Identity and Difference in Kind: The Metaphysics of Pleasure at the Beginning of Plato’s Philebus

I

Plato’s Philebus, known as a remarkably challenging philosophical text, presents a puzzling argument right at its start. The dialogue sets up a debate between two parties. On the one side is the character Philebus, who maintains that enjoyment, pleasure, and a family of related kinds are “good for all living things” (11b4–6). (Philebus immediately hands over responsibility for defending this position to another character, Protarchus.) On the other side is the character Socrates, who argues that knowledge, intelligence, memory, and a related family of kinds are better than pleasure, for those who can attain them (11b6-c1). At the first attempt to move this debate forward, Socrates tells Protarchus that although the word, ‘pleasure’, makes it sound like pleasure is only one thing, it is also “various”. As a result, their discussion must begin with an inquiry into pleasure’s nature (12c1–8). To make his case, Socrates offers some contentious examples: we speak of the pleasure the temperate person takes in temperance, as well as the pleasure the intemperate takes in intemperance, and similarly of the pleasure the wise person takes in wisdom and the foolish in folly (12c8-d6). This counts against calling all pleasures “like” each other. But Protarchus retorts that in each of these cases the pleasure is no different, even though the sources of enjoyment are (12d7–8). Protarchus also disputes Socrates’ claim that some pleasures are good, others bad (13b1): in his view, no one contending that “pleasure is the good” would concede that only some are good, while others bad (13b6-c2). Yet Socrates appears to think that this second, normative claim, is jeopardized by the metaphysical thesis that pleasures are in some way unlike. He insists that Protarchus’ attempts to evade the metaphysical thesis are mistaken and that the discussion cannot proceed without his concession (13c6-d8).¹

The logic of this exchange is hard to follow, and Socrates’ own positions are somewhat obscure. According to several prominent commentators, in this passage Socrates puts pressure on his hedonist interlocutor only by fallaciously inferring that some pleasures are bad and others good from the premise that pleasures are unlike in some way.² Moreover, while Socrates’ claim about pleasure’s internal structure is rightly read as an anticipation of the “one and many” metaphysical problems that are soon centralized in the discussion (especially 14c1–15c3),³ it is not clear why Protarchus, who does not yet grasp these problems, should find Socrates’ position that pleasures are unlike acceptable at this stage. To address this, scholars sometimes suggest that Socrates is proposing a conception of pleasure as a representational state whose content is determined by the activity that causes it. By contrast, Protarchus takes pleasure to be a non-representational sensation. So, in Protarchus’ view, differences in the underlying cause make no difference to the pleasure.⁴ Although this interpretation of the basis of the disagreement fits well with later parts of the dialogue (e.g., 36c-38a), the precise dispute about the representational nature of pleasure is unlikely to be the real point of contention here. Socrates focuses on the internal heterogeneity of an apparently unified kind in general, not just pleasure (he gives parallel examples of color and shape at 12e4–13a5 and speaks generally at 13d3–8).

How, then, are we to make sense of this passage? From this brief introduction we can recognize at least three questions: What is Socrates’ metaphysical thesis? Why should Protarchus accept it? And why does accepting it also put pressure on Protarchus’ defense of hedonism? The goal of this paper is to defend answers to these questions. I believe that such a defense can be made by bringing out an interesting connection between Plato and contemporary metaphysics. Sections III-IV argue that Socrates thinks of pleasure as exhibiting the metaphysical structure characteristic of what we today would call a determinable property. While this metaphysical structure has been noted as relevant by some scholars,⁵ it is rarely centralized in this passage. Moreover, it is often overshadowed by the alternative model of a genus with species, as we will see. The novelty of this paper is to show how the metaphysical structure of determinables and determinates (as opposed to genera and species) emerges organically from the issues at this point of the discussion, what features of this structure are relevant to the dialectic, and how they can answer the pressing questions about the passage.

The core of my argument is that the type of identity and difference advanced by Socrates in this passage of the Philebus is best understood as witnessing a key structure of determinates and determinables. On the one hand, what makes a determinable property (color, mass) what it is, is a function of what its determinate properties (violet, 1 kg) are. On the other hand, what makes determinates what they are is also what makes them different from each other. Taking these claims together, the differences among determinates are the very features that constitute, in some way, the identity of the determinable. Drawing on the two models (παραδείγματα, 13c8) Socrates produces to clarify his contention about pleasure—color and shape (12e4–13a5)—I argue that this is the metaphysical thesis about pleasure Socrates advances: the difference-making features of the pleasures are their pleasure-making features, which constitute the nature of pleasure as a whole. This is crucial to his engagement with hedonism because if the difference-making features of the pleasures are the very features in virtue of which they are pleasures, then the goodness of one kind of pleasure qua pleasure does not entail the goodness of all pleasure. Section V argues that this is a challenge to Protarchus’ hedonism, which he could overcome by articulating the different kinds of pleasure. This is the task to which Socrates is trying to orient him at the start of their discussion.

Two notes of warning to the reader. First, given that the determinable-determinate framework is contemporary, I argue below only that Plato is interested in a structural feature of what we understand as determinables and determinates and that we can locate this entirely within his own theoretical framework. My argument is that part of the scaffolding of the metaphysics of kinds in this passage of the Philebus is also part of the scaffolding of the metaphysics of determinables and determinates. In fact, Plato might have other ideas about the metaphysics of kinds that are foreign to the metaphysics of determinates and determinables. Second, I do not think that Socrates’ goal is to convince Protarchus, at this stage, that there are bad pleasures, but rather that this is an open question for them to settle through discussion. I will also only show that Protarchus is under pressure to accept Socrates’ thesis given his own claims about identity and difference. Alternatives may go unexplored. Still, my point is that Socrates presents not a sophism or a question-begging argument but an interesting and subtle view, dialectically motivated in its context and an important anticipation of more familiar ideas.

II

Before defending my main claims, I want to get the basics of the central passage on the table. Here is Socrates’ initial claim about pleasure, in full:

[T1] As for pleasure, I know that it is various (ποικίλον), and as I said, we should take our starting point from this and inquire into whatever nature (φύσιν) it has. For hearing it thus [named], it is simply one thing (ἁπλῶς ἕν τι), but I presume (δήπου) it takes shapes (μορφὰς) that are diverse and in some way unlike each other (τινα τρόπον ἀνομοίους).⁶ For consider: we say (φαμεν) that the intemperate person feels pleasure, and that the temperate feels pleasure in his temperate activity; again that the one lacking intelligence, full of unintelligent beliefs and hopes, feels pleasure, and again that the wise feels pleasure in his own wisdom. How could someone saying that each of these pleasures are like (ὅμοιος) each other not rightly appear foolish? (12c4-d6)

T1 asserts that while pleasure sounds, on the basis of its name, like “simply one thing”, it is also various, taking on shapes “in some way unlike”. As Socrates implies, he already spoken of pleasure’s ambiguity in this regard. Just before, he describes Philebus as insisting on calling “Aphrodite” by the name, ‘pleasure’ (12b7–9). But he is himself afraid of calling gods by the wrong names (12c1–4).⁷ T1 explains why: the simple unity implied by naming pleasure ‘pleasure’ is undermined by our other speech-acts about pleasure. For instance, we say that temperate and intemperate people are pleased by different activities, and similarly for wise and foolish people. Socrates thinks this makes it seem “foolish” for a person to say that these different pleasures are “like” each other.

Protarchus is not convinced by this argument. To the contrary, he denies that these examples show that pleasure is different but only that pleasure, which is one thing, arises from different sources:

[T2] Well, that’s because they come from opposite things (ἀπ᾽ἐναντίων…πραγμάτων), Socrates, but not because they (αὐταί) are opposite to each other. For how could pleasure not be most like (ὁμοιότατον) pleasure, this very thing to itself (τοῦτο αὐτὸ ἑαυτῷ), of all things? (12d7–10)

Protarchus denies the unlikeness of pleasures on the grounds that the differences in Socrates’ examples have to do with each pleasure’s sources, not what each pleasure is. Pleasures taken in intemperance or folly as opposed to temperance or wisdom are pleasures from opposite things, but they are not themselves opposed. Rather, each pleasure is “most like” each other pleasure, because each pleasure is self-identical, or stands in a relation of “this very thing to itself”. Thus, we always call the same thing ‘pleasure’.

Socrates offers a rejoinder to this objection. Protarchus fails to acknowledge the respects in which relations of identity and difference hold. As we have seen, he initially says that pleasure is unlike pleasure in some way (τινα τρόπον ἀνομοίους, 12c8). He elaborates, now in response to Protarchus:

[T3] As well as for color, my good man, with respect to color (χρῶμα…χρώματι): in this respect itself (κατά γε αὐτὸ τοῦτο), no color will differ at all, and yet we all know that black is different from white, and in addition is really most opposite. And shape, too, in relation to shape (σχῆμα σχήματι), in the same way (κατὰταὐτόν). All are one in kind, but as for the parts with respect to its own parts (τὰ δὲ μέρη τοῖς μέρεσιν αὐτοῦ), some are most opposite each other, while I suppose others really have immense difference, and we will find many other things so disposed. Don’t, therefore, put your faith in this argument, which makes a unity out of all the most opposite things. I suspect we will find some pleasures opposite to pleasures. (12e11–13a5)

Here, Socrates concedes a point to Protarchus. In the relationship of “color to color” (χρῶμα…χρώματι), and of “shape to shape” (σχῆμα σχήματι), an analogous claim to Protarchus’ thesis about pleasure holds. Color does not differ from color and shape does not differ from shape (just as pleasure does not differ from pleasure as “this very thing [standing in relation] to itself”). But he qualifies this identity as a relational fact that holds in one respect, but not in another. For while as “color to color” no color differs, as “black to white” (τό γε μὴν μέλαν τῷ λευκῷ) these colors are “different” and “opposed”. Similarly, some “parts” of shape are “different” and others “opposed”, while being “one in kind (γένει)” nonetheless. The passage concludes with an analogous claim about pleasures. They will discover some pleasures “opposite” to pleasures and so should not trust the argument that “makes a unity out of all the most opposite things”—by which Socrates means, in context, the argument that makes a simple, unqualified unity out of opposites.⁸

Socrates’ emphasis on qualifying identity and difference in the right way gives us an important indication as to Plato’s purpose in this passage. Predicational paradoxes, often taking the form of contraries predicated of contraries, form an important bedrock of Plato’s theorizing about reality and our ability to know it. In a few related dialogues, he appears to maintain that accepting the possibility of contrary predications is necessary for philosophical inquiry, which can then discover the complex, interwoven structure of intelligible reality (e.g., cf. Parmenides 129d-e with 136a-c, 156b-c, 157a; Sophist 236e-239c, 250c-d, with 255b-d, 256a-b, 257b-c, 259b-260a). Arguably, T1 and T3 represent Socrates’ attempt to get Protarchus to take on this perspective. He must recognize that pleasure can be both like and unlike, both same and different, since it has the ontological structure of a composite kind, like color and shape. It is true that in T1, he characterizes calling the pleasures “like” as foolish (12d4–6), and at the end of T3, he asks Protarchus not to believe the argument that “makes a unity” out of opposites (13a3–4). But Socrates also insists that all the pleasures are pleasant and wants Protarchus to see that this is not what he is disputing (13a9–10). Similarly, he concedes Protarchus’ point about unity, when qualified as relations of “color to color” and “shape to shape”. Socrates’ view is that unity does not exclude multiplicity; Protarchus thinks that it does. The importance of recognizing complex multiplicity within intelligible reality is also represented later in the Philebus: Socrates gives an account of the “intermediates” (τὰ…μέσα, πάντα…μεταξὺ) of the divine method, which lie between the unified one form and the unlimited many and which ground technical expertise (16d7–17a3). Grasping these, Socrates says, shows us not only that the original, unified form is “one”, but also how it is a determinate “many” (16d5–7). This is what experts in a domain (e.g., music, literacy) know, such that they are experts (17b3–9, c1-e6). Protarchus rejects this perspective at the outset by denying that the “many” are a many of pleasure: instead, they are different virtues, or activities, persons, etc., which happen to be conjoined with pleasure. Socrates’ metaphysical thesis, by contrast, commits to the intrinsic differences among pleasures.

The foregoing argument is meant to show why it is important to Plato that for Protarchus to engage in philosophical, knowledge-conducive inquiry with Socrates, he needs to accept that the shared identity of each pleasure is respect-specific and compatible with their intrinsic multiplicity in other respects. But this does not help us to see why Protarchus should accept such a thesis, given his own perspective at this stage of the dialogue. Moreover, even if he accepts that some kinds are as Socrates insists, why should he accept that these are “models” (13c8) for pleasure?⁹

To be clear, this is the beginning of a long and complex dialogue, which need not stack the deck against the hedonist right from the start. The discussion here is a negotiation, with the parties agreeing to the substantive framework of their debate. Nonetheless, Socrates presses his point that Protarchus is missing something important by insisting on the absolute uniformity of all pleasure. I suggest that this is because Socrates has an advantage within the dialectical context, due to the generality of Protarchus’ position. This emerges in the next and final text I will discuss in this section. In his reply to Protarchus’ denial that the pleasures are unlike “to the extent that they are pleasures” (οὔτι καθ’ ὅσον γε ἡδοναί) (13c3–4), Socrates says:

[T4] We are brought back to the same argument, Protarchus: will we not say that pleasure does not differ from pleasure (ἡδονὴν ἡδονῆς διάφορον), but all are alike (ὁμοίας), and do the models we were just talking about have no influence on us, and rather should we do and say what those who are basest of all and novices concerning arguments [do and say]?

PR: How do you mean?

SO: That, imitating and defending against you, if I dare to say that the most unlike is to the most unlike, of all things, most like (τὸ ἀνομοιότατόν ἐστι τῷ ἀνομοιοτάτῳ πάντων ὁμοιότατον), then I will be able to say the same things as you. (13c6-d5)

In T4, Socrates says that instead of allowing the models—color and shape—to convince them of pleasure’s internal heterogeneity, Protarchus acts like a dialectical novice by continuing to maintain that “pleasure does not differ from pleasure, but all are alike”. Socrates characterizes Protarchus’ position as the view that “the most unlike is to the most unlike, of all things, most like”. One natural way to read this is that Socrates takes Protarchus to advance a generalized principle corresponding to his claim that every pleasure is most like every other pleasure, as the relation of something to itself (T2). Roughly, this principle says:

For any x and y, if x and y are G, then x and y are maximally similar qua G.¹⁰

Since Protarchus maintains that the pleasures are “most like” (12d8-e2), it seems reasonable to understand Socrates’ to employ “most unlike” as a name for the opposite pleasures, such as wise and foolish pleasure, and to imitate Protarchus by saying that these most unlike things are (as Protarchus had said) most like.¹¹ Protarchus calls opposites such as temperate and intemperate or wise and foolish pleasure “most like” because they share a property in common, namely, pleasantness. But the metaphysical principle that grounds this thesis is completely general. It says that any tokens of a common type are maximally similar with respect to that type. This is what Socrates articulates when he says that “the most unlike is to the most unlike, of all things, most like”. If Socrates were to show that some kinds violate this principle, he would successfully undermine the particular defense Protarchus undertakes in our passage. This is the pressure he puts on Protarchus to agree that pleasures are unlike in the very particular way he understands it.

Still, why, exactly, do color and shape—or pleasure, for that matter—violate the principle? To address this issue, we need to turn, now, to the core of my paper: the metaphysics of kinds Socrates advances in this passage.

III

I contend that the most illuminating model for Socrates’ claim about the structure of pleasure, color, and shape in this passage, is what contemporary metaphysicians call “determinables” and “determinates”.¹² Some scholars of Plato have noted that Socrates’ examples in T3—color and shape—are paradigmatic determinables, and the metaphysics of determinates and determinables have been discussed in the context of the divine method (16c-18d). Moreover, determinability is often associated with Aristotle’s notion of a genus.¹³ Nonetheless, my contribution here is to highlight the specific feature of determinates and determinables that Socrates attributes to pleasure in this passage, why it is not the same thing as the metaphysics of genus and species, and what role it plays in the discussion at this stage. Before turning to the text of the Philebus, I will provide a brief overview of the relevant aspects of determinates and determinables.

In the contemporary philosophical landscape, paradigmatic determinates are the shades of color: red, blue, yellow, etc. are “determinates” of the determinable property, color. Color is generally understood as a set of dimensions (e.g., hue, brightness, saturation), and any object is colored only insofar as it instantiates concrete (and exclusive) values within those dimensions.¹⁴ For instance, a table is red only if it has some determinate combination of hue, brightness, and saturation, which are incompatible with the determinate combination of a blue table. Nonetheless, which properties are determinate and which determinable is relative to the level of determinateness. While red and blue are determinate in relation to color, they are determinable in relation to their own shades (e.g., maroon and scarlett, cerulean and taupe). Generalizing, we can say that, relative to some level of determinateness, some properties are domains in which other properties witness some specific value or range of values. It is also usually assumed that there is some level at which determinateness is maximal, and that at this level we find the fundamental reality that grounds the determinable properties we ordinarily speak and think about.

The feature of determinables and determinates I find in Socrates’ argument concerns how determinates at the same level differ from each other and how this grounds their similarity within the determinable of that level. For example, blue’s difference from red is a function of how they have different values within the property-domain of color. Let’s say, again, that they differ in their specific hue, brightness, and saturation. How navy differs from taupe is a function of their differences within the specific constellation of hue, brightness, and saturation that demarcates blue. In general, how each determinate differs from each other determinate at the same level is intrinsically connected to their shared determinable at that level. They differ with respect to their shared determinable (e.g., navy differs from taupe with respect to their being blue).¹⁵ Scholars sometimes articulate this by saying that a determinate is a way of being its determinable—e.g., blue is a way of being a color; taupe is a way of being blue.¹⁶ As a result, the similarity determinates have as determinates depends on the differences between them. That is to say, the difference-making features of the determinates ground the similarity uniting the whole domain: what the determinable property is flows from the different identities of the determinates, since the different identities of the determinates marks off the boundaries and contents of the determinable’s constitutive dimensions.

Attributing this metaphysical outlook to Socrates poses a challenge for the way his argument is traditionally understood. Many interpreters of the Philebus claim that Socrates’ point in our passage is that pleasure is one genus pluralized in many species.¹⁷ Understood in the right way, this claim is fine by me. But there is at least one—not implausible—understanding of genera and species which is incompatible with the metaphysics of determinates and determinables. The standard view in contemporary metaphysics is that species are classes of individuals characterized by conjunctive definitions, with one conjunct corresponding to a generic property and another to a differentia specifica.¹⁸ For instance, say the definition of the human species is a set of generic properties—what makes something an animal, a mammal, and a primate—and a specific difference, such as being fully bipedal, so that:

Human = animal & mammal & primate & fully bipedal.

In this model, the properties that individuate species—their specific differences—are independent of the properties uniting them at a higher level—their generic unity. For instance, what makes a human being distinctive—being fully bipedal—is not intrinsically connected with being a primate. In principle, there could be non-primates distinguished by being fully bipedal. (To give another, related example, bird species can be differentiated by the color of their feathers, yet the same color can differentiate different species.) What makes something belong to a genus, in this sense, is typically not related in any intrinsic way with what makes it belong to its species. However, metaphysicians often take determinable-determinate relations to contrast with genus-species relations in exactly this way. Unlike the independence of a species from its genus, there is a tight metaphysical connection between a determinate and its determinable.¹⁹ This is one reason why determinates are not analyzable into conjunctions in the way that a species can be analyzed into a specific difference and a generic property. Determinates are specifications of a determinable, not additions to it.

This contrast between determinates/determinables and species/genera is important, because the conception of species as conjunctions of independently realizable properties fails to make sense of the dialectic across our T1–4. There is nothing unacceptable to Protarchus in T2 about a diversity of pleasures defined by their pleasantness plus another, separate property. Indeed, he maintains exactly this position. Intemperate and temperate pleasures, in his view, are maximally similar in virtue of sharing the property uniting their kinds—pleasantness—and are distinguished only extrinsically by their causal sources. Hence, Protarchus would accept that temperate and intemperate pleasures are species of the genus, pleasure, insofar as he would accept that the definitions of temperate and intemperate pleasure are conjunctions with a conjunct corresponding to pleasantness and conjuncts corresponding to temperate and intemperate activities, respectively, but which share no intrinsic connection. Socrates’ resistance to Protarchus’ position means that he has something else in mind.

One lesson we can take from this is that there must be a closer connection between the differentiating properties (what makes the pleasures distinct) and the unifying properties (what makes the pleasures one kind) than one version of a genus-species interpretation can offer. I am proposing that determinate-determinable relations capture this connection. Before defending this as a reading of the text, let me add two qualifications to my proposal.

First, the distinction between genera and species and determinables and determinates may not be clean.²⁰ Aristotle is often thought to hold that the specific difference of a species is a determinate of a determinable power of the genus. Some scholars have located a similar view in the divine method of the Philebus.²¹ Nonetheless, we should be conscious of the fact that there is at least one conception of genus-species relations (the one that contemporary metaphysicians typically assume) that will not capture T1–4 adequately. My claim is that whatever discourse of kinds we use for this passage, it should respect one key aspect of the metaphysics of determination.

Second, one might reasonably wonder whether there are alternative metaphysical models than determinables and determinates for making sense of T1–4. It is not necessary for my argument to exclude this possibility. My claim is that Socrates picks up on one aspect of how we today understand determinates and determinables. There might be other models that also witness that aspect, although I am not aware of them. Moreover, Socrates may understand the metaphysics of pleasure in ways that significantly depart from determinates and determinables as a whole. For example, whereas same-level determinates are equally instances of their determinable, Socrates will go on to argue that not all pleasures are equally genuinely pleasures (42b-c, 52d-53c).²² Nonetheless, the metaphysical structure I have articulated, in which the difference-making features of same-level determinates are the grounds for their similarity with respect to their determinable, captures the specific point Socrates is making here and is compatible with his own understanding of ontological priority among pleasures. The important idea is that the features that make pleasures different also make them pleasures. As far as I am concerned, this leaves space for additional types of structure in the metaphysics of kinds as Socrates understands it here and as it is developed over the course of the dialogue.²³

IV

So far I have sketched the main texts of interest to me and a basic metaphysical framework derived from determinables and determinates. I turn now to putting these two sketches together. We have seen that Socrates emphasizes a certain compatibility of likeness with unlikeness. When he responds (in T3) to Protarchus’ claim (in T2) that pleasures differ only in their sources, he says that self-identity holds of colors in respect of being colors, and similarly for shapes; yet, in respect of being a specific color or shape, each differs from the other, and some are even opposed. This compatibility of being both identical in one respect and different in another is like the unity of a set of determinates within a determinable domain. In one relation, determinates are the same—i.e., they are the same with respect to their shared domain—but in another relation, they are different—i.e., they are different with respect to each other as distinct values in the domain. And this sameness-and-difference is not an accident but a result of the very structure of the property in question: part of what it is to be a color, or a shape, or, for that matter, a pleasure, is a function of how the kinds of color, shape, or pleasure differ from each other. In this respect, Socrates’ metaphysical thesis in these passages witnesses a core, structural feature of determinates and determinables.

To make my case for this reading, I will initially focus on the two relations Socrates singles out: opposition and difference. His examples in T1 are intemperate and temperate, wise and foolish pleasure, which Protarchus characterizes as having opposite sources (12d6).²⁴ Socrates preserves Protarchus’ characterization, arguing that black and white are opposite colors, shape has opposite parts, and that it will turn out that there are opposite pleasures (12e-13a, in our T3). This emphasis on opposition is significant because opposites have features that are essentially connected to being the opposites they are. For instance, black, in virtue of its being black, has a certain phenomenological profile—say, it is what it is in virtue of its reflectivity. This profile serves the dual function of both differentiating black from white and unifying black with white as a coordinate opposite of a common kind. That is, black’s reflectivity profile distinguishes it from white, but it is also what makes black a color: for to be a color is, perhaps among other things, to have a certain kind of reflectivity profile. In this way, the properties of the opposites ground both the differences between them and the similarity in a common kind—just like the distinct identities of determinates.

The analysis of color in Plato’s Timaeus offers a plausible model for this conception of the opposition between black and white. According to Timaeus:

Color is a flame which flows forth from bodies of all sorts, with its parts proportional to our sight so as to produce perception…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 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. (Timaeus 67c-e, tr. Zeyl, emphasis in original).

That is, color is a ray of fire projected by visible bodies with parts that are either larger than, smaller than, or equal to the size of the parts of the fire-rays projected by the eyes. Color-rays with parts that are larger than the parts of the sight-rays they contact make the sight-rays contract, while those with parts that are smaller make the sight-rays dilate. For a color-ray to be black is for it to make the sight-ray contract, while for a color-ray to be white is for it to make the sight-ray dilate. Thus, Timaeus’ analysis of color illustrates how black and white exhibit a shared unity grounded in the intrinsically different properties of each kind. Black’s essential feature is being a flame with parts of a certain size—say, size s—projected by visible objects. White’s essential feature is being a flame with parts of a certain size—say, size r<s—projected by visible objects. Having parts of size s differentiates black from white and having parts of size r differentiates white from black.²⁵ But having parts of sizes r and s respectively also makes each a color, that is, a flame of with parts of a certain size projected by visible objects and interacting in proportion to the internal rays of sight.

Given this view of color, it is plausible that when, in our T3, Socrates describes black and white as opposite yet colors as self-identical, he understands opposites to differ in the way that determinates at the same level differ. Opposite colors differ from each other in the way each instantiates the common feature with respect to which each is an opposite, that is, in its nature as a color. Thus, opposite colors provide a model for Socrates to capture the relevant metaphysical structure for pleasure—without, it is worth emphasizing, him needing to have anything about determinateness in mind. Insofar as pleasures are opposites, they differ in or with respect to their pleasure-making properties. This is because what makes each pleasure a pleasure just is what makes it opposite to its coordinate pleasure. For instance, the pleasant experience of temperate activity is opposite to the pleasant experience of intemperate activity, yet each is the soul’s experience of an activity as pleasant to a certain degree (cf. 33c-34b).

Socrates’ second example, shape, provides another, complementary model. Like color, Socrates says that some shapes are “most opposite”, while others are “different”. The inclusion of both opposition and difference is important for the metaphysical picture on offer. In Plato’s Sophist, the Stranger distinguishes being different (ἕτερος) from being opposite (ἐναντίος). The former is a less specific property than the latter: being different does not entail being opposite but being opposite entails being different (257b-258b).²⁶ This distinction can help explain how in T3, the kinds of shape can be either opposite or merely different (13a1–3). Of course, Socrates suggests that, like black and white, some shapes are “opposite”. Perhaps Plato has in mind the analysis of all two-dimensional shapes into two kinds of right-angled triangles—isosceles and scalene—in the Timaeus (Timaeus 53c-d). Or perhaps he is thinking of the primary bodies constructed out of these triangles and how there are two extremes—fire and earth—with two intermediaries—water and air (Timaeus 49b-d, 53d-57d). Whatever the case may be, the most important point for my purposes is that shapes instantiate values that are exclusive and yet cohere as part of a common domain, such that by having the exclusive values, they are simultaneously united in a common kind. For instance, what makes the atomic triangles of the Timaeus different is that the division of the right angle in the isosceles triangle is equal, while the division of the right angle in the scalene is unequal (53d). But for each triangle, it is the similarity between these different angles which make it the case that each is a shape at all. To be a shape, on this model, is to be like other shapes in virtue of different shape-profiles. In the Meno Socrates accepts the definition of shape as “the limit of a solid” (76a),²⁷ and the same point applies. In virtue of distinctive “limits”, one shape is both different from another and instantiates the common property of being a shape (limiting a solid). In the plane-geometry underwriting the solids of the Timaeus, shapes are the limits of 2-dimensional spaces. Here, the character of the arrangement of lines (e.g., the lengths and points of intersection) determine both the properties that differentiate one shape from another (e.g., differently distributed angles) and the more general property, limiting a space.

By offering us two different models and by highlighting two distinct relations, Socrates tasks Protarchus with picking up on what is common to them, which is the point he wants to get across. I have argued that this point of overlap is the form of difference-and-sameness characteristic of determinates: differing in the way or manner of having a common property, so that the relata are alike and distinct in virtue of the same properties. It makes no difference that the terminology of determinates and determinables is due to a textbook published in the 20^th century (Johnson 1921).²⁸ Socrates could identify a core feature of determinates and determinables without conceiving of determinates and determinables as specific classes of properties. Indeed, he seems to have in mind a broad range of relations including part-whole, and as I said above, he may also attribute other features to the metaphysics of kinds like pleasure that outstrip or are incompatible with the metaphysics of determination. Nonetheless, I have argued that there is one aspect of determinables and determinates that fits neatly with the dialectic across T1–4, and that Plato can conceptualize the relevant metaphysical claims in terms of his own theories. Protarchus’ mistake, on the view I have defended, has nothing to do with determinates and determinables per se but only a feature of them. His mistake is to think that it is impossible for each pleasure both to be a pleasure and to be different in virtue of the same properties.²⁹ Color and shape are thus models insofar as they demonstrate how the unity of a generic kind is a relation of similarity that obtains in virtue of more specific, and hence intrinsically different, sub-kinds. As I will argue below, Socrates’ point in bringing up this aspect of pleasure’s nature is to show to Protarchus that they must agree to articulate the different kinds of pleasure in order to grasp what pleasure is (and, in turn, whether this is good).

Before moving on from this line of argument I want to clarify one way in which my position is continuous with existing scholarship on this section of the Philebus, and one way in which it departs from it. This dispute about pleasure anticipates the metaphysical issues brought out in the much more well-studied passage on the “one and many” (14c1–15c3). Gibbons and Legg (2013) argue that this later passage raises a number of interesting metaphysical puzzles associated with “hylomorphic dispersal”, notably three related dispersal problems at the level of universals (so-called “higher-order dispersal” problems).³⁰ My argument is entirely continuous with this view, insofar as I agree that T1–4 introduce metaphysical issues that apply primarily to intelligible forms and often (but not always) focus on their internal relations and properties, as Socrates goes on to illustrate.³¹ I have also deepened our appreciation of the connection with contemporary metaphysics by showing yet another way in which Socrates anticipates the structural configurations of higher-order dispersal. But I depart from these views insofar as I see T1–4 as focusing not on these issues in the abstract, but on a specific feature relevant to the discussion: how, as a result of pleasure’s being “dispersed” among many kinds and those kinds combining to compose pleasure, each kind is intrinsically different. What remains to be shown is why this premise is relevant to Protarchus’ normative position, in Socrates’ view. The fact that it is this normative consideration that ultimately motivates Socrates is significant. Here metaphysics enters only to the extent that it is part of ethics. My account makes better sense of this than the observation that the passage illustrates one-and-many metaphysics in the abstract, by showing that the metaphysical issues that come to dominate the next part of the discussion in their abstract formulation emerge due to the connection between one relevant metaphysical structure and the discussion about pleasure, knowledge, and the good human life.

V

One of the central roadblocks to understanding our passage is the appearance to some that Socrates infers from the unlikeness of pleasures to the normative division of pleasures into good and bad. After all, in T1 he distinguishes virtuous from vicious types of pleasure. In an important part of their exchange, Socrates clarifies his position in response to Protarchus’ question about the significance of there being different pleasure (following up on our T3). He explains:

[T5][1] [The risk to your position is] that you, we will claim, call those unlike things by a different name (προσαγορεύεις αὐτὰ ἀνόμοια ὄντα ἑτέρῳ…ὀνόματι): for you say that all the pleasures are good (λέγεις… ἀγαθὰ πάντ’ εἶναι τὰ ἡδέα). [2] Well, no argument contends that the pleasures are not pleasant. [3] But now with many of them being bad and some good, as we claim, nevertheless you call all of them good, while agreeing that they are unlike, if someone presses you on your argument. What, then, is the same thing present in the bad and alike in the good by which you call all the pleasures good? (τί οὖν δὴ ταὐτὸν ἐν ταῖς κακαῖς ὁμοίως καὶ ἐν ἀγαθαῖς ἐνὸν πάσας ἡδονὰς ἀγαθὸν εἶναι προσαγορεύεις;) (13a7-b5)

Socrates’ speech in T5 consists of three related moves (bracketed [1]-[3]). First, he points out a structural parallel in the hedonist’s position. The hedonist’s claim that “all pleasures are good” is analogous to the claim that “all pleasures are pleasant”. While the name, ‘pleasant’, applies to all the pleasures, the hedonist calls all pleasures ‘good’: hence, ‘good’ stands to each pleasure as ‘pleasant’ does. Second, he clarifies that he agrees that every pleasure is pleasant. Instead, he is disputing whether each pleasure is good. In the third and final move, Socrates clarifies why Protarchus faces a challenge, which I reconstruct as follows:

• (1) Protarchus calls all the pleasures good.

• (2) Protarchus admits that all the pleasures are unlike.

Therefore:

• (3) Protarchus must show that there exists one thing in all the pleasures, which justifies calling them all good (in addition to pleasure).

In other words, (2) puts pressure on (1) so that its defender has a substantive task of demonstrating its truth by satisfying (3). When Protarchus replies to T5 that no hedonist worth their salt would concede that some pleasures are bad (in other words, no hedonist would deny premise 1), Socrates retorts, “but you will say that they are unlike and some opposite” (13c3–4). Thus, again, the heterogeneity of pleasure is somehow a threat to its universal goodness. Protarchus doubles-down on his original denial that pleasures differ except in their sources by insisting that pleasures do not differ “insofar as they are pleasures” (καθ᾽ ὅσον γε ἡδοναί) (13c5),³² and Socrates responds with our T4, which again focuses on defending the specific account of unlikeness based on the models of color and shape. The challenge for an interpreter is to show why Protarchus’ reductive interpretation of (2) is problematic for his defense of (1) and why Socrates’ preferred understanding would put pressure on (1) such that Protarchus is burdened with (3).

My interpretation of the metaphysics of identity and difference in kind in terms of the structure of determinates and determinables meets this challenge well. I argued that, like determinates of a determinable, the differences among the pleasures are the same features that make them pleasures. This is Socrates’ preferred interpretation of (2), that “the pleasures are unlike”, which he gets Protarchus to concede after our T4. Protarchus also maintains, as an advocate of hedonism, that pleasure-making features are good-making features. This is what it means for him to commit to (1), that all the pleasures are good. Putting (1) and (2) together, it follows that the differences among the pleasures are also the sources of their goodness. Hence, maintaining both (1) and (2) requires that the differences that distinguish the pleasures are features in virtue of which they are all good. This commonality among the differences would be the “same good thing present alike” such that all are good—in parallel to the “same thing” making them all pleasure—thereby burdening Protarchus with (3). That is, on the account I defended above, Socrates thinks that what makes each pleasure a pleasure, or one—what the “same thing” present in all cases of pleasure is—is not an invariable property indistinguishable across its instances but a relational principle grounded in the unique natures of each pleasure. So to show that goodness stands to pleasure as pleasantness does—more precisely in Socrates’ formulation, to show that there is an ontological reality grounding our parallel use of ‘good’ and ‘pleasure’—the hedonist must find a similarity among the pleasures such that they are one as good in addition to being one as pleasure.

To be sure, there are two potential limitations of this strategy. First, in T5 Socrates interprets the hedonist position as a universal generalization about pleasure: all pleasures are good. Protarchus follows this up by stating his position as “pleasure is the good” (13b7). These views may not be the same. But each is, nonetheless, vulnerable to Socrates’ argument. If pleasure is the good, then whatever holds of pleasure holds of the good.³³ And the universal generalization is presumably an essential generalization, that is, a claim about the nature of pleasure as intrinsically good.³⁴ Hence, pleasure-making features must be innately good-making, so that the task of finding a common good-making element in all the pleasures inherits the metaphysical structure of the pleasure-makers.

A more significant challenge arises from the fact that, as we have seen, Philebus’ original position is that enjoyment, pleasure, delight, and their kin are “good for living things” (11b4–6). This appears to be a weaker formulation than either the universal generalization or the identification of pleasure with the good. The weaker formulation is compatible with pleasure and goodness having fundamentally different structures as long as pleasures are generally beneficial for living creatures (thus it may even be weaker than co-extensiveness: pleasures must only be generally good for animals). Some interpreters therefore suppose that there is an ambiguity in the treatment of hedonism at this stage of the dialogue.³⁵ This is compatible with my reconstruction of the dialectic. In fact, my reconstruction helps to explain why the one-and-many metaphysics is thought to be relevant to the ethical dispute once the strong version of hedonism is on the table, but drops out after this strong version is refuted (20c-22c).³⁶ But it is also worth noting that anything weaker than Socrates’ essential and universal generalization about the nature of pleasure is unlikely to be endorsed by Protarchus, or Philebus, at this stage of the debate. Even though Socrates describes his position as pleasure being generally beneficial, Philebus himself expresses his confidence that pleasure will always best any competitor (12a7–8). Moreover, Socrates and Protarchus agree that each disputant wants to identify his candidate with the state of soul capable of making a creature happy (11d1–10). These ideas suggest that the hedonist position, as all parties recognize it, is that pleasant activity is, because pleasant, good. As a result, it is reasonable for Socrates here to target the differences among what makes activities pleasant in order to give his interlocutor the substantive task of showing that these differences are compatible with their current thesis.

Second, while I am happy to call Socrates’ speech in T5 an ‘argument’—since I think it highlights logical relations between premises endorsed by his interlocutor in order to derive a conclusion—it is a mistake to think that the unlikeness of pleasures entails their normative division, as interpreters who attribute this to Socrates and allege fallacy suppose. That is to say, while Socrates indeed thinks that something follows from pleasures being unlike, he does not say that what follows is the existence of some bad pleasures. Rather, what follows is the epistemic possibility that some pleasures are bad. This is because the metaphysical structure of unlikeness, as we find it in the models of color and shape, entails that the nature of one kind in the domain does not fully account for the nature of the whole domain. Even if—as a hedonist will maintain, and as Socrates concedes—some pleasures are good, it does not follow from this that all pleasures are good, any more than it follows from yellow being bright that all colors are bright, or that all pleasures have a certain nature because temperate or foolish pleasures have that nature.

Hence, the hedonist could both accept Socrates’ metaphysical thesis and meet his challenge, in principle. To so do, they would need to articulate each kind of pleasure, in its uniqueness, demonstrate that each kind is good, and that these different kinds of good pleasure form a coherent unity. In the other direction, Socrates would need to show that the principles of organization among pleasures are such that there are bad pleasures. This requires investigation and cannot be settled at the start. Such an investigation is precisely the project to which Socrates is trying to orient Protarchus at this early stage of the dialogue, and which Protarchus resists by denying the metaphysical principle that serves as a point of entry for the inquiry. This is likely why Socrates introduces a method for determining the nature and number of pleasure’s kinds (18d9–19a2, 19b1–8): to identify the principles of organization among the pleasures and see if, when pleasures have been properly collected as a single, but appropriately heterogenous, kind, it is true that what makes something pleasant also makes it good.

VI

I have argued that in the opening moves of his debate with Protarchus, Socrates appeals to a specific notion of relational identity to characterize the metaphysics of pleasure, and that this relational identity is best explained in terms of the unity of distinct determinates within a determinable. By way of conclusion, it is worth asking what, if anything, we might learn about the nature of determinates and determinables from my account of this passage in Plato. To be sure, I do not think that Plato here discovers what we now call determinates and determinables, only that he develops a structural feature of kinds that we today identify with determinates and determinables. Still, this is itself an interesting result. It is evidence that one of the appeals of the metaphysical framework associated with determinables is that it captures a kind of complexity of identity and difference, which can easily be missed. The challenge is to be able to make sense of forms of difference that simultaneously ground a common identity, and likewise forms of identity that depend on underlying differences. In my view, Plato’s Socrates articulates this feature of determinates and determinables because he needs to make sense of such phenomena in order to advance his engagement with hedonism. Indeed, this ethical motivation is also worth dwelling on. It is a reminder that the project of articulating the structure of reality is not always only about building an accurate theory but sometimes also about helping us to make sense of the best way to live. This is not necessarily a motivation one finds on the surface, at least, of contemporary metaphysics, but it is certainly a perspective that Plato takes seriously.³⁷