2. The unlimited

Socrates divides “all that exists” (23c4) into four kinds: the unlimited (to aperion), the limit (to peras), the mixture (to meikton) of limit and unlimited, and the cause (aitia) of such mixtures. Let us start with the unlimited.

The essence or “mark of the nature of the unlimited” (24e4–5)Footnote ² is that it is “becoming more and less” (24e7). Wherever more and less apply, “they prevent everything from adopting a definite quantity” (24c3) or, as Socrates also put it, they “do away with all definite quantity” (24c6). By its very nature, then, the unlimited excludes definite quantity. Socrates helpfully explains this exclusion further: the unlimited is “always in flux and never remain[s], while definite quantity means standstill and the end of all progression” (24d4–5).

Consider Socrates’s most frequently used example of the unlimited: the “hotter and the colder” (24a7–8, b4, d3, 25c5–6). Footnote ³ In what sense is the hotter and colder “becoming more and less”? For the moment, focus on just the hotter. A hotter temperature is not simply one that is hot.Footnote ⁴ For “hotter” implies more heat whereas “hot” does not. This fact about the hotter is expressed by Socrates in his saying that the hotter is “always in flux and never remaining.” A hot temperature, by contrast, rests at the temperature at which it is; a hot temperature need not be increasing. Accordingly, the hotter, which is always “becoming more,” must not refer to any particular definite temperature, for any particular definite temperature is not becoming more nor is it always increasing and not resting. The temperature 102° is hot (for a human body). But we are looking not merely for the “hot,” so to speak, but rather for the “hotter.” And 102.1° is hotter than 102°. In searching for the hotter, however, we cannot rest content with 102.1° either. For 102.11° is hotter than 102.1°. But then 102.111° is hotter than 102.11°, and so on. Thus, when we think of “hotter” in itself (that is, not in comparison to some other temperature), there is no definite temperature of which we could be thinking. This is the sense in which the hotter (as an example of the unlimited) “excludes” definite quantity. Mutatis mutandis, the same example could be given for the colder.Footnote ⁵ The hotter and colder together, then, trace out a continuous range of temperatures extending in both the direction of more heat and in the direction of less heat. The hotter and colder is a range or continuum of temperatures and not any particular temperature on that range. More generally, the unlimited consists of continua that stretch between two opposed qualities (e.g., hotter and colder, higher and lower, greater and smaller, etc.) in this same way.Footnote ⁶

3. Measure and limit

Measure is first introduced in the Philebus as something that stands in opposition to the unlimited. “Definite quantity and due measure” (24c7) drive out the more and the less, they bring the unlimited to “standstill” (24d5), and they stop it from “always advancing and not remaining” (24d4–5). Given the nature of the unlimited as previously explained, it is fairly clear what Socrates is claiming here. Consider again the hotter and colder. The introduction of a definite quantity into this continuum results in a particular temperature. This particular temperature is not “always advancing” and “never remaining” in the sense previously described, but rather remains and stands still. The temperature 102° is 102°. It is not becoming 102.1° nor is it necessarily fluctuating and unstable. More generally, when definite quantity and due measure are introduced into the unlimited, something (viz, a mixture) is produced. And that produced thing has a particular amount or degree of the quality of which the relevant unlimited is a continuum.Footnote ⁷

Things which bring the unlimited to a standstill, Socrates goes on to claim, are examples of limit, the second of Socrates’s four kinds. Thus, measures are limits.Footnote ⁸ Members of limit do not admit the “more and less.” Rather, they admit opposite qualities such as “the equal and equality,” “the double,” and “everything which is a number relative to number or a measure relative to measure” (25a7–b1). As he goes on to explain, the equal, the double, and limit generally “put an end to the conflicts there are among opposites, making them commensurate and harmonious by imposing a definite number on them” (25d11–e2).

In his explanation of limit, Socrates seems to be particularly influenced by Pythagorean musical theory. Consider the unlimited that is relevant to pitched sound: “the high and the low (oxei kai barei)” (26a2). What are the “equal,” “double,” and so forth as they relate to pitched sound? The most obvious answer is the various intervals. Not only are the intervals highlighted as essential to musical science earlier in the Philebus (see 17c11–d2), but the intervals perfectly fit Socrates’s description of limit. Consider first the “equal.” Two equal quantities or measures stand, in virtue of their equality, in a 1 to 1 ratio with each other. Pythagoreans (and their musical theorist descendants even today) have described a particular interval, namely unison, in terms of just such a ratio. The “double,” or 2:1, is another interval—the octave. The perfect fifth (3:2) and perfect fourth (4:5) and indeed all other intervals are likewise clear examples of things “which are a number relative to number or a measure relative to measure.”

4. Mixture

To understand mixture, let us consider an example, namely that of a violinist playing a particular note, say, middle C.Footnote ⁹ The relevant unlimited in the case of the violinist’s middle C is, again, the high and low. In playing the violin, the violinist brings a determinate pitch, middle C, to bear upon the high and low. And the audible middle C produced by the violinist is not becoming higher or lower, but rather is staying what it is, namely, middle C. This is true even if the violinist quickly changes notes. For in those moments when the violinist was playing middle C, the audible middle C was a stable middle C.

As is perhaps obvious, the limit in this example is middle C. For middle C is a stable determination of pitched sound. Now to be clear, in its role as limit, middle C is not itself audible. It is an abstract measure that stands in mathematically describable relationships to other such measures. The audible middle C is produced when the violinist brings this inaudible middle C to bear on the unlimited (the high and low). The audible middle C is the result of “mixing together” the limit middle C with the high and low. It is, in other words, an example of the third kind, mixture.

Now consider what makes this mixture what it is—what makes it a middle C. While this mixture has the high and low as a constituent, the high and low cannot be what does this. For the high and low is equally present in all pitched sounds and obviously not all pitched sounds are middle Cs. The high and low is responsible merely for the mixture’s being audible—for it being a pitched sound. Rather, the limit middle C, which is also a constituent of the mixture, must be what makes the mixture the particular kind of thing that it is. That is to say, in virtue of being the mixture’s limit, (inaudible) middle C makes the mixture a(n) (audible) middle C. Measure is responsible for what a thing (a mixture) is. Were a mixture to have a different measure, it would be a different kind of thing.

Now in Socrates’s view, reflection on the role of measure in the crafts (such as music) is a guide to the role of measure generally. After claiming that it is “necessary that everything that comes to be comes to be through some cause” (26e3–4), he goes on to claim that “there is no difference between the nature of what makes and the cause, except in name, so that the maker and the cause would rightly be called one” (26e6–8). Produced things, such as the objects made by the crafts, and generated things, such as you, me, plants, and animals, are equally mixtures and are equally produced by a cause. That is to say, they have the same ontological structure (viz, mixtures of limit and unlimited) and they are produced in structurally similar ways (viz, by bringing limit to bear on the unlimited).

In claiming this, Socrates seems to be assuming that everything that is generated is composed of limit and unlimited—that is to say, that every generated thing is a mixture. Indeed, there is good reason to think that he in fact thinks this. The fourth kind, cause, is introduced as that which combines limit and unlimited to make mixtures (23d7–8). But then when discussing cause at greater length from 26e to 27c, Socrates refers to it as the cause of “everything which comes to be (panta ta gignomena)” (26e3) and as the craftsman of “all these things (panta tauta)” (27b1) where “these things” refers to “things which have come into being (ta … gignomena)” (27a11). The rather clear implication is that everything that comes to be is a mixture. As such, everything in the generated world here around us would have a limit that makes it the kind of thing it is. So not only objects of the crafts, but roses, frogs, humans, and rocks are all mixtures as well.Footnote ¹⁰

These mixtures are clearly more complex than a single audible note. And while Socrates never gives an extended explanation of how exactly these more complex mixtures are composed of limit and the unlimited, he indicates how such an explanation would likely proceed at 26a2–4. In this passage, Socrates claims that music (and not just a single note) is created out of several unlimiteds; in particular, he mentions “the high and the low” and “the fast and the slow.” To create music, the relevant limit must be mixed with each unlimited. So not only must the intervals (perfect fifth, octave, etc.) be mixed with the high and the low to create the particular tonal quality of the music, but also a certain measure or limit must be mixed with the fast and the slow to produce the tempo of the music. Though Socrates mentions only these two unlimiteds, presumably there are—and nothing in what Socrates says precludes there being—other unlimiteds relevant to music as well. To identify further unlimiteds in a complex mixture such as music, one simply needs to identify some further quality that admits of more and less and that the mixture in question necessarily has to some degree or other. For example, a fuller analysis of music may include the unlimited related to volume (perhaps it could be called “the louder and the softer”) and whatever unlimiteds may be related to timbre (perhaps, “the brighter and the duller,” or “the harsher and the softer,” among others).

The more complex mixtures mentioned above can be analyzed similarly. Consider first a product of a craft, a table. Presumably, it would have unlimiteds and measures for the qualities relevant to its material constitution (e.g., hardness, tensile strength, weight, etc.) and also for each of its three dimensions. These spatial measures would determine not only, say, the height of this one leg, but also the structure or shape of the table itself. For example: In order for this one leg to be of the appropriate measure in its height, it must be proportionate to the other legs of the table. And in order for the tabletop to be appropriately wide (or narrow), its width must stand in a particular proportion to the height of the legs, and so on. Further, to be a table, an object must also be suitably hard, suitably resistant to tensile forces, and so on. In this way, having certain measures of, say, the “taller and the shorter,” the “wider and the narrower,” the “harder and softer,” and all the other relevant unlimiteds is what makes a mixture a table. The same could be said, mutatis mutandis, for statues, shoes, jars, and so on. Measures make a product of a craft what it is, even when there are several unlimiteds relevant to the product in question.

A similar analysis could be given of organisms. From 31d to 32b, Socrates suggests some of the details of how such an analysis would proceed. He claims that organisms are a “natural combination of limit and unlimitedness” (32a9–b1b), and that the dissolution of this combination is pain, while the restoration of it is pleasure (32b2–4). Socrates’s specific examples of pains and pleasures indicate what some of the unlimiteds relevant to the ontological constitution of organisms are. “The process that fills what is dried out with liquid is pleasure” (31e10–2a1). The relevant unlimited in this case is “the dryer and the wetter” and thus Socrates is indicating that organisms are constituted, in part, by the limit that imparts in them a specific measure of wetness (or dryness). Another of Socrates’s examples concerns a kind of pain that results from an “unnatural separation and dissolution” caused by “heat” (32a2–3). “The natural restoration of cooling down,” he continues, “is pleasure” (32a3–4).Footnote ¹¹ The relevant unlimited in this case is the hotter and the colder, and thus organisms are constituted, in part, by the limit that imparts in them a specific measure of temperature.

Of course, many other measures and unlimiteds would be relevant to the constitution of organisms. Presumably many of the unlimiteds mentioned earlier in the discussion of the table would also be germane to the constitution of organisms, for example, those unlimiteds relevant to the spatial dimensions of a mixture (the longer and the shorter, the wider and the narrower). Socrates, however, does not give a complete analysis of the ontology of organisms or of products of the crafts for that matter. He leaves enough clues, however, to see how a development of these analyses would proceed.Footnote ¹²

Let us now turn to the other passage on measure in the Philebus and discuss in detail the relationship between goodness and measure.

5. Measure and the form of the good

In the closing pages of the dialogue, measure takes center stage. It is crucial both to the discussion of goodness in general, and to the ranking of the various goods that humans might possess. Consider what Socrates says about “the good”:

The mixture mentioned in this passage is that of pleasure and knowledge in a human life (see 61c4–8), and this mixed life was earlier identified as the good, happy life (see 21e3–2b8 and 61b4–6). In this passage, Socrates claims that the goodness of the mixed life is caused by the goodness of beauty, proportion and truth—that these three are somehow responsible for the goodness of the mixed life. Indeed, this trio is what makes any good thing good.

Of particular interest presently is the reference to “proportion (summetria).” In two subsequent references to this member of the trio, Socrates refers not to “proportion (summetria),” but rather, to “due measure” (“metriotêtas” at 65b8, “metriotêta” at 65d4). This slight shift in terminology becomes particularly important when Socrates turns to the final ranking of goods (66a4–d2), for there, due measure and proportion receive different ranks. First place goes to “measure and due measure and the right time and all such things” (66a6–7), while proportion comes in second place, along with beauty.Footnote ¹³ As other commentators have argued, measure ranks above all other good things—even the trio of beauty, proportion, and truth—because it is the ultimate cause of goodness.Footnote ¹⁴ While being beautiful or well-proportioned may indeed cause a beautiful, well-proportioned mixture to be good (just as 65a1–5 claims), being measured is what causes such a mixture to be well-proportioned and beautiful, and thus is ultimately responsible for its goodness.Footnote ¹⁵

As has been noted by others, Socrates’s view of causation in the Philebus is similar to his view in the Phaedo.Footnote ¹⁶ In the Phaedo, Socrates claims that the cause of some quality (for example, beauty) in something else (for example, a painting), must itself have that quality in a higher or superior way and, indeed, must somehow be that quality (see 99d–100e). Thus, the Form of Beauty would be the ultimate cause of the beauty in a painting, and the Form would be more beautiful than any painting; indeed, the Form of Beauty is the most beautiful thing there is. Likewise, in the Philebus, inasmuch as measure is the ultimate cause of goodness in other things, it must also be the best thing there is, for it is ultimately responsible for the goodness of every other good thing. Moreover, the causal power of measure is similar to that of the Forms insofar as both are independently subsisting causes of certain immanent structural features.Footnote ¹⁷

While brief, this account of the relationship between measure and goodness explains why it is that being of an appropriate measure renders something good: It is because measure is itself good. It is the goodness of measure that makes the things that have achieved measure good. Presumably, the converse holds true as well: insofar as a mixture exceeds or falls short of due measure, it is bad, and indeed, it is this very exceeding or falling short that is its badness. And this is true not just for the products of the crafts, but for anything that might achieve measure, such as natural phenomena, human lives, and, more generally, all mixtures (see 64d3–e3).

Measure thus plays two roles in the Philebus. At 23c–7c, measure plays the role of an ontological constituent, one that makes generated things (mixtures) what they are. Here at 65a–6a, measure is said to be responsible for the goodness of mixtures in that to conform to measure is to be good. And so, both the goodness and the being of a mixture are determined by measure. This holds true, as I shall argue, in the case of bad or imperfect mixtures as well. But first, let us examine the relationship between these two roles in more detail.

6. The two roles of measure

Why does Socrates think that these two significantly different roles are filled by one and the same thing, measure? The example of musical notes is illuminating once again, in that it makes this convergence of roles plausible and intuitive. To see this, consider the system of musical tones.

All musical tones fall along the continuum of pitched sound. To be a musical tone, however, requires more than simply this. It requires that the tone be a member of an interval. And because musical scales are constructed out of intervals, to be a musical tone requires that the tone find a place in various musical scales. In short, tones are musical tones because they find a place in various musical scales.Footnote ¹⁸ Thus every musical tone will be harmonious not only with those tones that are some particular interval away from it, but also with whatever scales it is a member of. Measure produces proportion and harmony in pitched sound (see 25d11–e2) by producing tones that are proportional to, and harmonious with, one another and with the scale of which they are a part.

Any particular tone that I sing will fall along the continuum of high and low pitch inasmuch as the tone is a pitched sound. If one were to ask what some sung tone is, the answer would refer to the system of musical notes (i.e., the various scales) just described. That is to say, any tone that I sing will receive its identity from where the exact location it occupies falls on the continuum of pitched sound. This includes imperfect tones. If I am flat, then the C I sing will be too low. It is nonetheless still a C (albeit a bad one) since it falls close to C on the continuum of pitched sound. Here, then, we see the ontological role of measure. Particular tones are the tones they are because of their approximation to a note (i.e., to the relevant measure).

The notes, however, have an additional function. They supply us with standards for evaluating particular tones. This is already apparent in the above example. My flat C is flat because it is lower than it ought to be—it is lower than C. The notes of a scale give us targets at which to aim, and any tone that is significantly higher or lower than the intended target is a defective tone (such as a flat C or a sharp F). Because these notes thus play the role of an evaluative standard, and because a note is a measure, measure also plays an evaluative or normative role.

More generally, something which perfectly observes the relevant measure is perfectly what it is (a perfectly sung C is a perfect C), while something which either significantly falls short of or significantly exceeds its measure, such as my flat C, nonetheless still receives its identity from what it imperfectly approximates. In short, possession of measure, be it perfect or only approximate, makes the mixture what it is (e.g., it makes my sung tone a C), and that very same measure is the relevant standard for determining whether or not the mixture is good (e.g., determining whether my sung tone is on pitch [i.e., good] or out of tune [i.e., bad]). In the case of musical notes, the unity of these two roles is quite intuitive and plausible.

According to Socrates, of course, it is not just in the case of music that measure plays these two roles. In addition to music, Socrates also draws our attention to (1) health (25e7–8), (2) the seasons (26a6–b3), and (3) lawful and orderly behavior (26b5–c2). And although music offers the clearest and most plausible example of the convergence of these roles, we should nonetheless examine how these roles may have been supposed to converge in these other cases. Unfortunately, Socrates is of little help in this regard as he goes into very little detail about these other cases. Nonetheless, we can piece together brief, and admittedly speculative, accounts of how these other cases might work.

(1) As was discussed above, organisms are mixtures of a variety of unlimiteds and limits. And among these unlimiteds are the dryer and the wetter, the hotter and the colder, and unlimiteds related to spatial dimension (e.g., the longer and the shorter). When a body falls away from one of the measures imparted on these unlimiteds, perhaps through an “unnatural coagulation of the fluids” (32a6–7) (thus becoming too dry), or through an “unnatural separation and dissolution” caused by heat (32a2–3) (thus becoming too hot), the body becomes diseased and pained; it comes to be in a bad condition. By contrast the restoration of the appropriate measures produces the good condition of the body, health (25e7–8; see also Timaeus 87c1–6). A good (i.e., healthy) body closely approximates these measures; a bad (i.e., diseased) body, fails to do so. Thus, measure plays a normative role with regard to the bodies of organisms. These very same measures, however, also play an ontological role. Recall that Socrates introduces these examples of pain and pleasure in the context of discussing the ontological constitution of organisms. Organisms are mixtures of limit and unlimited, and the pains described above occur when an organism falls away from the measures or limits that are part of its constitution. Further, he claims that a return to the relevant measure is a “return to its own being (eis tēn autōn ousian)” (32b3). So while Socrates never names what the relevant measures are, it is clear that these measures are responsible for the organism being what it is.Footnote ¹⁹ Thus, the very same measures that serve as normative standards also play an ontological role in the case of organisms.

(2) Consider now the seasons (26a6–b3). Socrates begins with a claim about climatic conditions. “Limit” takes away “the great excesses and unlimitedness” of “wintry chill and stifling heat,” and thereby produces “moderation and proportion (to … emmetron kai hama summetron)” (26a6–8). Through this mixing of limit and unlimited, Socrates continues, “the seasons and all sorts of fine things of that kind” (26b1) are produced. A season, then, is a mixture, and while the relevant limit goes unnamed, the relevant unlimited is related to wintry chill and stifling heat. Presumably there are several such unlimiteds, two of them surely being the hotter and colder and the dryer and wetter as they relate to atmospheric conditions.

What makes a season what it is? Consider winter. It is a period of, among other things, dry coldness.Footnote ²⁰ That is, it is a period characterized by particular measures of atmospheric temperature (the hotter and colder) and humidity (the dryer and wetter). Approximation to these measures is, in part, what makes winter what it is.Footnote ²¹ This is the ontological role of measure: approximation to measure makes the seasons what they are.

Weather, of course, can be unseasonal. A heat spell in early January is not normal. It is a period of excessive warmth, a period in which the heat is inapt or inappropriate by being higher than the appropriate measure. And while winter is the coldest of the seasons, a winter of temperatures consistently well below freezing would also be excessive and not fitting for the season. In both cases, one could sensibly describe the winter as exceeding due measure with regard to temperature: “winter was excessively warm (or cold) this year.” And although we are perhaps likely to judge the seasons relative to our comfort (and so perhaps likely to judge an excessively warm winter a “good one”), nonetheless we can readily make sense of the claim that an excessively warm winter is an imperfect or defective winter. It is a winter that is bad qua winter. Thus, measure also plays a normative role with regard to the seasons.

(3) Lastly consider Socrates’s remarks about lawful and orderly behavior (26b5–c2). The Goddess, recognizing that our “insolence and wickedness” allows for “limit (peras)” in neither our “pleasures nor their fulfillment,” imposes “law and order” as a “limit (peras)” on them. The relevant unlimited in this case is pleasure,Footnote ²² and law and order are the measures or standards for behavior that is concerned with pleasure. Thus, law and order would prescribe pursuing pleasures to certain particular degrees. To experience pleasures beyond those degrees would be unlawful and disorderly.Footnote ²³

When we closely adhere to these standards, our behavior is lawful and orderly; when we deviate significantly from them, it is unlawful and disordered. Now in the same way that a tone can be a middle C only by reference to Pythagorean musical theory, so too can behavior be (un)lawful and (dis)orderly only by reference to the Goddess’s limits. That is to say, just as a tone can be (un)musical only by reference to certain musical norms, so too can behavior be (un)lawful or (dis)orderly only by reference to certain ethical norms. These measures, both the various musical notes and law and order, make the things which approximate them (whether closely or not) the very things that they are. The various musical notes make the tone a(n) (un)musical tone; law and order make the behavior (un)ethical behavior. In this way, law and order play an ontological role with regard to such behavior—they make such behavior ethically significant in the same way that Pythagorean musical theory makes tones musically significant.

Law and order clearly also play a normative role. Close approximation to law and order in our behavior renders it good, while significantly deviating from them makes our behavior bad. The proper standard for evaluating our ethically relevant behavior is law and order, the very thing that makes our ethically relevant behavior what it is.

In short, that which makes something to be a certain kind of thing is also the relevant standard for evaluating instances of that kind of thing. Normative evaluation is grounded in the ontological structure of the thing being evaluated.

7. Interpretive debates: measure and defective mixtures

The interpretation of the Philebus developed above is at odds with how several commentators have read Socrates’s ontological and ethical remarks. In particular, my account of the relationship between limit, mixtures, and goodness is controversial in at least two different ways. First, several commentators have interpreted the Philebus to be claiming that there are no bad mixtures; that every mixture is good. Second, of commentators who agree with my interpretation that there are indeed bad mixtures, several have thought that bad mixtures have different limits than the relevantly similar good mixtures. Let us consider these rival views in more detail.

First consider what has become one of the more common interpretative routes, of which Dorothea Frede is the leading contributor.Footnote ²⁴ According to this line of interpretation, there are no bad mixtures, and everything which one might be tempted to call a bad mixture is actually a member of the unlimited. Such an interpretation requires a conception of the unlimited that is significantly different from the one presented above, and Frede gives us one which is both clear and succinct: “Anything that can retain its identity through a change in quantity belongs to the apeiron [i.e., the unlimited]” (Reference Frede1993, xxxv). My flat C could become higher or lower but nonetheless remain exactly what it is—a flat C. My flat C, then, is not a (bad) mixture, according to Frede, but rather a member of the unlimited. Frede cites two reasons for this interpretation (xxxiv–vi). The first is that all of the examples of mixtures in the Philebus are of good things such as health, fair weather, and music (see 25e3–6b7). On her view, a flat C or a fever, not being good, must not be mixtures and so must belong to the unlimited. The second is that Socrates says that something which lacks measure is not really a mixture at all (64d9–e3). Flat Cs, fevers and bad things generally all lack measure, and so, on Frede’s interpretation, must not be mixtures.

In reply to the first reason, Sayre has argued that close attention to what Socrates says at 25e3–6b7, far from undermining his (and my) interpretation, supports it (Reference Sayre2005, 141; 1987, 57). For what Socrates says is that the “right combination (orthê koinônia)” of limit and unlimited produces health, fair weather, and music.Footnote ²⁵ It would be not only redundant, but highly misleading of Socrates to mention a “right combination” if all combinations were right. And so we should infer that some combinations are wrong or defective.Footnote ²⁶ Further evidence for this view comes from the fact that Socrates on numerous occasions describes all generated things (which, of course, would include bad generated things such as flat Cs) as mixtures (see 27a1–3, a11–12, 30d10–e2). And so, while it is true that all of the specific examples of mixtures that Socrates offers are good, it is false that Socrates refers only to good mixtures. Accordingly, Socrates’s focus on good combinations does not prove that, nor should it even be taken as a sign that, there are only good mixtures.

Turn now to the second reason. It is drawn from the following fact about mixtures of which Socrates avers everyone is aware—namely:

Verity Harte concedes that Frede’s first reason is inconclusive (and that it is so for the reasons that Sayre had suggested). Nonetheless, she defends Frede’s interpretation for she believes Frede’s second reason establishes that interpretation (see Harte Reference Harte2002, 210–11). Harte offers a more detailed analysis of this passage than Frede does, so let us turn to what Harte says. According to Harte, that a flat C (or any bad generated thing for that matter) belongs to the unlimited follows from the fact that a flat C lacks measure (211). Notice, however, that Socrates never explicitly says that something like a flat C (i.e., a bad generated thing) lacks measure. Harte supports this claim by drawing our attention to the fact that immediately after the above passage, Socrates tells us that “measure and proportion manifest themselves in all areas as beauty and virtue” (64e6–7). According to Harte’s interpretation, Socrates is claiming that if something has measure, then it is beautiful and excellent. Since a flat C is obviously neither beautiful nor excellent, it must not have measure and so, in light of 64d9–e3, it must not be a mixture. Not being a mixture (nor a cause, nor a limit), it must belong to the unlimited. And so, it is 64d9–e3—not the lack of examples of bad mixtures—that establishes that there are no bad mixtures, according to Harte.

Such a reading, however, mischaracterizes what Socrates says about the relationship between mixtures and measures at 64d9–e3. Harte interprets Socrates as putting forward a binary, all or nothing, view of the possession of measure: something either possesses measure, in which case it is good and is a mixture, or it does not, in which case it is bad and belongs to the unlimited (Reference Harte2002, 212).Footnote ²⁷ But Socrates does not put forward such a view. Quite the contrary. He says that any mixture that does not in some way or other (hopôsoûn) possess measure is not really a mixture. The clear implication is that there are many ways in which a thing might possess measure, presumably some better or more fully than others. Socrates’s point, then, is that if something in no way at all possesses measure (that is, if something fails to possess measure even defectively), then it is not really a mixture.Footnote ²⁸ We can agree with Harte that a flat C does not possess measure perfectly, but what reason is there for denying that it possesses measure imperfectly or incompletely? What this passage strongly suggests, then, is that flat Cs (and other imperfect things) possess measure in a way, namely, an imperfect way. Accordingly, they are mixtures (since they in some way possess measure and limit) and not members of the unlimited.

Furthermore, despite Frede and Harte’s focus on Socrates’s examples of mixture, their binary view of the possession of measure does not easily accommodate all of Socrates’s examples. Frede expresses this binary view clearly, saying that mixtures “are either ‘just right’” or not mixtures at all (Reference Frede1993, xxxv). But several of Socrates’s examples of mixture could not plausibly be claimed to be “just right” or not a mixture at all. Consider Socrates’s claim that the seasons are mixtures (26b1–3). Frede’s view implies that either the temperature, pressure, humidity, etc. are “just right” for winter or the season is not winter at all (and likewise for the other seasons). But surely a winter could be warmer or drier than is typical and still nonetheless be winter (that is, be a mixture). Or consider Socrates’s claim that organisms are mixtures (31a9–2b1). Again, Frede’s view implies that the moisture and heat of an organism are attuned “just right,” or the thing in question is not an organism at all. And given Socrates’s idea that disease results from a falling away from the measures that in part form an organism (see section 6), Frede’s view is committed to saying that a sick organism is not an organism. It is hard to imagine that this is the view Plato meant to put forward in the Philebus. Footnote ²⁹

Several commentators on the Philebus have agreed that, contrary to Frede and Harte, there are such things as bad mixtures. One group of such commentators, however, has offered an analysis of bad mixtures markedly different from the one presented here. The first of these commentators was Henry Jackson.Footnote ³⁰ Jackson sought to establish the difference between good and bad mixtures on a distinction between “definite quantity (to poson)” and “due measure (to metrion).” Recall that, at 24c4–d2, both definite quantity and due measure are cited as things which drive out the more and less. The fact that Socrates cites both of these is the key for understanding bad mixtures, on Jackson’s interpretation. For, according to Jackson, due measure is a particular kind of definite quantity, namely, the right one. This implies that all of the other definite quantities are incorrect. When one of these incorrect definite quantities is imposed upon the unlimited, the result is a bad mixture. Good mixtures are produced when and only when the right definite quantity, due measure, is imposed upon the unlimited.

According to this line of interpretation, there will be a particular limit for C, a particular limit for a slightly flat C, a particular limit for a significantly flat C, and so on. Indeed, seeing as the continuum of pitched sound is continuous, there will be an infinite number of limits (one for every possible tone). The problem with Jackson’s interpretation is that it is simply false that there is such a plethora of limits. Recall the nature of limit. Limit comprises the equal, the double, and everything that is a number relative to a number. Defective tones, however, fail to exhibit these properties. There is no ratio (such as equal, double, etc.) that corresponds specifically with my flat C. The ratios all correspond with the notes of the scale. The only number (or “definite quantity”) that is relevant in the case of my flat C, then, is that which corresponds with C. The relevant limit for my flat C is just C. Being a bad singer, I have imperfectly mixed the limit of C with the unlimited of pitched sound, resulting in the mixture that is my flat C. I have not mixed a definite quantity, one in between C and B, with sound, for there are no “definite quantities” or limits in between C and B. In short, in the Philebus there is no distinction between definite quantity and due measure, and so Jackson’s interpretation is incorrect. The pairing of to poson and to metrion at 24c7 is best thought of as a case of apposition.

This raises the question: if flat C and C have the same limit, what marks the difference between them? Well, clearly not their limit. Nor would it be the relevant unlimited, the high and low. The difference lies in their combination. An inexpert singer is bad at combining the relevant limits with the high and the low. I try to produce a C, but because of my inability, it comes out flat; it is lower than due measure. Jackson’s interpretation seems to imply that the problem with inexpert singers is that they reach for the wrong limits. A more plausible story would be that they reach for the right limits (e.g., I am trying to sing a C), but they lack the ability to realize fully those limits in the mixtures they produce (e.g., the C I sing comes out flat because I lack the ability to observe measure in my singing). An advantage of my interpretation is that it harmonizes well with the Plato of the Phaedo, Republic, Phaedrus, and Timaeus—the Plato who thought that sensibles were imperfect instantiations of Forms. For, on the view argued for in this paper, a flat C is an imperfect instantiation of C. Jackson, by contrast, would have to hold that flat Cs are, to put it in the words of G. M. A. Grube, “perfect copies of imperfect formulae” (Reference Grube1935, 302), which, as Grube notes, seems decidedly un-Platonic.

8. The account of normativity in the Philebus

Which standards are relevant to some particular thing, then, is determined by what the thing in question is. And simply in virtue of being a particular kind of thing, the thing in question will be subject to certain norms, namely, those measures that make the thing what it is. And thus, we see the Philebus’ answer to the question of why norms bind the things that they bind: An x is bound by some norm (i.e., measure) y, because y is what makes x an x in virtue of being an ontological constituent of x. In short, to be an x is to be bound by the relevant norm, y.

This is a very different account of normativity than is often attributed to Plato. For what exactly x’s achievement of measure consists in, and so what exactly it is for x to be good, is dependent upon what x is. As we shall see, this claim puts the Philebus at odds with many commentators’ interpretations of the Republic. For now, however, let us develop this account of normativity in more detail by drawing out some of its implications.

There is no one measure which all things must achieve in order to be good; indeed, it is hard to even make sense of how that could be so. For measures are always measures of something: length, height, pitch, temperature, and so on. And a measure in height, for example, could not possibly be the measure in temperature, if for no other reason than that the former is a measure of feet (or inches, or miles, etc.), and the latter, of degrees. Furthermore, even when two objects are being measured with regard to the same dimension, say height, what the achievement of measure will consist of will not necessarily be the same. A flagpole that achieves measure will be of a very different height than a radio tower that does the same.

The upshot is that measure, when used as an adjective or predicate, is what Peter Geach has helpfully labeled an “attributive adjective.”Footnote ³¹ An attributive adjective is one such as big in the following sense: There is no such thing as just “being big (period),” but rather a thing is a big house, or a big planet, or a big molecule, and so on. Whether or not x is big depends on what kind of thing x is. In this way, attributive adjectives are different from what Geach calls “predicative adjectives.” An example of the latter is red. When we say, for example, that a car is red, we do not mean it is red for a car, but, rather that it is simply red (period). Whether or not the car is red does not depend at all on the fact that it is a car. To put the point generally, a predicative adjective, F, is such that one can ascertain that an x is F independently of ascertaining that the x is an x; an attributive adjective is such that one cannot do this.

Given this criterion, achieving measure is clearly attributive. For one cannot ascertain that an x has achieved measure without ascertaining that the x is an x. One cannot do this because whatever information one gathers for determining whether or not the x has achieved measure must simultaneously indicate what the x itself is. Take the example of my singing a tone of 261 Hz (the frequency of middle C). In order to ascertain whether my note is on pitch (i.e., whether it achieves measure), one must know what my note is. If my note is a middle C, then it is on pitch; if it is a C# instead, then it is decidedly flat. The fact that my tone is 261 Hz is not, in itself, information that would determine whether or not my note achieves measure. In order to constitute such information for me, I would have to know what my note is. More generally, to know whether or not x has achieved measure, one must know what x is. Thus, measure is attributive.

Recall that Socrates claims in the Philebus that measure is an aspect of goodness, or, as he also indicates, that measure is goodness. Measure is responsible for the goodness of mixtures in that achieving measure amounts to being good. Now as we have just seen, an x cannot simply achieve measure (period). Rather, x achieves the measure for xs; the specific measure that, in addition to serving as the relevant norm for xs, makes an x an x. Given that achievement of measure functions this way, and further, that measure is identified with goodness, the Philebus seems to suggest that good is an attributive adjective. There is no such thing as just “being good (period),” but, rather, a thing, if good, is a good x: a good pair of shoes, a good sung note, a good human being, and so on. The goodness of a thing cannot be determined apart from knowing what kind of thing it is. Because it makes no sense to talk about a thing achieving measure (period)—as opposed to, say, the measure of height for a flagpole—it accordingly makes no sense to talk about a thing being good (period).

This is not how Plato’s thoughts about good are typically understood. Plato is often interpreted such that he held (or would have held had he the terminology) that good is a predicative adjective.Footnote ³² Indeed, such a view of Plato seems to harmonize well with the standard view of his metaphysics. For, according to that view, a sensible particular has the qualities it has in virtue of participating in the Forms of those qualities: e.g., a thing is red in virtue of participating in the Form of Red. Likewise according to this view, a thing is good in virtue of participating in the Form of the Good. It seems, however, that whether or not x participates in the Form of the Good is independent of whether or not x participates in the Form of Dog, or in the Form of Human, or in the Form of Shoe. In other words, whether or not x is good seems to be independent of what (kind of thing) x is. One can ascertain that x is good simply by ascertaining whether or not it stands in a certain relationship to (i.e., “participates in”) the Form of the Good. One need not ascertain in what else it participates.

Interpretations of Plato according to which he treats good as a predicative adjective focus almost exclusively on the middle dialogues, particularly the Republic. Here is not the place to engage in a detailed examination of the Republic and its account of goodness, but if the argument about measure and goodness in the Philebus above is sound, then the Philebus offers us a very different account of good than is typically attributed to Plato. One advantage of the Philebus’ account of goodness over the account allegedly found in the middle dialogues is that the former gives us a plausible and comprehensible account of what it is for a thing to be good; the latter, by contrast, only gives us the rather uninformative claim that for a thing to be good it must “participate” in the Form of the Good. And quite famously (see Aristotle’s complaint at Metaphysics I.6 987b13–14), Plato never gives a direct account of what exactly participation is. By contrast, the Philebus gives us a much more detailed account of what it is for a thing to be good. For a thing to be good is for that thing to conform to, or closely approximate, those measures that make the thing what it is. So though the Philebus eschews the terminology of participation, it nonetheless gives us an account of the relationship between goodness and particular, sensible things.Footnote ³³