living Thing are at work in the Timaeus. Consider the geometrical analysis of the elements. Circa 54a, we are introduced to two fundamental triangles: one isosceles and one half- equilateral scalene. These triangles are variously rearranged to create the Platonic solids, and each of those solids are assigned to a classical element. Fire, earth, air, and water are thus

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analyzed in terms of their shapes; what it is to be fire is to be a certain sort of tetrahedron.119 It is hardly an eager leap for someone used to reading Plato to think that what we’ve been given by

Timaeus here is an account of the Form of Fire: it’s a certain kind of tetrahedron; it is the mathematical object that grounds all visible sensible property instances.

It is of course an open possibility that the fire facts are somehow grounded in the Living

Thing. Perhaps, that is, the geometrical facts about fire are somehow contained in the essence of the Form of the Living Thing. The Demiurge, when he’s assembling the elements, is just repeating what he’s already done on this story: he’s looking to one Form, the Living Thing, and reproducing a fire, earth, air, and water, each of which are parts of it. The Living Thing, then, would be a sort of higher-order Form, one that explains a variety of properties.

There is some evidence for this sort of view. The Living Thing, as we see early on, encompasses all sorts of living things; ‘the world is like, above all things, to that Living Thing of which all other living things, severally and in their families, are parts’ (30c). This seems to suggest that when the Demiurge is looking to make the species deer, he is not looking to the

Form of the Deer; he is looking to the Living Thing, which contains within itself not just the model he needs in order to make deer, but also elk and moose, and antelope and impala. The

Form contains its parts. Given that deer, elk, and moose – and perhaps even antelopes and impalas – are made out of the classical elements, the Living Thing might contain Fire and Earth and the rest in the same way that in contains Elk and Deer. The entire kosmos, then, would be modeled on one (extraordinarily complex) Form.120

119 Precisely what sort of tetrahedron must be discussed below; it’s obvious that not every tetrahedral thing is on fire.

120 This seems to be a sort of Form-monism. There is one Form, the Living Thing, in virtue of which the kosmos has all of its properties. That Form, however, is highly structured and complex; the way that it explains every sensible property of the kosmos is by itself instantiating those properties. But it does not do so in any particularly interesting or explanatory way; in order to make sense of what sensible fire is, we must still look to Fire – it just turns out that Fire is part of the Living Thing. Here, it’s worth looking to Armstrong’s Truth and Truthmakers. Discussing the

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This might be a distinction without a difference. These lower-level Forms, Elk and Deer and Fire and Earth, make up the structured whole Living Thing in the same way they make up very small parts of the kosmos. But they are still very much parts of the Living Thing and have structures of their own. Consider The Last Supper. It is, trivially, not just a painting of Jesus and

Judas and the rest, taken together. It’s also a painting of Judas. It represents the parts of the scene as well as the wholes. If we’re looking to explain why it is that Judas is painted this way rather than that, the answer will not be cast primarily in terms of the properties of the entire scene, but instead in the properties of Judas, a part of the scene. Similarly, even if we accept the higher- order Form view of the Living Thing, on which the other Forms of sensible properties are mere parts, it will turn out that those Forms still exist and still play an explanatory role. They may, however, depend upon the Living Thing.

Whether or not Fire and Earth are fundamental, then, it is plausible both that they exist and that they play an important explanatory role in the Timaeus. But this only brings us back to the first problem. The account of representation that we saw earlier requires that the representing agent reproduces individuating features, their sort determined by the sort of representation in which he is engaged, in his model. This account might, with some finessing, make sense of the geometrical elements; perhaps what distinguishes fire from not-fire really is its tetrahedral shape.121 But the case of eternity poses a serious problem for the individuation account, and it is

proposal that the world might be the truthmaker for any sentence, he calls it ‘the least discerning’ and ‘most promiscuous’ truthmaker (pp. 18-19) and holds that it’s of no use for philosophical speculation. Similarly: the Living Thing might well in fact and at some level of remove explain every sensible property instance. But it does so by way of the explanatory powers of lower-level Forms, and it is to these we should look.

121 As I said above, this can’t be quite right; there are lots of macro-level tetrahedrons that are not on fire. Something must distinguish them from the micro-tetrahedrons that are fiery, something distinct from their shape. Again, I’ll say more about this below. But it seems to me the options include: (1) claiming that macro-tetrahedrons have fiery dispositions that go unactualized (2) claiming that macro-tetrahedrons are insufficiently pure to manifest fire behavior and (3) claiming that there’s no such thing as a perfectly tetrahedral macro-object.

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not alone.122 At best, the Living Thing distinguishes itself from concrete physical objects by its being properly eternal and outside of time. But Good and Justice and Beauty are eternal too, and not because they partake in the Living Thing. So, reproducing eternity in the sensible world does not serve to individuate the world as a copy of the Living Thing rather than as a copy of Justice.

Cornford provides us with the start of a solution to this problem. He suggests that it is not the Living Thing that serves as the Demiurge’s model, but instead the whole realm of the Forms

(1937: 28). He understands the Living Thing as ‘all the subordinate generic and specific Forms and differences that would appear in the complete definitions of all the species of living creatures existing in our world, including the created gods’ (40-41). Insofar then as we are considering the kosmos’ status as a living thing and something that contains living things, the Demiurge’s model is indeed the Living Thing. But when we instead conceptualize it as a copy of the whole world of

Forms, a world that isn’t just alive but also beautiful and just and good (and red and green and sempiternal), we have some license to think that sempiternity is, in fact, an individuating feature.

Every Form is eternal. That was, after all, the problem we were faced with for the individuating condition on representation. But the Demiurge is trying not just to reproduce the character of a single Form, one that has eternity in common with all its brethren. The Demiurge, on the Cornford-style view, is in fact trying to reproduce the whole world of the Forms. That is, he is looking to the eternal model referenced at 29a. And what distinguishes this model from its

122 The kosmos also doesn’t have the character of a part because the Living Thing doesn’t have the character of a part. The Living Thing is in no way unique in this way, unless we accept a radically revised ontology of the Forms on which every other Form depends on the Living Thing – including Justice and Good and Beauty – and the Living Thing does not depend on any other Form. Perhaps the Living Thing contains all sensible properties, but Aristotelian testimony suggests that Plato thinks that the Good is fundamental (and in no way depends upon something’s being alive). That said, there is some evidence from the Sophist that Being might be alive: life, along with motion and wisdom and soul are said to be present in Being at 249e. And this seems to be the product of something of a generalizable argument: because Being ‘completely is’, it must have understanding, and since it has understanding, it must be alive. If every Form has pantelos existence – and that seems like part of what it is to be a Form – then every Form is alive. This provides some grounds for thinking that the Living Thing is a wholly foundational Form. If Timaeus thinks that every Form is alive, then there are even better reasons for the kosmos not to have the character of a part: being a whole, not a part, is special (perhaps special in a restricted way) to the Living Thing.

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rival, the model that has come to be, precisely is that it is unchanging and eternal, that it is kata tauta and aidion. The individuation thesis makes sense, then, if we hold that the Demiurge looks to the entire world of the Forms rather than merely a single Living Thing.

The story, then, goes like this. The Demiurge is copying or representing the Living Thing insofar as he creates a kosmos that is (a) itself alive and (b) replete with all the various species of living things that the Form itself contains. Being alive and being full of the relevant species just is the essence of the Living Thing. These are the properties that distinguish the Living Thing from the rest of the Forms. And it’s true that he’s also representing the Living Thing when he makes this kosmos eternal. But he’s copying that model’s eternity only insofar as he’s copying the world of the Forms, a world which is distinguished from the sensible world explicitly by its being aidion. His looking to the Living Thing when reproducing its eternity, then, is just a way of looking to the world of the Forms taken entirely.

Eternity is a difficult case and requires a complex story. But there are easier ones, one that seem more obviously to meet the individuation condition on representation. Take the case of fire, mentioned above. As we’ve seen several times by this point, the Demiurge is looking to reproduce certain geometrical magnitudes, magnitudes that distinguish the classical elements from each other. Fire is tetrahedral, earth cubic, and so on (as usual, setting aside the other conditions which complicate but do not change the story). Once we accept Timaean mathematical physics, we are perfectly capable of recognizing what is represented where; we look for the varieties of tetrahedron and find fire. Fire’s essence, its geometrical properties, are reproduced in the sensible world, and it is by this essence that we identify the Form so instantiated.

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There are good reasons then to think that the sensible world really is an image of the world of the Forms in the very way that words are meant to be images of their referents in the

Cratylus, or, more simply, busts are images of their subjects in the Sophist. There’s a craftsman, a craftsman who looks towards a certain model upon which the copy depends, reproducing some of that model’s individuating properties in the copy. None of what I’ve said here, of course, is decisive. But given how surprising this account of representation was in other contexts, it’s notable that the Timaeus apparently assumes this same account.

The argument from representation does not show anything especially radical: it merely supports what’s taken by many to be a perfectly standard (if misguided) Platonic claim, that

Forms have their own proper features. If the Forms and the sensible world stand in the same sort of relation as statue and subject, then it simply follows that Forms and sensibles do share features; they share essences, geometrical magnitudes in the cases of the elements. The Form of fire is fiery in the very same way that fire is; Justice is just in the very same way that the kallipolis is.

INTERLUDE I: THE LIVING THING AND THE WORLD OF THE FORMS

We’ve seen above that Timaeus goes through some trouble in order to reproduce the character of the Living Thing in our kosmos. Consider the passage in which that Form is introduced:

…let us lay it down that the universe resembles more closely than anything else that Living Thing of which all other living things are parts, both individually and by kinds. For that Living Thing comprehends within itself all intelligible living things, just as our world is made up of us and all the other visible creatures. Since the god wanted nothing more than to make the world like the best of the intelligible things, complete in every way, he made it a single visible living thing, which contains within itself all the living things whose nature it is to share its kind (30c-31a).

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Above, I took the Living Thing to be an everyday Form: it has a proper feature, living, that it explains in all of those things that are modeled upon it. And Timaeus has characterized it strangely by suggesting that it contains within it all of the species in our kosmos – this is something of an extensional definition of ‘life’, it seems – but it is an otherwise unremarkable

Form.

We could, however, take Timaeus at his word when he reasons that the best way to make the kosmos complete is to model it after the Living Thing because that Form is ‘complete in every way’ (κατὰ πάντα τελέῳ). Why, we might ask, is that in any way special to the Living

Thing? The Good, the Just, even the Table are ‘complete’ in the same way the Living Thing is if it is unremarkable in the way I’ve understood it above. One way to have this claim – and the claim that the Living Thing in no way has the character of a part, made just prior to our passage

– come out both true and contentful is instead to say that the Living Thing is special: it is the world of the Forms taken together.

There is some further textual evidence for this suggestion. The Living Thing, Timaeus says, contains all intelligible living things. This might remind us of an argument in the Sophist.

The Eleatic Stranger asks, wholly rhetorically:

…are we going to be convinced that it’s true that change, life, soul, and intelligence are not present in that which wholly is, and that it neither lives nor thinks, but stays changeless, solemn, and holy, without any understanding (248e- 249a)?

Theaetetus, as is his wont in the Sophist, quickly assents – such a consequence is allegedly unthinkable. The natural reading of this passage – the one Owen (1966: 338) gives, for instance – is that the Forms, all of them, must be living things if they’re to be proper Beings. If all of the

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Forms are alive, then the Living Thing isn’t just bizarrely extensional for a paradigm; instead, it’s the whole structured world of the Forms.

Further, consider one of Timaeus’ first arguments, one that demonstrates that the kosmos must have been modeled after the eternal paradigm rather than the one that came to be.

Which of the two models did the maker use when he fashioned it [the kosmos]? Was it the one that does not change and stays the same, or the one that has come to be? Well, if this world of ours is beautiful and its craftsman good, then he clearly looked at the eternal model. But if what its blasphemous to even say is the case, then he looked at one that came to be. Now surely it’s clear to all that it was the eternal model he looked at, for, of all the things that have come to be, our universe is the most beautiful… (29a).

Two parts of this passage move us to think that the Living Thing might not be a regular Form but instead the whole world of the Forms. On the assumption that the Living Thing is a Form like any other, the argument does not in fact demonstrate that the universe is modeled on that particular Form. All it shows is that it is a copy of some Form; any Form will do. But if the world is being modeled on a World, not a regular Form, then this argument is more powerful: it shows us exactly what the Demiurge was looking at when he made the kosmos, explaining why

Timaeus chooses to introduce the Living Thing without comment soon afterwards at 30c. Notice in addition that for most of this passage the generated model is not in fact graced with the definite article – it is not picked out as a unique generated model. At 29a4, the Demiurge looked towards a generated one if the blasphemous obtains; the universe is the most beautiful of all of the generated things. In contrast, the world of the Forms is picked out as definite in each instance. Timaeus might be meaning to pick out something specific here. And if he’s doing that, then he must mean the whole world of the Forms – he should otherwise just say that our kosmos is modeled after some eternal thing or another. It’s possible, then, that just as our kosmos is a

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living world containing multitudes of properties and objects, so too is the world of the Forms. It lives in the sense that everything in it does: the Good and the Just and the rest.

If we think that the Living Thing is the structured whole, the world of the Forms itself, we can help ourselves to some major explanatory advantages. In the first part of the dialogue, before the second beginning, the Demiurge makes use of a very limited set of Forms: Being,

Sameness, Difference, and the Living Thing. He makes use of the first three as a mixture out of which he makes the World Soul, among other things. And the last is an all-purpose explanatory model. But the Demiurge makes a kosmos that instantiates properties that aren’t well explained by reference to a single Living Thing understood as a common Form. The kosmos is beautiful; it’s eternal; it’s good (or at least as good as possible). It’s true – the Living Thing is indeed beautiful and good. But to be doctrinaire Platonists, we should expect that Beauty and the Good explain the kosmos’ beauty and goodness, not the Living Thing. And if participation is representation, it follows that the beautiful and good parts of the universe are copies of just those

Forms. This result is easier to obtain if we take the Living Thing not to be a single Form, but in fact to be the whole world.

These results can be obtained in other ways. We could think that the Living Thing is a standard-issue Form and that Timaeus simply does not mention the other Forms of which the

Demiurge makes use, or that the kosmos becomes beautiful and good because the Demiurge copies the ideal features of the Living Thing as well as its proper features. Given that our world is both a world and copy of something else, though, it stands to reason that the Living Thing, the original, is itself a universe.

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TAKING SELF-PREDICATION SERIOUSLY

If the argument from representation is sound, then self-predication is not a mere idiosyncrasy that does no real theoretical work. When Socrates says in the Phaedo, the Symposium, and the

Phaedrus that nothing is more beautiful than Beauty itself, he means it. A plausible account of the relation that Timaeus uses to tie together the kosmos and the Forms entails it. What follows for the Theory of Forms?

In a related literature to do with the Third Man and the other objections of the

Parmenides, the question of Self-Predication regularly arises. (It was, after all, coined by Vlastos in his famous paper that started the modern Third Man debate.) And one way of interpreting the

Parmenides’ pros qualifiers, the way that Meinwald takes them, is to hold that Forms and sensibles are just and large differently. This is mustered as a solution to the Third Man; it denies that Large and large things in fact have some property in common in need of explanation. This is neither here nor there for our purposes. But this is a way of not taking Self-Predication seriously.

Justice, that property that explains what all just things have in common, is just pros heauto; the kallipolis is just pros ta alla.123 Justice, to use Meinwald’s phrase, is just, but not in the same way that the kallipolis is.

The strongest form of Self-Predication holds that Justice and the just things are just in the very same way. It’s not mere homonymy, and as Gill (2012) shows, the Meinwald-style account of the pros qualifiers doesn’t quite fit the text. The reason, though, that people tend to go in for an account of merely-metaphorical property sharing is that literal property sharing seems to entail obvious absurdities. Consider, for instance, the Form Large. Numbers can be large. They

123 Specifically capturing Meinwald’s view here is difficult. One way to get at it is to distinguish being some property as opposed to having some property. Justice might be just pros heauto – being just exhausts Justice’s essence. But the kallipolis merely has justice pros ta alla; there is more to what it is to be the kallipolis than being just.

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do this by being either absolutely or contextually high (a large number of atoms and a large number of political scandals tend to come in different orders of magnitude). Elephants can be large. But elephants are differently large. Their bigness consists in taking up a lot of space. How could one Form explain these very different properties by having both of them essentially?

Something that is essentially a quantity in the numerical sense cannot take up space.

There is a related, and more obvious and pressing, issue. There are properties that are necessarily spatiotemporal. Color, for instance, has to do with reflectance and absorption properties of material objects (or, for Timaeus, with the interaction between internal fire, external fire, and the water in the eyes). But these are the kinds of properties that abstract objects simply can’t instantiate. Non-spatiotemporal objects can’t reflect light, nor are they made out of fire. As such, they can’t be red or green or blue. But if there are to be Forms of colors and those Forms are to share features with the property instances that they explain, then this entails that there must be a red Form. But this is impossible. So Self-Predication, we tend to conclude, must be false.

This is obviously too hasty; we rely on premises other than Self-Predication in order to generate the absurdity, and we should be open to the possibility that one of those could be reasonably abandoned. To see this, let us start by noticing that there are, of course, some properties that can be instantiated both by spatiotemporal and non-spatiotemporal objects.

Beauty and the Good, the classic Forms, number among these. But so do mathematical properties: Unity, for instance, can be instantiated as well by an object that isn’t in space and time as one that is.

The sorts of properties that we’ve talked about thus far in this chapter are properties of the second sort, properties that Forms can comfortably instantiate in the very same way that sensibles do. Some of them, like eternity, are indeed better instantiated by the Forms. The same

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goes for having the character of a unified whole rather than a part. And perhaps most interestingly, the account of the elements renders them instantiable by non-spatiotemporal objects. They are, after all, geometrically characterized; they are tetrahedra and dodecahedra, fundamentally, not burning things or red things or wet things. And these solids are paradigmatically the sorts of things that can exist outside of space and time, or at least can coherently do so if you’re a Platonist. They can be expressed by ratios and relations; they need not be anywhere at all. If we take Self-Predication seriously, then this comes as no great surprise.

If Forms share features with sensible particulars, and the classical elements have Forms, then it simply follows that the Forms of these elements must be geometrical or mathematical or be characterizable thus.

All of this is merely suggestive and is to be worked out after we review the evidence from our examination of precosmic physics. But if Self-Predication is true, Plato should propose an ontology on which the Forms only explain properties that they themselves can instantiate, properties that make no essential reference to matter, space, or motion. If there’s a Form of Red, then we must provide an analysis of Red that does not rely on quenching or contracting or on the reflectance of light. That Plato should do something doesn’t entail that he does. But it’s a start.

THE LIKENESS REGRESS: PARMENIDES RETURNS

If Timaeus is making use of a representationalist theory of participation, then we should think that he has a solution to the objection raised against it in the Parmenides. Some, Lee (1966) for instance, have suggested that the solution to the Likeness Regress rests in the Receptacle. I suggested in the previous chapter that I don’t think that his solution works, but there’s a sense in which it would be better if it did; given that it is clearly incumbent on any representationalist to

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have a solution to the Likeness Regress, it would be best if such a solution made use of one of the major innovations of the Timaeus. In this section, I’ll offer a solution that is available to

Timaeus and is consistent with the text. Further, that solution rests on us thinking carefully about what precisely representation consists in, and it is part of my view that this is part of what takes place during the composition of the dialogue. However, I concede it would be preferable if such a solution was proclaimed more clearly in the text itself.

In the first chapter, I reconstructed the Likeness Regress as follows.

1) All beautiful things partake of the Form of Beauty.

2) If x partakes of y, then x is a likeness of y (132d1-3).

3) If x is a likeness of y, then x is like y (132d3-4).

4) If x is like y, then y is like x (132d5-7).

5) Beautiful things are like the Form of Beauty, and the Form of Beauty is like the beautiful

things.

6) All like things partake of the Form of Likeness.

7) The Form of Likeness is like the Form of Beauty and the beautiful things.

8) The Form of Likeness cannot partake of itself.

9) The Forms of Likeness and Beauty and the beautiful things partake of some Form

Likeness2 (132e6-133a3).

The objector starts by noting that on a representationalist theory, any beautiful thing is a representation of Beauty. So, Helen is a copy of Beauty. And being a copy, Parmenides thinks, entails that you have something in common. Presumably, these are the properties that were reproduced in order to make Helen a likeness of Beauty. (In this case: beauty.) But if Helen is like Beauty, then Helen and Beauty partake of the Form of Likeness. And if they partake of that

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Form, they are representations of that Form, and as such are like Likeness. Now we’re faced with explaining what it is that these three entities have in common and, if we won’t allow that

Likeness explains its own likeness, we must posit another Form. There is no principled way to stop the regress and it certainly seems vicious. So, we should discard the representationalist theory of participation.

There are a few ways we might be tempted to solve the regress. We could deny that being a likeness entails being like, for instance. Or given that the eighth premise comes out of nowhere

– it’s not at all obvious why Likeness can’t explain its own likeness – this might be where we’re tempted to focus our attention. But if we’re both to deny this claim and be thoroughgoing representationalists, we’re faced with something of a problem. It doesn’t seem as if a copy of some x explains its having x’s features. More concretely: insofar as a sculpture is a copy of a face, all the properties that they have in common are explained by the face, not the sculpture.

And since we’re asking for explanations in terms of chains of representation relations on a representationalist view, this is a serious concern. If we’re asking for the grounds of some property at a model and a copy have in common, the answer seems always to be in the model, not the copy. Likeness cannot, it seems, explain its own likeness.

In carefully tracking why it is that we can’t deny the eighth premise, though, we make available the resources we need in order to avoid the regress. The correct way to paraphrase an explanatory demand on representationalism is: in virtue of what model does this copy have the feature under discussion? But this demand contains a false presupposition. When we’re considering a Form and its proper feature, the Form simply is the original with respect to that feature.

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Consider a simple aesthetic case and set aside any representationalist metaphysics for a moment. Imagine all of the various copies and reproductions of Van Gogh’s Starry Night. What explains why it is that they have certain colors, shapes, and styles is that they’re all copies of an original: Starry Night. And (assume for the sake of argument) Starry Night itself has all of those same properties because it is meant to be a representation of some particular actually starry sky.

But, we might ask, in virtue of what original does that particular sky have its properties? Here we seem as if we’re making a mistake. There is a causal story that explains why it is that the sky has the properties that it has. But there isn’t a representationalist story, because the sky isn’t a copy of anything at all.

Assume representationalism again for the sake of argument. Likeness is like the starry sky, the one that isn’t paint on canvas. In terms of representation, there simply is no story as to why it is like. It is the original like thing, that thing on which the others are copies. Asking of what it is a representation – or more precisely, of what its likeness is a representation – is simply to misunderstand the theory. Put another way, asking of a model of what it’s a copy simply is to ask a question that doesn’t make any sense at all. We can block the regress, then. And the answer is related to the eighth premise, though it doesn’t involve its denial. Instead, we deny that 1-8 entails 9: there simply is no explanation of Likeness’ likeness on a representationalist view. The explanatory chain stops with the Form.

INTERLUDE II: REPRESENTATION AND CHANGE

There is at least one apparent cost to thinking that the participation relation is a strict sort of representation. The Demiurge is clearly involved in the framing and construction of the kosmos: he builds the World Soul (34c), he introduces time (37c ff.), he gives the fundamental physical

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magnitudes their characteristic powers and shapes using Forms and numbers (53b). And he – or at least, the lesser gods – create the mortal races (42e). But at no point are we given the impression that he continually intervenes in history, or that Timaeus’ world has a god that is responsible, in the efficient sense, for every action or event.

But this, we might expect, is exactly what a fully and strictly representationalist view of participation would entail. If Juno partakes of the Cat, then presumably she is a representation of the Cat. And if that’s so, then she was made in the Cat’s image by some representing agent. The

Demiurge should have made her, and indeed intervened in history whenever any property change whatever occurred. This hardly seems like a point that Timaeus would have failed to mention, were it true. So perhaps the Demiurge set up the world, bringing it into relation with the Forms.

And it is by this representation relation that the Forms do their explanatory work. But it’s not at all obvious how it is that they are meant to explain anything at all after the world is made.

Interestingly, Aristotle makes roughly this point in his criticisms of Plato. In Metaphysics

Alpha, he complains that Forms ‘cause neither movement nor any change’ in anything at all

(991a11); in Zeta, he similarly argues that the Forms could not explain the coming to be or change of any substances (1133b19-34a5). He levels the same charge in Metaphysics Mu and

Generation and Corruption II.9. Forms, that is, can’t explain what happened when Juno was born, coming to partake in the Form of the Cat.124

Though the case of visual or sculptural representation might lead us to imagine that the

Demiurge would need to intervene to explain any change, reflecting on other cases can provide us with a way out of the worry. Instead of imagining the Demiurge as a sculptor, take him to be a

124 That Aristotle makes this complaint might well be evidence for the view I’m defending here, though I will argue that the objection isn’t fatal.

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director of a play.125 He wrote the script, designed the sets, gave the actors their directions; put more generally, he is responsible for the parameters of the play, the laws that govern how it will progress. But he’s a hands-off director; he doesn’t intervene in the performance once it has started. At any moment in the play, though, we can say that the director has represented something precisely by setting up those parameters, even though he did not efficiently cause it.

Put another way: he set up what we might call the initial conditions and the laws of nature and then let the play take its course. Similarly, the Demiurge, looking to the Forms, designed the world as it was at the very start and the natural laws that govern it. Changes may not be representational in the same way sculptures are. But this is because change takes place over time and we’re considering representations that are timeless. Changes are representational as temporally-extended art is; the Demiurge is the composer-conductor of an orchestral performance, the playwright-cum-director of a play.

RATIONALIST PHYSICS

The argument from representation shows that we should take Self-Predication seriously, and taking Self-Predication seriously requires thinking carefully about what sorts of properties Forms can instantiate. But there are lots of properties in the world that Forms can’t instantiate: color and smell and the rest of the properties in the sovereign domain of the senses. These cases present the

Platonic physicist with a choice. We could deny that these are genuine properties, in the spirit of

Lee’s insubstantial images.126 If there are no such properties, we don’t need to explain them. But

Timaeus spends the second major part of the dialogue explaining such properties and marshaling

125 And producer, set-designer, writer... Let ‘director’ stand in for ‘everyone that sets up the play before it starts’.

126 See chapter 2 on Lee.

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them to explain other things; independent of the plausibility of Lee’s specific view, the reader who thinks that there aren’t really such properties tells a deeply revisionist story about the physics after the second beginning. Apples really are red; roses really do smell sweet; middle C really does have a sound.

The Platonic physicist then must countenance necessarily sensible properties, properties that the Forms can’t instantiate. But unless she wants to admit of as many brute facts as there are objects of sensation, these sensible properties present her with a serious problem: they’re inexplicable in terms of Forms and not fully explicable in terms of the Demiurge’s intentions.

So, she must introduce another explanatory principle. In the second chapter, we saw that matter’s nature has a plausible claim to the role of explanatory principle: this nature grounds the limits of physical possibility. But the Platonic physicist is trying to explain more than possibility. Its ambition is to explain the whole kosmos.

Taking Self-Predication seriously limits the scope of the Theory Forms. But this is only plausible if we don’t correspondingly limit the explanatory power available to the Platonist. We have to see, then, whether we can still do physics with a mathematical Theory of Forms and a non-Formal fundamental material nature. And not only should this be possible; there also must be good reason to think that that’s what Timaeus is doing. We’ll be looking, then, to confirm two pieces of the theory: first, that from the second beginning, Timaeus cites geometrical and mathematical features of the Forms to explain some properties;127 second, that he explains all other properties by appealing to a feature that might be explained by the nature of the Receptacle

127 He is so committed to a geometrical theory of the elements that he’s famously willing to deny part of the phenomenological data: that all the elements can change into each other. Three of the elements can be fashioned solely out of half-equilateral scalene right triangles, but the earth, which is cubic, is made of isosceles triangles (55b). As such, he’s forced to say that earth can’t change into or out of the rest, a claim that stands in tension with experience.

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itself.128 To see whether this is the case, let’s turn to the second part of the Timaeus, beginning with the geometrical account of the elements.

Taking a detour through a toy version of Cartesian physics before turning to Timaeus will help to clarify the sort of physics I have in mind. In what follows, I’ll present Williams’ (1978) version of Cartesian physics, and it will be an incomplete presentation without much of an eye for detail. The comparison is valuable for their shared structure; a simplified Cartesian physics has all the same major properties that I hope to bring out in Plato’s late physics. Particularly,

Cartesian physics give us a point of reference for what I mean when I call Timaeus’ proposed physics geometrical.

In a letter to Mersenne from 1638, Descartes writes:

…I have only decided to give up abstract geometry, that is to say, research into questions which serve only to exercise the mind; and I am doing this in order to have more time to cultivate another sort of geometry, which takes as its questions the explanation of the phenomena of nature. If he [Desargues, a French mathematician] cares to consider what I have written about salt, snow, the rainbow etc., he will recognize that all my physics are nothing but geometry (27 July 1638: II 268, Williams trans.).

Descartes understands his physics as fundamentally geometrical or mathematical: he is trying to explain the properties of the physical world using only properties that we could predicate of geometrical objects. It isn’t hard to imagine Timaeus writing a similar letter (indeed, using at least one of the same examples: salt, which we will discuss below).

128 To this point, I have been agnostic on the nature of the Receptacle; the argument so far has not required a firm stand on the issue. From here on out, though, the argument relies on the Receptacle being both matter and space. For a discussion of this view, and a helpful analogy in understanding it, consult Zeyl (2010). Roughly, the view goes that the Receptacle is like the water of the ocean: it both is that out of which a wave is made and the space through which it moves. This echoes the language that Timaeus uses to describe the Receptacle: it is shaped and reshaped by the things that enter it (50b) and it is also space (52b), something in which the images inhere (52c). Fundamental material properties – and fundamental spatial properties – will thus be properties explained by the Receptacle’s nature, strictly speaking. The Receptacle just is matter, just as it is space.

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But, like Timaeus, Descartes is in fact using more than mere geometrical form to do physics; to use the language of the ancients rather than the early moderns, form must be instantiated in some matter. And the Cartesian conception of matter, too, is Timaean. Take

Williams’ (236) characterization:

…the properties that matter has are just the properties contained in the fundamental attribute of extension. That this should be so can be seen when one recalls a feature of Descartes’ notion of essence…To discover the essence of a substance is to discover its essential attribute, and any property that a thing has must be some mode of its essential attribute. We cannot, according to Descartes, conceive of a physical thing’s having any property which is not a way of being extended, of occupying space. Hence the only properties that physical things can really have are those of occupying space to such-and-such an extent (volume), with such-and-such boundaries (shape), and of moving: which last means that the boundaries may change, or the body may occupy different places at different times.

Setting aside shape for the time being as a geometrical property, the remaining notions, extension and motion, should strike us as familiar. The Receptacle explains precisely these notions. As we saw in chapter two, it is a fundamental part of matter’s nature to move, a part, that is, that is not amenable to further explanation.129 It is no less a part of the Receptacle both to be and fill space, though that was not the case we took up there.

Finally, Cartesian matter is continuous. Williams, again:

The physical universe for Descartes consists of one, infinitely extended, homogeneous, three-dimensional thing…It has, and can have, no gaps in it…There are, further, no ultimate atoms, or parts of matter which are ‘indivisible of their own nature’ (Principles ii 20) – matter, in Descartes’s conception of it, has necessarily the geometrical property of being continuous (253).

There is no void in Cartesian physics, no space for some atom to come to occupy. There is, however, an underlying homogenous three-dimensional stuff that undulates, coming to

129 It is important to emphasize that this is a toy Descartes, possibly a Descartes*. Descartes has a version of the Galilean law of inertial motion – something that isn’t acted upon will rest. This is not obviously true of Timaeus.

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instantiate certain shapes. There are no atoms bouncing around, hooking together, and coming to be structured; instead, some undifferentiated substrate takes on different shapes. Read alongside with the Timaeus, the similarities are striking:

Now the same account, in fact, holds also for that nature which receives all the bodies. We must always refer to it by the same term, for it does not depart from its character in any way. Not only does it always receive all things, it has never in any way whatever taken on any characteristic similar to any of the things that enter it. Its nature is to be available for anything to make its impression upon, and it is modified, shaped, and reshaped by the things that enter it. These are the things that make it appear different at different times (50b-d).

Though the triangles, as we’ll see, are taken on as if they are the ultimate geometrical principle, it does not follow that they are the ultimate material principle; the Receptacle is not constituted by triangles bouncing around in the void. The Demiurge fashions those triangles out of the undulating precosmic soup; they are made of and subsist in the Receptacle. Timaeus is not any more an atomist than Descartes.

Our toy Descartes then has rather a lot in common with the Timaeus we will meet below.

Given that Descartes and Plato share a general commitment to mathematical rationalism and to the explanatory power of non-spatiotemporal objects, this overlap should come as no particular surprise. But notice that the toy Cartesian physics would meet the requirements set out for a physics that takes Self-Predication seriously. The only Forms he needs to explain the sensible world – setting aside his commitment to dualism about minds and souls – are geometrical ones, ones that fix shapes. That is, he thinks that he can explain the world – salt, rainbows, and snow – by referring to volume, motion, and shape. These first two properties can be grounded in the nature of the Receptacle; the third is explicable in terms of Forms that are capable of instantiating their own proper features. The sensible world, then, can literally be an image of the intelligible one, an image in a material medium. If Timaeus’ physics is Cartesian – or, more

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appropriately, if Descartes’ physics turns out to be Platonic – then they are consistent with the argument from representation.

TIMAEUS’ PHYSICS

By definition, Timaeus thinks, the sensible world must be made out of the classical elements. It is visible, so it must be made of fire. It’s tangible and thus earthy. And we notice, when we look at the world, that things change. Water evaporates into air, wood feeds a fire. And more basically, the food and drink we consume becomes our flesh and blood. Timaeus proposes that these changes, if the elements are truly fundamental, are difficult to countenance. In this spirit, he proposes his famous puzzles of gold and elemental change (50a and 49b, respectively).

Imagine that someone were shaping and reshaping gold before your eyes, first a pyramid, then a cube, then a ring. When you’re asked what’s in his hands by a spectator, Timaeus thinks, by far the ’safest’ answer is to say ‘gold’ (50b). The shapes, the arrangements, are nothing but ‘suches’, ways of arranging some substances. The substance itself, the gold – that’s what we’re asking about when we ask what something is. It’s a ‘this’. (49d-e). The same holds for the elements: they appear to be elements or substances. In fact, they’re arrangements of some more fundamental thing and mere suches. This puzzle about change forces Timaeus to propose a more basic material level as a substratum for change: the Receptacle, the ‘nature which receives all the bodies’ (50b).

The Receptacle underlies the classical elements. And it is ‘devoid of any of those characters that it is to receive from elsewhere’ (50d-e); it lacks determinate shape. It is by taking on shapes that the Receptacle becomes fiery or watery. These shapes must be three-dimensional, as the elements ‘are bodies’ and ‘everything that has bodily form also has depth’ (53c). Every

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three-dimensional object has a surface, ‘and any surface bounded by straight lines is composed of triangles’ (ibid.).130 And those triangles, in turn, can be analyzed into two ultimate right triangles: the isosceles right triangle and a special scalene (half-equilateral) triangle (53d). These two triangles, then, can act as the basis for any three-dimensional body; they build up into the surfaces which are in turn mustered to explain the character of the elemental bodies. These triangles are ‘the originating principle of fire and of the other bodies’ (53d).131

The elements have geometrical structure. Fire is tetrahedral, the tiniest solid, because fire is the most mobile and most fit for cutting (56a-b). Earth is cubic, because it’s immobile and plastikos, amenable to taking on a variety of shapes but able to hold them (55e). Air has an octahedral shape, in virtue of being less mobile and sharp than fire; and water is an icosahedron, being closer to earth than to fire (56b).132 Recombinations of half-equilateral scalenes make up fire, air, and water; earth alone is made of the right-angled isosceles.

Timaeus characterizes the elements in terms of geometry, then. What makes fire fire – and indeed what makes it fiery, as we’ll see – is its shape and that shape’s relationship to the others. A correspondingly geometrical theory of Forms, then, can ground the elemental property instances. To explain the elements, Timaeus requires at most a small number of Forms: the two basic triangles, the two-dimensional surfaces they combine to make, and the four three-

130 Sometimes, this is at a couple of layers of removal. The square – the face of the cube – is made out of triangles, despite the fact that the face itself isn’t triangular. The same goes for the dodecahedron and its pentagons (though the pentagon can’t be made out of the triangles that Timaeus here mentions as the fundamental sort).

131 Timaeus leaves it open – and indeed hints – that there are more fundamental principles than the triangles (53d). And this must be right; two-dimensional objects can undergo the exact same process of devolution that he performs on bodies with depth. Triangles are made of lines, and these lines can be analyzed in terms of numbers. We’ll continue to talk as Timaeus does, as if the triangles are the most fundamental things. But any story we tell in these terms could equally well be told in terms of other, more basic, mathematical objects.

132 The whole kosmos, though made out of these elements, does not instantiate any one of them. Instead, it’s a dodecahedron, and can’t be constructed out of the two-dimensional triangles. This is further reason for thinking that there is a more fundamental physical magnitude still (55c).

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dimensional objects that can in turn be generated out of those surfaces.133 Timaeus’ references to

Formal explanations thus far are both geometrical and economical. Taking Self-Predication seriously, we’d expect this.

To this point, Timaeus has only explained the elements. And the picture he has painted resembles the picture of the kallipolis that Socrates complained about at the start of the Timaeus: it is like gazing ‘upon magnificent animals, whether they’re animals in a painting or even alive but standing still’ (19b). We don’t really understand them until we see them in motion, performing their characteristic functions. Until we see how it is that these geometrized elements explain our experience in the macro-world, then, we don’t really understand the elements. And it is here we might worry that we require more than geometrical Forms.

Timaeus proceeds to build the whole world out of these elements. But to bridge this gap, he must first explain paradigmatically sensible properties: colors, tastes, sounds, smells, and textures. The hypothesis we’re entertaining makes no room for Forms of such properties; non- spatiotemporal objects can’t be hard and soft, hot and cold, red or blue. The hypothesis meets its first major challenge here, then: Timaeus must explain these inextricably material properties in terms of mathematics and the fundamental properties of the Receptacle.

We can’t plausibly cover every sensible property here in detail. But an examination of any of them will bear out the central claims here.134 In what follows, we’ll consider three such

133 Why ‘at most’? The number of Forms depends on the status of composites. If Plato thinks, as I think he does, that ‘natural’ composites are something over and above their parts, there must be Forms of surfaces and Platonic solids. But Plato as a mereological nihilist – someone who thinks that all that exists are the fundamental parts, and that there are no wholes properly speaking -- wouldn’t need such things: he would only need the two triangles (or whatever the more basic principles that underlie them are).

134 In an appendix on the biology of Plato’s moral psychology I take up bitterness as a central sensible feature. Though its focus is not on geometrized Forms and material explanations, a reader is invited to look to that case to see whether it too supports the hypothesis.

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properties, those that Timaeus puts to substantial use later and that he explains in detail: heat

(61d-62a), hardness (62b-c), and color (67c-68d).

Fire explains heat; something is warm to the extent the fire can manifest its heat-causing properties (61d). Timaeus says:

We notice how fire acts on our bodies by dividing and cutting them. We are all well aware that the experience is a sharp one. The fineness of fire’s edges, the sharpness of its angles, the minuteness of its parts, and the swiftness of its motion – all of which makes fire severely piercing, so that it makes sharp cuts in whatever it encounters – must be taken into consideration as we recall how its shape came to be. It is this substance, more than any other, that divides our bodies throughout and cuts them up into small pieces, thereby giving us the property…that we now naturally call hot (61e-62a).

In the first instance, fire heats by cutting. When something is burnt, it is being divided and cut up at the micro-level; fire separates its parts from each other. Timaeus suggests that we know this because of the phenomenology of burning: ‘the experience [of being burnt] is a sharp one’. To explain heat, then, we’re looking to explain a certain kind of cutting. And fire has been geometrically defined to be most suitable for cutting. It has leptos edges, edges that are small and refined and capable of passing through the gaps in other bodies; its angles come to sharp points to help it push through; it has small parts to fit in any space. Its geometrical properties render it capable of cutting other elements apart (like the elements that make up flesh). Being the smallest solid with the sharpest edges, it is best suited to this task.

Notably, Timaeus does not just cite the geometric properties of fire here; lots of inert tetrahedra exist innocuously enough, innocent of arson. After listing the mathematical facts that make fire the most suitable element for burning, he notes a further physical fact: fire moves quickly. Motion explains why not all tetrahedra burn; the innocent ones, like the Great Pyramids,

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are not prone to fast movement.135 But the basic fire-tetrahedra are the most mobile because they have the fewest faces (56a); they require the least effort to move. We saw in chapter two that motion is best explained by matter’s nature; I won’t rehearse those arguments here. So, fire moves because it is material, and it moves quickly – moves in a way that helps it burn – because it has the fewest faces. Math and matter, then, explain its characteristic motions. And geometry explained the rest of its capacity to cut. Given that heat is just varying degrees of especially fine cutting, Timaeus has explained fire’s heat in the terms we’d expected: geometrical Forms and motion, which is itself grounded by matter’s nature. The first sensible property bears out our hypothesis, and it will help us make sense of color below. The Form of Fire, the pure tetrahedron, is not hot. But at the same time, fire can be.

Hardness appears to prompt a much briefer explanation on Timaeus’ part. All he says about it directly is: ‘hard we call whatever our flesh gives way to’ (62b). Something’s being hard or soft then is a matter of its relation to our flesh: the density of our flesh fixes whether we give way to some object or some object gives way to us. As such, to understand hardness, we need to take a brief detour in to the nature of flesh at 74c and following. This will also require us to take up the question of the alloyed elements; we need to understand saps, brines, and acids. But the biological account is unilluminating without first having clarified flesh’s purpose.

At 74b and following, Timaeus gives us a teleological account of flesh. Rather than creating a world of Halloween skeletons of pure bone, the Demiurge chose to encase living things in flesh. Bone, being incapable of bending, is liable to break, and to be worn down by heat

135 Nor are the tetrahedra that tend to jump to mind, like the Pyramids, the right size to be doing very much cutting. This is a contingent fact; if there were lots of bodies that dwarfed the Pyramids in their vicinity, and if the Great Pyramids were prone to moving towards them, then Timaeus might be committed to saying that the Great Pyramids burn those objects. (This is of course not quite right; the pyramids, of course, are more earthen than fiery. But let us pretend for the sake of argument that they’re purely tetrahedral.) But, luckily for him, this is a distant counterfactual. The reason they’re not prone to movement is that they’re primarily made of an immobile element, earth; if they were tetrahedra made of tetrahedra – fire – then and only then would they be able to burn.

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and cold. Flesh, then, insulates us against the elements. But it also protects us against injuries by acting as padding; if we fall, the softness of flesh absorbs the impact (imagine if all minor injuries felt as severe as toe-stubbing). And it must be both moist and fiery, so that it can cool us in the summertime and warm us in the winter. So, flesh must be moist and fiery, flexible, and soft.

Timaeus gives us a further story, not just about flesh’s nature but also about its distribution over the body. Too much flesh, densely packed, makes the organs it covers insensible. If our heads were fleshy, that is, our thinking would be ‘less retentive and more obscure’ (74e). Too thick a layer of flesh prevents sensory information from reaching the nerve centers of the body. Our fleshy parts – our thighs and calves, hips and arms, and so on – are low on marrow and ‘devoid of intelligence’ (75a). But the Demiurge encases those parts of us that are intelligent – our fingers for touching, our eyes for seeing, our heads in general – in barely any flesh at all so that we’re better able to perceive and think. Our flesh must be soft and pliable (so far as possible, of course), so that information can be delivered to the senses and the soul.

The Demiurge designs flesh so that it can fulfill these ends. Timaeus claims that he

‘molded us like wax’:

…he made a mixture using water, fire, and earth, which he adjusted together, and created a compound of acid and brine, a fermented mixture which he combined with the previous mixture, and so he formed flesh, sappy and soft (74c5-d2).

Flesh is the mixture of two compounds: fire, water, and earth on the one hand and acid and brine on the other. The account defies detailed analysis, but a sketchy picture emerges from it. The first compound, the one that is merely a combination of three elements, is clearly amenable to geometrical analysis; the elements themselves are defined in terms of their mathematical properties, and they are mixed, presumably, in a certain ratio. And though brine and acid present

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more of a mystery, the same plausibly holds for them. Brine, or saltiness, has a specific elemental structure: it is ‘made up of the finest parts of earth’ and are only ‘semi-solid’ and still soluble (60d). Brine, then, makes flesh earthen, but not thoroughgoingly so.

Setting aside acid for a moment – Timaeus does not give as cogent an account of acidity as he does of brine – we can see how the materials here help to fulfill the Demiurge’s goals regarding flesh. He was looking to make a substance that was soft and sensitive so that sensory information could pass through it. But it further needed to be able to heat and to cool, to ground basic tangibility, as well as to provide some protection from impact. At a very basic level, the initial list of elements speaks to these interests: fire to heat, water to cool, and earth to protect.

But this mixture doesn’t immediately answer to the sensory need, that flesh be soft enough to pass sensory messages along to the soul. Enter brine, which contributes to this goal in two ways.

First, brine, though earthy, isn’t impenetrable and stable in the same way that pure earth is. It, as we saw, is merely semi-solid. If softness is a matter of giving way to the objects with which it comes into contact, then brine’s semi-solidity contributes to flesh’s softness.

Furthermore – and this is perhaps the significance of the acid part of the mixture – salts and acids both tend to dissolve or corrode many things with which they come into contact.

Consider, for instance, the effect that salt has on metal, causing it to rust and to corrode.136 Acids

– substances that are closely chemically related to brines in the Timaeus – are those things that taste bitter; this bitter flavor is in turn analyzed as the dissolution of the tongue by the acid (65d).

Both substances, then, tend to break down the bodies with which they come into contact, by corrosion or dissolution. Plausibly, then, the acidic briny compound helps to soften the elemental

136 How Timaeus would explain this process is not at all obvious. Salt contracts flesh in Timaeus’ biology (65d); little else is said about its chemical effects.

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compound, rendering it capable of passing sensory information along – or at least, rendering the flesh less likely to block the passage of sensory information.

Flesh is soft and pliable, moist and fiery. And it has these properties in virtue of its geometric features. What makes something hard, further, is its relation to flesh. We saw that what softens flesh is the inclusion of substances that either counterbalance earth’s density and stability or somehow lessen it. An object is only hard in relation to flesh, this complex mixture of elements and alloys. The Form of Earth, then, won’t be hard, even though earth is the element responsible for hardness in the same way that fire is responsible for heat. Hardness is defined in terms of a relation to flesh, a relation that no Form can stand in. Despite that, the geometrical properties of that Form fix most of the facts about hardness; we can predict whether some object will be hard or soft in virtue of its elemental composition, perhaps by measuring its relative proportion of earth. And it will only in fact be hard once materially extended in space. This can be done by the Receptacle alone.

Color, like heat and hardness, is a relational property. And it too is explained by fire.

Timaeus starts:

Color is a flame which flows forth from bodies of all sorts, with its parts proportional to our sight so as to produce perception (67c).

Something has a color just in case it gives off a certain kind of flame. Presumably, variations in the properties of this flame (and, of course, in the physical makeup of the recipient’s perceptual organs) will fix the object’s perceived color. Timaeus continues:

Now the parts that move from the other objects and impinge on the ray of sight are in some cases smaller, in others larger than, and in still other cases equal in size to, the parts of the ray of sight itself. Those that are equal are imperceptible, and these we naturally call transparent (67d).

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Timaeus reintroduces the ray of sight, a beam of fire (akin to daylight) produced by and exuded from our eyes that enables us to see (45b). The fire given off by other objects interacts with this internally produced fire and changes it in various ways; it is those changes that fix the properties of visual perception. In the earlier passage, we saw what looks like a plausible account of the perception of shape: once the visual fire and daylight coalesce the beam is capable of rendering information back into the eye; the beam ‘transmits the motions of whatever it comes into contact with’ (45d), relaying the shape of the perceived object. In our present passage we get a similar account of color, one that relies on the physical interaction of the visual stream from the eyes and the flame given off by the external objects. (Presumably, daylight plays the same enabling role it did earlier.) Instead of motion, though, it is the relative size of the flame particles that explain transparency; if the particles of the visual stream and those given off by the object are the same size, Timaeus seems to say, then the visual stream is undisturbed. As a consequence, we don’t perceive any color at all.

To perceive shape we rely on the motion communicated by the visual beam, and to perceive color at all we need the flame given off by the objects to be of a different size than the flame given off by our eyes.

Those that are larger contract the ray of sight while those that are smaller, on the other hand, dilate it….So black and white, it turns out, are properties of contraction and dilation…This, then, is how we should speak of them: white is what dilates the ray of sight, and black is what does the opposite (67d-e).

Something is transparent if its flame particles are the same size as ours. Timaeus explains black and white by making use of the same spectrum. He makes the perfectly sensible inference that we perceive something as dark if it contracts our pupils and bright if it expands them – the aperture is made larger or smaller, allowing more or less light in. And it is the size of the tetrahedra surrounding our visual stream that causes contraction or dilation; when the larger

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particles of a black object surround our perceptive fire, their greater size overwhelms it and shrinks it as if by weighing it down. The white tetrahedra do the opposite, giving it space into which to expand, and increasing the amount of light allowed into our eyes. The size of certain tetrahedra, then, and their relation to our visual stream fix the relative brightness (and, it seems, opacity) of the colors that we experience.

The motions that fix the facts about the brightness of our visual perceptions are the narrowing or broadening of our visual stream. A different sort of motion helps to generate color by entering the eyeball itself through the visual stream:

…when a more penetrating motion of a different type of fire pounces on the ray of sight and dilates it right up to the eyes, and forces its way through the very passages within the eyeballs and melts them, it discharges from those passages a glob of fire and water which we call a tear. The penetrating motion itself consists of fire, and as it encounters fire from the opposite direction, then, as the one fire leaps out from the eyes like a lightning flash and the other enters them but is quenched by the surrounding moisture, the resulting turmoil gives rise to colors of every hue. The disturbance so produced we call ‘dazzling’, and that which produces it we name bright and brilliant (67e-68a).

A certain type of fire can penetrate the eyeball. And it does this, Timaeus claims, by dilating the visual stream to the point that it can push into the eye, opening the space wide enough to enter.

Presumably, this sort of fire is not capable of entering the eye under normal conditions – the aperture is too small – and the dilation gives it enough space to enter. This is puzzling, though; what caused dilation in the prior passage was that the external fire gave the visual stream room to breathe, so to speak. The tetrahedra were smaller than those that make up the visual stream. But, simultaneously, the visual stream was the same size as the aperture of the eyeball, the space from which it is issued. How, then, can some both dilate the stream and require that dilation to enter the eyeball at the same time?

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The original thought – that dilation is caused by small particles giving the visual stream room to expand and contract by large particles that shrink it – isn’t quite right. Imagine that the visual stream as a party balloon with a fine filter at the end from which you’d inflate it. At the other end, we’ll use a pin to poke a small hole, and we’ll somehow design the box such that the pinhole attaches to a larger hole in the box (that is otherwise inaccessible). The contents of the box – specifically, the relation of the size of their parts to the size of the filter – will fix the behavior of the balloon. If you put coarse-grained objects into the box – rocks, for instance – then the balloon will have any residual air pushed out of it and will contract. If you put water in the box, though, you’ll end up with a balloon filled with water. The water will increase the pressure inside the balloon, and that pressure will cause the water to move through the pinhole. If the balloon is like our visual stream, then, white tetrahedra dilate it by penetrating and inflating it.

The phenomenon of dazzling is yet more complex. Whiteness doesn’t in fact enter the eye in the same way that water exits the pinhole in the balloon; it changes the size of the visual stream and doesn’t go anywhere in particular. This is because the size or the fineness of the fire tetrahedra is not the only relevant question; Timaeus cites the ‘penetrating motion’ of the fire that dazzles as an explanation for why it enters the eyeball. Dazzling fire, then, is distinct from white fire insofar as it has different distinctive motions; it can push through the membrane of the eyeball by, for instance, building up more speed when moving towards it.

Once the fire has entered the eyeball, the process becomes relatively simple. The dazzling fire is immediately quenched by the moisture of the eye, and this quenching allows us potentially to see any of the standard colors of the rainbow. (After all, it is precisely light bent through water that explains the character of the rainbow itself.) With a sufficiently speedy tetrahedron, then, we

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can be dazzled. But if we’re to see a specific color rather than all of them, we need a fire particle that is differently quenched:

On the other hand, the type of fire that is intermediate between white and bright is one that reaches the moisture in the eyes and blends with it, but is not brilliant. As the fire shines through the moisture with which it is mixed, it yields the color of blood, which we call red. And when bright is mixed with red and white, we get orange. But it would be unwise to state the proportions among them, even if one could know them. It is impossible, even approximately, to provide a proof or a likely account on these matters (68b).

Some sorts of fire reach the eye and are quenched but shine through the eye’s moisture as red.

And when red is lightened by the addition of white, we get orange. But the mechanics of this process are left more or less mysterious. (Perhaps faster-moving particles are quenched more violently and that’s why they dazzle us, but slower-but-still-sufficiently-fast particles are quenched less violently and refract only one color when mixed with water.) The account continues in this fashion, generating recombinations of white, black, brilliant, and red (as well as their derivatives) that explain visual qualities.

Like hardness and heat, then, Timaeus explains color with reference to properties whose

Forms need not instantiate necessarily sensible features like being hot or being hard. Our perception of redness does not depend on Red; what it requires is that several sorts of tetrahedra bear a variety of mathematical relations to each other – some are larger than others, some finer, and their interaction along these geometrical lines do a great deal of the explanatory work. The rest, as in the case of the penetrating motion of red, can be done by the Receptacle.

Given how Timaeus closes his discussion of the common sensory properties, this result should come as no great surprise:

And so all these things were taken in hand, their natures being determined then by necessity in the way we’ve described, by the craftsman of the most perfect and excellent among things that come to be, at the time when he brought forth that

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self-sufficient, most perfect god. Although he did make use of the relevant auxiliary causes, it was he himself who gave their fair design to all that comes to be. That is why we must distinguish two forms of cause, the divine and the necessary. First, the divine, for which we must search in all things if we are to gain a life of happiness to the extent that our nature allows, and second, the necessary, for which we must search for the sake of the divine. Our reason is that without the necessary, those other objects, about which we are serious, cannot on their own be discerned, and hence cannot be comprehended or partaken of in any other way (68e-69a).

Timaeus characterizes the section that precedes this pronouncement as a description of how it is that necessity fixes the natures of the sensible qualities that we experience, of color and taste and sound. The picture that emerges from this passage is one on which the Demiurge has taken some pre-existing tendencies, those tendencies that existed in the precosmic world, and redirected and organized them, worked them up in accordance with his purposes. He hasn’t imbued the world with motion, for instance. He has taken what’s already there and given them a ‘fair design’, a design that points towards him and to the Forms.

But the Forms to which he points us aren’t Heat and Hard and Red. Timaeus, we should note, has modeled the behavior that he thinks we must imitate if we’re to be happy: he has looked for the divine in (literally) everything, and used necessity as an (epistemic) guide to that divinity. And in so doing, Timaeus’ account has us pointed by necessity to the mathematical structure of the universe, back to the Platonic solids. If we’re meant to be like Timaeus, then, we should do the same; we shouldn’t posit a Form for each property that we’re investigating, but only look for the Forms we absolutely need, those Forms that, alongside the Demiurge, explain the underlying consistent structure of the universe.

The justification of this pursuit in terms of happiness isn’t just an appeal to the importance of wisdom to the good life. Recall that the pursuit of astronomy was justified in much the same way earlier in the dialogue:

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Let us rather declare that the cause and purpose of this supreme good [sight] is this: the god invented sight and gave it to us so that we might observe the orbits of intelligence in the universe and apply them to the revolutions of our own understanding. For there is a kinship between them, even though our revolutions are disturbed, whereas the universal orbits are undisturbed. So once we have come to know them and to share in the ability to make correct calculations according to nature, we should stabilize the straying revolutions within ourselves by imitating the completely unstraying revolutions of the god (47b-c).

We don’t do astronomy just because knowledge is intrinsically valuable and exact knowledge of difficult topics even more so. Astronomy has an instrumental purpose. To live a good life, the orbits of our souls must, to the extent that this is possible, imitate the orbits of the heavenly bodies. And we discover these orbits by calculating, by discerning the underlying mathematical structure of heavenly motion. To be happy, we need not know the Form of Virtue or Good – or at least, we need not only know these. We need to shut up and calculate; we need to do mathematical astronomy.137

The methodological passage in which Timaeus sums up his account of sensory qualities, then, doubly points to a Theory of Forms that takes self-predication seriously. He reduces the explanation of explicitly biological phenomena, of sight and sound and the rest, to explanations at the level of fundamental physics. And these explanations, as we’ve seen, are cast in terms of the mathematical structure that the Demiurge has imposed on the precosmic soup, productively redirecting its energies. So, on the scientific level, Timaeus’ account makes use of a Theory of

Forms that seems only to require mathematical properties. And the ethical part of this investigation has the same result. We’re looking for Forms of a certain sort, Forms by which the

Demiurge ordered the universe and after which we can model our own behavior. When this

137 As Burnyeat (2000) argues, it’s not just the mathematics is a sort of ‘mental sharpening’ (5). He says: ‘Mathematics and dialectic are good for the soul, not only because they give you understanding of objective value, but also because in so doing they fashion justice and temperance with wisdom in your soul’ (77).

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behavior is described mathematically – and the physical phenomena we’re meant to be imitating is as well – this gives us good reason to think that the Forms, too, are mathematical.

As we’ve seen, though, Timaeus’ ambitious physics can’t be merely mathematics and geometry. He recognizes that he needs to make use of motion and extension as well. This aspect as well is evident in both the natural philosophical passages and the ethical ones. To explain color, for instance, we need to cite different sorts of motion; it is this motion that distinguishes the grounds of the experience of white from the grounds of the experience of red. The correct arrangement of the human soul in the same way includes an appeal to motion. We need not merely instantiate the right shapes or the right ratio of the Same to the Different. To live a good life isn’t to have a soul that is stable and unmoving, but instead to have one that is a moving image of eternity in the same way that the planets and stars are.

If we allow that the Demiurge and the Forms explain structure and the Receptacle explains motion, we can fully characterize these explanations with an appeal to a minimal

Theory of Forms. Consider the simplest of the sensory phenomena we examined: heat. Heat, recall, was a sort of cutting, one that was a matter of fine fire tetrahedra pushing apart the joints of the coarser elements out of which other things are made.138 Imagine that we’re trying to explain why it is that my hand burns when I put it into a campfire. My flesh is a complex mixture, but it’s primarily water and earth. Because it is made of the two coarser elements, fire penetrates it. In the first instance, then, I am prone to burning because of the Forms of Fire,

Water, and Earth. The Form of Flesh, if Timaeus needs to posit one, need only mention a ratio and other Forms; it too lacks any inextricably sensible content. But this doesn’t yet explain why I burn when I stick my hand in the fire; it only explains the possibility of my being burnt. The

138 This account, incidentally, does a fairly good job of capturing what sorts of materials burn. Air doesn’t burn (easily); it is the second finest element, and it’s harder for fire to pry it apart from itself.

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Forms don’t burn because they don’t move; sensible fire, in virtue of its instantiation in the

Receptacle, moves. And for anything to pierce anything else, there needs to be both space – somewhere to go – and motion. These two properties are what the Receptacle is suited to explain.

We can see, then, that Timaeus’ physics are of the sort that could, in principle, avoid positing Forms that run into ontological trouble if they instantiate their own properties. His Heat

(and his Fire) aren’t hot in the sense of their tending to pass on a certain amount of energy or to cut in some specific way. They have merely the geometrical properties required to render these changes possible; they, because they’re not instantiated in the Receptacle, don’t undergo those changes themselves. This, I would like to suggest, is no coincidence. We saw good reason to think that Timaeus posits a representation relation between Form and sensible world, and that that relation is one that entails the literal sharing of properties. The best reason not to think this is that it’s metaphysically absurd; Red can’t be red in the same way apples are, Large can’t be large in the same way elephants are. But paying close attention to Timaeus’ cosmic and precosmic physics suggests that he makes use of a Theory of Forms that does not suffer such problems.

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CONCLUSION: ON GEOMETRICAL PARADIGMATISM AND NATURAL PHILOSOPHY

In chapter one, I asked three questions, the answers by which we might individuate different kinds of theories of Forms. They were:

1) Participation: What is the nature of participation, the relation that ties together the world

of the Forms and the world in which we reside?

2) Nature: Closely related to (1), what are the Forms?

3) Scope: How many Forms are there and for what sorts of properties?

In the above, I’ve tried to answer all three and provide a worked-out and philosophically satisfying Theory of Forms from the text of the Timaeus. ‘Philosophically satisfying’ is doing rather a lot of work here: it must be possible not only to extract such a theory from the Timaeus, but also to show first why the theory would be a natural fit, given the topic, and second that it doesn’t suffer from any debilitating defects that Plato himself would have noticed and found persuasive. The theory that I’ve presented here, this geometrical paradigmatism, has answers to our three questions and is, at least in the second sense, philosophically satisfying. But, we might wonder, why should Plato have returned to a representationalist theory late in his career? What about the topic of the Timaeus makes it apt for the sort of analysis that seemed so problematic in the Parmenides?

Appropriately, given that the Timaeus introduces both the Receptacle and the Demiurge into Plato’s ontology, it seems to me that the most likely answer is twofold. On the one hand,

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representationalism (in the strict sense that I’ve been understanding it) fulfills the promises that

Anaxagoras’ Nous made, promises about which Socrates was hopeful in the Phaedo.139 There, he says:

One day I heard someone reading…from a book of Anaxagoras, and saying that it is Mind that directs and is the cause of everything. I was delighted with this cause and it seemed to me good, in a way, that Mind should be the cause of all. I thought that if this were so, the directing Mind would direct everything and arrange each thing in the way that was best. If then one wished to know the cause of each thing, why it comes to be or perishes or exists, one had to find what was the best way for it to be, or to be acted upon, or to act (97c, trans. Grube).

Socrates, of course, was disappointed. And the Phaedo records his thoughts on the project on the last day of his life. It’s notable, of course, that he isn’t the main speaker in the Timaeus: it’s

Timaeus that presents the teleological physics that so transparently resemble the hoped-for

Anaxagoras. Timaeus, after all, pursues questions of human anatomy at least partially by asking what would be best, as he argues the Demiurge must have done. Representationalism, I’ve argued, requires that there is a Demiurge trying to represent the world of the Forms. Of the answers we surveyed in chapter one, it is best-suited to providing the sort of teleological explanation that Socrates craves in the Phaedo.

I said the answer was twofold and we’ve provided the Demiurge’s half. The Receptacle provides us with the second. The Timaeus is Plato’s most sustained engagement with issues in natural philosophy, with how it is the universe came to be and what laws govern its physical magnitudes. Any Theory of Forms that we propose in a context where natural (physical) objects are the target of its explanations quickly runs up against a problem we noticed in chapter four: how is it, precisely, that Forms can instantiate properties that seem to be inextricably physical, properties such as size or color or heat? If we want to explain these properties, properties that are

139 This is hardly a novel observation: Cornford (1939), Johansen (2004), and Broadie (2012), among many others, all make it.

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central to our experience of the sensible world, we need either to abandon Self-Predication or introduce a purely material explanatory principle, one that can help us to bridge the gap from the non-spatiotemporal to the world in which we live. Timaeus does the second, if I’m right, and introduces the Receptacle as an explanatory principle.

Once we’ve introduced the Receptacle as part of our earnest engagement in natural philosophy, we find that we can restrict the scope of the Forms radically. Consider, one last time, the case of fire and heat. On a semantic theory of Forms, we would expect that there is a Form for each: Fire to explain fiery things, Heat to explain hot ones.140 But once we introduce the

Receptacle and use it properly to analyze fire, we find that we do not, in fact, need Heat. Heat, as will be familiar to readers of chapters two and four, just is explained by the characteristic motions of sensible fire (61e-2a). That is, the Receptacle and the (geometrical) Form, working together, render a further Form redundant. The Receptacle, by lessening the explanatory burden on the Forms themselves, enable Timaeus correspondingly to limit their number precisely in the way that Self-Predication requires of him: he no longer need posit Forms of inextricably sensible properties.141 Put another way: taking up a cosmogonic project naturally leads us to ask the question of what Forms there are and what Forms there can be.

Timaeus opens the Critias with a closing prayer. After concluding his account, saying that ‘[o]ur one universe, indeed the only one of its kind, has come to be’ (Tim. 92c), he carries on:

I feel the relief of the traveler who can rest after a long journey. Now I offer my prayer to that god who was ancient in deed, but who has now been created in my

140 Recall from chapter one that a semantic theory of Forms holds that there’s a Form associated with each property that would be recognized as a genuine predicate in a language, roughly.

141 Or, if he does, such properties need only mention arrangements of other geometrical properties, leaving the ‘sensible’ part to the Receptacle. Either way will do.

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words [τῷ δὲ πρὶν μὲν πάλαι ποτ᾽ ἔργῳ, νῦν δὲ λόγοις ἄρτι θεῷ γεγονότι προσεύχομαι] (Critias 106a-b, trans. Clay with modifications).

Identifying this as a prayer might cause us to miss its basic scientific impulse. Timaeus takes himself to have ‘created’ the Demiurge in his words. A presupposition of my discussion here has been that he is not meaning to suggest that the Demiurge is (merely) mythical or a storytelling device, one to which he is not fundamentally and seriously committed. But this talk of the

Demiurge having been created in logos helps us to characterize the entire project. The world as we experience, the phainomena, cries out for explanation. And in order to make sense of it, we have to make certain explanatory posits, ones we’re justified in believing just insofar as they manage to do the work we assign to them. It is in that spirit that Timaeus posits not only Forms for those kinds that we find at the world’s joints but also a Demiurge, someone to tie the Forms to that very world.

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WORKS CITED Ackrill, J. L. (1966). ‘Plato on False Belief: Theaetetus 187-200.’ The Monist 50: 383-402.

Ackrill, J. L. (1994). ‘Language and Reality in Plato’s Cratylus’, in A. Alberti (ed.) Essays on Plato and Aristotle, Oxford: Oxford University Press, 1997: 33-52.

Allen, R. E. (ed.) (1965). Studies in Plato’s Metaphysics. London: Routledge & Kegan Paul.

Allen, R. E. (1997). Plato’s Parmenides. Translated with comment. New Haven: Yale University Press.

Armstrong, D. M. (1978). Universals and Scientific Realism (2 vols.) Cambridge: Cambridge University Press.

Armstrong, D. M. (2004). Truth and Truthmakers. Cambridge: Cambridge University Press.

Barney, Rachel (1992). ‘Appearances and Impressions,’ Phronesis 37: 282-313.

Barney, Rachel (2001). Names and Natures in Plato’s Cratylus. New York: Routledge.

Barney, Rachel, Brennan, Tad & Brittain, Charles (eds.) (2012). Plato and the Divided Self. Cambridge University Press.

Bobonich, Christopher (2002). Plato’s Utopia Recast: His Later Ethics and Politics. Oxford: Clarendon Press.

Bostock, David (1988). Plato’s Theaetetus. Oxford: Clarendon Press.

Brisson, Luc (1974). Le même et l’autre dans la structure ontologique du Timêe de Platon. Paris: Klincksieck.

Brisson, Luc (1997). ‘Plato’s Theory of Sense-Perception in the Timaeus: How it Works and What It Means,’ In Cleary and Gurtler (eds.) Proceedings of the Boston Area Colloquium in Ancient Philosophy vol. 13. 147-76.

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Brisson, Luc (2000). ‘Le rôle des mathématiques dans le Timée selon les Interprétations Contemporaines’ in Neschke-Hentschke, A. (ed.), Le Timée de Platon: Contributions á l’Histoire de sa Réception. Paris: Editions Louvain. 295-315.

Broadie, Sarah (2012). Nature and Divinity in Plato’s Timaeus. Cambridge: Cambridge University Press.

Burnet, J. (1900-7). Platonis Opera (5 vols.). Oxford Classical Texts. Oxford: Clarendon Press.

Burnyeat, Myles (1990). The Theaetetus of Plato. Trans. M. J. Levett, revised by M. F. Burnyeat. Indianapolis: Hackett.

Burnyeat, Myles (2000). ‘Plato on Why Mathematics is Good for the Soul.’ In T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy. Proceedings of the British Academy. Oxford: Oxford University Press. 1-81.

Calvo, T. and Brisson, Luc. (eds.) (1997). Interpreting the Timaeus – Critias: Proceedings of the IV Symposium Platonicum: Selected Papers. Sankt Augustin: Academia Verlag.

Cherniss, Harold (1944). Aristotle’s Criticism of Plato and the Academy. Baltimore: The Johns Hopkins University Press.

Cherniss, Harold [1957] (1965). ‘The Relation of the Timaeus to Plato’s Later Dialogues.’ American Journal of Philology 78. Repr. In R. E. Allen (ed.), 1965. 339-78.

Code, Allen (1985). ‘On the Origins of some Aristotelian Theses about Predication.’ In J. Bogen and J. E. McGuire (eds.). How Things Are: Studies in Predication and the History of Philosophy and Science. Dordrecht: Reidel. 101-31.

Cooper, John M. (ed.) (1997). Plato: Complete Works. D. S. Hutchison (Assoc. ed.). Indianapolis: Hackett.

Cornford, F. M. (1935). Plato’s Theory of Knowledge. The Theaetetus and the Sophist of Plato translated with running commentary. London: Routledge & Kegan Paul.

Cornford, F. M. (1937). Plato’s Cosmology. The Timaeus of Plato translated with running commentary. London: Routledge & Kegan Paul.

Cornford, F. M. (1939). Plato and Parmenides. Parmenides’ Way of Truth and Plato’s Parmenides translated with a running commentary. London: Routledge & Kegan Paul.

143

Crivelli, Paolo (2008). ‘Plato’s Philosophy of Language’ in Fine (ed.) Oxford Handbook of Plato. Oxford: Oxford University Press. 217-242.

Crombie, I. M. (1963). An Examination of Plato’s Doctrines (2 vols.). London: Routledge & Kegan Paul.

Denyer, Nicholas (1983). ‘Plato’s Theory of Stuffs.’ Philosophy 58: 315-27.

Duke, E. A., W. F. Hicken, W. S. M. Nicoll, D. B. Robinson, J. C. C. Strachan (1995). Platonis Opera. Vol 1. Oxford Classical Texts. Oxford: Clarendon Press.

Ferrari, G. R. F. (1989). ‘Plato and Poetry’ in G. Kennedy (ed.) Cambridge History of Literary Criticism vol. i. Cambridge: Cambridge University Press. 92-148.

Fine, Gail (1977). ‘Plato on Naming.’ Philosophical Quarterly 27: 289-301.

Fine, Gail (1980). ‘The One over Many.’ Philosophical Review 89: 197-240.

Fine, Gail (1993). On Ideas: Aristotle’s Criticisms of Plato’s Theory of Forms. Oxford: Clarendon Press.

Fine, Gail (ed.). (2008). The Oxford Handbook of Plato. Oxford: Oxford University Press.

Frede, Dorothea (1993). Plato: Philebus. Indianapolis: Hackett.

Frede, Michael [1980] (1987). ‘The Original Notion of Cause.’ In M. Schofield, M. Burnyeat, and J. Barnes (eds.), Doubt and Dogmatism. Oxford: Clarendon Press. Repr. In M. Frede, Essays in Ancient Philosophy. Minneapolis: University of Minnesota Press. 125-50.

Frye, P. H. (1938). Plato. The University. Fujisawa, N. (1974). Echein, Metechein, and Idioms of ‘Paradeigmatism’ in Plato’s Theory of Forms.’ Phronesis 19: 30-58.

Geach, Peter (1956). ‘The Third Man Again.’ Philosophical Review 65: 72-82.

Gerson, Lloyd P. (2013). From Plato to Platonism. Ithaca: Cornell University Press.

144

Gill, Christopher (1997). ‘Galen vs. Chrysippus on the Tripartite Soul in Timaeus 69-72.’ In Brisson & Calvo (eds.) Interpreting the Timaeus-Critias. Sankt Augustin: Academia Verlag. 267-73.

Gill, Christopher and McCabe M. M. (eds.) (1996). Form and Argument in Late Plato. Oxford: Clarendon Press.

Gill, M. L. (1987). ‘Matter and Flux in Plato’s Timaeus.’ Phronesis 32: 34-53.

Gill, M. L. (1996). ‘Introduction’. In M. L. Gill and P. Ryan, Plato: Parmenides. Indianapolis: Hackett.

Gill, M. L. (2012). Philosophos: Plato’s Missing Dialogue. Oxford: Oxford University Press.

Gill, M. L. and Paul Ryan (1996). Plato: Parmenides. Indianapolis, Hackett.

Goldschmidt, V. (1947). Le paradigm dans la dialectique platonicienne. Paris: Presses Universitaires de Frances.

Goodman, Nelson (1965). Fact, Fiction, and Forecast. Indianapolis: Bobbs-Merill.

Goodman, Nelson (1968). Languages of Art: an approach to a theory of symbols. Indianapolis: Hackett.

Grube, G. M. A. (1935). Plato’s Thought. London: Methuen.

Harte, Verity (2002). Plato on Parts and Wholes: The Metaphysics of Structure. Oxford: Clarendon Press.

Harte, Verity (2008). ‘Plato’s Metaphysics,’ in Fine (ed.) Oxford Handbook of Plato. Oxford: Oxford University Press. 191-216.

Jackson, Frank (1997). ‘Naturalism and the Fate of M-Worlds.’ Aristotelian Society Supplementary Volume 71: 247-82.

Jelinek, Elizabeth (2011). ‘Pre-cosmic Necessity in Plato’s Timaeus.’ Apeiron 44: 287-305.

Johansen, T. K. (2004). Plato’s Natural Philosophy: A study of the Timaeus-Critias. Cambridge: Cambridge University Press.

145

Kahn, Charles H. (1973). ‘Language and Ontology in the Cratylus.’ In Lee, E. N., Mourelatos, A. P. D. & Rorty R. M. (eds.) Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory Vlastos. Phronesis Supplementary Volume I: 152-76.

Keyt, David (1971). ‘The Mad Craftsman of the Timaeus.’ Philosophical Review 2: 230-35.

Kretzmann, Norman (1971). ‘Plato on the Correctness of Names.’ American Philosophical Quarterly 8: 126-38.

Lee, Edward N. (1966). ‘On the Metaphysics of the Image in Plato’s Timaeus.’ The Monist 50: 341-68.

Lewis, David (1983). ‘New Work for a Theory of Universals.’ Australasian Journal of Philosophy 61: 343-77.

Lorenz, Hendrik (2006). The Brute Within: Appetitive Desire in Plato and Aristotle. Oxford: Clarendon Press.

Lorenz, Hendrik (2008). ‘Plato on the Soul.’ In Fine (ed.) Oxford Handbook of Plato. 243-66.

Lorenz, Hendrik (2012). ‘The cognition of appetite in Plato’s Timaeus.’ In Barney, Brennan, & Brittain (eds.) Plato and the Divided Self. 238-58.

Luce, J. V. (1964). ‘The Date of the Cratylus.’ American Journal of Philology 85: 136-54.

Malcolm, J. (1991). Plato on the Self-Predication of the Forms: Early and Middle Dialogues. Oxford: Clarendon Press.

Matthews, Gareth B. and Cohen, S. Marc (1968). ‘The One and the Many.’ Review of Metaphysics 21: 630-55.

Meinwald, Constance (1991). Plato’s Parmenides. Oxford: Clarendon Press.

Meinwald, Constance (1992). ‘Good-bye to the Third Man.’ In R. Kraut (ed.), The Cambridge Companion to Plato. Cambridge: Cambridge University Press. 365-96.

Moss, Jessica (2006). ‘Pleasure and Illusion in Plato.’ Philosophy and Phenomenological Research 72: 503-35.

146

Moss, Jessica (2007). ‘What is Imitative Poetry and Why Is It Bad?’ In G. R. F. Ferrari (ed.), The Cambridge Companion to Plato’s Republic. Cambridge: Cambridge University Press: 415- 44.

Moss, Jessica (2008). ‘Appearances and Calculations: Plato’s Division of the Soul.’ Oxford Studies in Ancient Philosophy 34: 35-68.

Moss, Jessica (2012). ‘Pictures and Passions in the Timaeus and Philebus.’ In Barney, Brennan, & Brittain (eds.) Plato on the Divided Self. 259-280.

Nails, D. (2002). The People of Plato: A Prosopography of Plato and other Socratics. Indianapolis: Hackett.

Nehamas, Alexander (1973). ‘Predication and Forms of Opposites in the Phaedo.’ Review of Metaphysics 26: 461-91.

Nehamas, Alexander (1975). ‘Plato on the Imperfection of the Sensible World.’ American Philosophical Quarterly 12: 105-17.

Nehamas, Alexander (1979). ‘Self-Predication and Plato’s Theory of Forms.’ American Philosophical Quarterly 16: 93-103.

Nehamas, Alexander (1982). ‘Participation and Predication in Plato’s Later Thought.’ Review of Metaphysics 36: 343-74.

Notomi, Noboru (2011). ‘Image-Making in Republic X and the Sophist: Plato’s Criticism of the Poet and the Sophist.’ in Destree, P. and Herrmann, F-G. (eds). Plato and the Poets. Mnemosyne Supplementa 328: 299-326.

Owen, G. E. L. (1953). ‘The Place of the Timaeus in Plato’s Dialogues.’ Classical Quarterly N. S. 3: 79-95. Repr. In R. E. Allen (ed.), 1965.

Owen, G. E. L. (1966). ‘Plato and Parmenides on the Timeless Present.’ The Monist 50: 317-40.

Panagiotou, S. (1987). ‘The Day and Sail Analogies in Plato’s Parmenides.’ Phoenix 41: 10-24.

Peterson, Sandra (1981). ‘The Greatest Difficulty for Plato’s Theory of Forms: The Unknowability Arguments of Parmenides 133c-134c.’ Archiv für Geschichte der Philosophie 63: 1-16.

147

Peterson, Sandra (1996). ‘Plato’s Parmenides: A principle of Interpretation and Seven Arguments.’ Journal of the History of Philosophy 34: 167-92.

Philip, J. A. (1961). ‘Mimesis in the Sophistês of Plato.’ Transactions and Proceedings of the American Philological Association 92: 453-68.

Prince, Brian D. (2014). ‘The Metaphysics of Health and Disease in Plato’s Timaeus.’ British Journal for the History of Philosophy 22: 908-28.

Quine, W. V. O. (1961). ‘On what there is.’ In From a Logical Point of View. Cambridge, Harvard University Press. 1-19.

Rashed, Marwan (2013). ‘Plato’s Five Worlds Hypothesis (Ti. 55cd), Mathematics and Universals.’ In Chiaradonna and Galluzzo (eds.) Universals in Ancient Philosophy. Pisa: Edizioni della Normale. 87-112.

Rickless, Samuel (2007). Plato’s Forms in Transition: A reading of the Parmenides. Cambridge: Cambridge University Press.

Robin, Léon (1935). Platon. Paris: Libraire Félix Alcan.

Ross, W. D. (1951). Plato’s Theory of Ideas. Oxford: Clarendon Press.

Ryle, Gilbert [1939] (1965). ‘Plato’s Parmenides.’ Mind N. S. 48. Repr. With Afterword in R. E. Allen (ed.), 1965. 97-147.

Ryle, Gilbert (1966). Plato’s Progress. Cambridge: Cambridge University Press.

Schaffer, Jonathan (2009). ‘On What Grounds What.’ In Manley, Chalmers, and Wasserman (eds.) Metametaphysics. Oxford: Oxford University Press. 347-83.

Schofield, Malcolm (1996). ‘Likeness and Likenesses in the Parmenides.’ In C. Gill and M. M. McCabe (eds.), Form and Argument in Late Plato. Oxford: Clarendon Press. 49-77.

Sedley, David (1998). ‘Platonic Causes.’ Phronesis 43: 114-32.

Sedley, David (2009). Plato’s Cratylus. Cambridge: Cambridge University Press.

Sider, Theodore (2011). Writing the Book of the World. Oxford: Oxford University Press.

148

Silverman, Allan (1992). ‘Timaean Particulars.’ Classical Quarterly 42: 87-113.

Smith, J. A. (1917). ‘General Relative Clauses in Greek.’ Classical Review 31: 69-71.

Sorabji, Richard (1983). Time, Creation, and the Continuum: Theories in Antiquity and the Early Middle Ages. Chicago: University of Chicago Press.

Tarán, L. (1971). ‘The Creation Myth in Plato’s Timaeus.’ In J. P. Anton and G. Gustas (eds.) Essays in Ancient Greek Philosophy vol. 1. Albany, SUNY Press. 372-407.

Taylor, A. E. (1926). Plato: The Man and his Work. London: Methuen.

Taylor, A. E. (1934). The Parmenides of Plato. Oxford: Clarendon Press.

Vlastos, Gregory (1939). ‘The Disorderly Motion in the Timaios.’ Classical Quarterly 33: 71-83.

Vlastos, Gregory [1954] (1965). ‘The Third Man Argument in Plato’s Parmenides.’ Philosophical Review 63. Repr. With Addendum in R. E. Allen (ed.), 1965. 231-65.

Warburg, M. (1929). Zwei Fragen Zum “Kratylos”. Berlin: Weidmann.

Wilburn, Josh (2012). ‘Curbing one’s appetites in Plato’s Republic.’ In Barney, Brennan, and Brittain (eds.) Plato on the Divided Self. Cambridge, Cambridge University Press. 128-49.

Wilburn, Josh (2014). ‘The Spirited Part of the Soul in Plato’s Timaeus.’ Journal of the History of Philosophy 52: 627-52.

Williams, Bernard (1978). Descartes: The Project of Pure Inquiry. Atlantic Highlands: Humanities Press.

Williams, Bernard (1982). ‘Cratylus’ Theory of Names and its Refutation.’ In Schofield and Nussbaum (eds.) Language and Logos in Greek Philosophy. Cambridge: Cambridge University Press. 83-94. Wittgenstein, Ludwig (1922) Tractatus logico-philosophicus. London: Kegan Paul, Trench, Trubner & Co.

Yablo, Stephen (2014), Aboutness. Princeton: Princeton University Press.

Zeyl, Donald J. (2000). Plato’s Timaeus. Indianapolis: Hackett.

149

Zeyl, Donald (2009). ‘Visualizing Platonic Space.’ In Mohr & Sattler (eds.) One Book, the Whole Universe: Plato’s Timaeus Today. Las Vegas: Parmenides Publishing. 117-30.

150