by Corry Shores
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[The following is summary. Proofreading is incomplete, so please excuse my typos. Bracketed commentary is my own.]
Summary of
Plato
Philebus
11a-25b
Brief summary:
Socrates and Protarchus (who is substituting for Philebus in this discussion) are debating whether the good life is a life of pleasure, of knowledge, or of neither of the two. Socrates establishes that the good is sufficient, meaning that whatever is good should be enough on its own. And thus were the life of pleasure or of knowledge the good, then they should be sufficient for a good life. However, a life of pleasure is lacking, because without knowledge and things related to it, like memory, right judgment, and calculation, we would not be able to remember our pleasures, be aware of current ones, or anticipate future ones. We would just be like a dumb animal. So in a sense the idea of living a life of pure pleasure is self-defeating. But similarly, a life of knowledge without pleasure is also not enough for a good life. Thus the combination of a life of pleasure and a life of knowledge is better than either of the two by themselves. Part of Socrates’ presentation in these pages is to show that in order to pass judgment on something, you need expertise in it. But to attain expertise, you need to grasp some field of knowledge both in its unity and in its variety (or, in its “unlimitedness”). For example, to know a unified field like music, you need to know all the different sorts of tones, their combinations, rhythms, and so on. Only when you know each variable component in all its variety can you pass judgment on the whole as a totality. As Socrates continues the argument, toward the end of these selected pages, he returns to this notion of limited and unlimited. He says that hotter and colder, as with all things that are matters of more or less, are always in a state of flux. It is not simply that something is hotter or colder than something else. Rather, for something to be hotter or colder, it must be hotter or colder than itself, in the sense of it becoming hotter or colder than what it was. As soon as it takes on a determinate quantitative value rather than being one currently under variance, then it is no longer hotter or colder. And were it to reach some ultimate limit, like becoming the hottest or the coldest, it will no longer be in its process of changing. And thus it again is no longer hotter or colder, since it then becomes no hotter or colder than it just was, now that its changing has stabilized. Thus hotter and colder, along with all other cases that are matters of more or less, are unlimited by their very nature; for, they are always in a state of flux with no singular, determinate values that hold for longer than a fleeting instant.
Summary
Protarchus will take-on Philebus’ argument that what is good is to enjoy life’s pleasures. Socrates will argue against this position. He thinks instead that knowing, understanding, and remembering, along with things going with them, like right opinion and true calculations, are better pursuits than pleasure (11a-c/399).
Socrates then reframes the debate by saying that both parties are trying to prove that “some possession or state of the soul to be the one that can render life happy for all human beings” (11d/400), with one side saying that this possession or state of the soul is pleasure and the other side saying it is knowledge.
Socrates then has us suppose {a} that there in fact is a third “possession” that is neither of these two options, but {b} that it is more closely related to pleasure. In that case, Socrates thinks, both sides will be wrong, but the side of pleasure will still be determined as better than that of knowledge (11e/400). And likewise, if this supposed more true option is closer to knowledge, then knowledge will get second place in the ranking, and pleasure loses.
Socrates begins the discussion with pleasure. He notes that what is pleasurable varies per person.
we say that a debauched person gets pleasure, as well as that a sober-minded person takes pleasure in his very sobriety. Again, we say that a fool, though full of foolish opinions and hopes, gets pleasure, but likewise a wise man takes pleasure in his wisdom. But surely anyone who said in either case that these pleasures are like one another would rightly be regarded as a fool.
(12d/400)
Protarchus acknowledges that pleasures come from opposite things [like the things that make a fool happy might be opposite to what makes a wise person happy]. But he clarifies that we are not saying that the pleasures themselves are opposed to one another. For something cannot be unlike itself. [The idea might be that pleasure has different causes, some of them opposing, but the pleasure each cause produces is the same or similar.] (12d/401)
Socrates responds by saying that the pleasures can still be opposed, even thought they all fall under the same category of things. He gives the analogy of how there are many different colors, all of them very unlike one another, but we still call them colors. The strongest example is black and white, which are not just different but opposite. Socrates concludes, “don’t rely on this argument which makes a unity of all the things that are most opposed. I am afraid we will find there are some pleasures that are contrary to others” (13a/401).
[Recall that Protarchus’ overall point is that what is good in life is seeking pleasure.] Protarchus then wonders how Socrates’ point affects his argument. Socrates’ reply is the following. Protarchus wants to say that there are many different kinds of pleasure, but they are all good. Socrates objects that if one pleasure is good, then we would think that its contrary pleasure could not be good. Socrates then asks, what is common among all pleasures that would allow them all to be good, even the contrary ones? (13b/401)
Protarchus then claims that anything which can be called a pleasure cannot be said to be unlike or opposite to anything else that is called a pleasure (13c/401).
Socrates’ reaction is that Protarchus is not being very thoughtful or rational. Protarchus has acknowledged the examples of opposing pleasures, and yet he is denying that they are opposite. [I am not certain, but perhaps the idea in the examples is that what makes a fool happy can make a wise person displeased, and vice-versa, as for example sources of amusement or entertainment, or certain public policies regarding education; I am not sure.] Socrates then proposes a compromise (12e/401). Socrates admits that were he to be questioned about all the different branches of knowledge, that he would have to acknowledge that some are very different from others, and in fact could even be opposite. Protarchus then says both parties should agree “that there can be many and unlike kinds of pleasures, but also many and different kinds of knowledge” (13a/402). [The idea here seems to be that Socrates is defending knowledge as the good, but it also has many different sorts. This means that Socrates’ original objection to Protarchus’ argument that different pleasures can all be good also applies to Socrates’ argument; for Socrates’ would also be saying that different and possibly opposing forms of knowledge can all be good.]
Socrates then cautions that the compromise does not settle the argument. Instead, both parties should be brave and face the possibility that their own argument is wrong and even possibly that both arguments are wrong. “we are not contending here out of love of victory for my suggestion to win or for yours. We ought to act together as allies in support of the truest one” (14b/402).
Socrates next wants both parties to agree not to get caught up in certain paradoxes which are really just conceptual tricks and are not of any real importance. They are related to problems of the ‘one and the many’. The idea is that someone can argue that the many are one or that the one are many, and both sides are easily disputed, depending on which side you arbitrarily decide to take. Protarchus notes one kind of these puzzles which is the most commonplace. He describes them in the following way. Someone tells you that you are one by nature, but that you are also many, because you are tall and short, heavy and light, and many other such opposites. [Protarchus does not give the reasoning for how one might be said to have these opposite traits. But perhaps it is that someone is tall compared to one thing but short to another. Or maybe they are short at one time in their life and tall at another. I am not sure.] Socrates notes that these sorts of arguments are not longer taken seriously. He adds another sort of trivial argument. It begins by having a person acknowledge that they have many body parts, but that they are identical with them as a whole. But then they say you have committed yourself to such absurdities that you think the one is many and the many are just one thing.
when someone who first distinguishes a person’s limbs and parts asks your agreement that all these parts are identical with that unity, but then exposes you to ridicule because of the monstrosities you have to admit, that the one is many and indefinitely many, and again that the many are only one thing. (14e-d/402)
Socrates notes that in these puzzles, the one is taken to be some physical thing in the world. But there is another sort of similar puzzles where the one is something taking on more of an ideal nature, like man, ox, the beautiful, or the good. Certain controversies arise when discussing these puzzles. One is the question of whether or not we can even say any such unity as the beautiful, the good, man, and so on really exist. And suppose they do exist. We still do not know how to characterize them. For example, do they come into existence and leave existence [like how living things are born and die]? And, is such an ideal unity really just one thing, even though it is found in numerous actual instantiations? For, it would seem that although it is one and the same thing in each case, it is also multiple given the multiplicity of cases. Another question is, “must it be treated as dispersed and multiplied or as entirely separated from itself, which would seem most impossible of all?” [I do not follow that problem very well. Is the idea that since the one unity is found in many actual cases, that we should determine whether the one is broken up into parts or is it repeated as a duplication? I am not sure.] Socrates says that these sorts of problems of the one and the many are worth real consideration [and they probably have bearing on the current discussion about whether or not many different things, some even opposed, can all be considered the same category of thing, like pleasure and knowledge.] (15b-c/403)
Socrates seems to diagnose the problem as resulting from the ambiguities or other complications that natural language creates when we use it to try to understand certain things. [So in this case, perhaps because we use the same word for many different things, it would lead us to think that those things are all the same while as well being all different.] Some people even take a lot of joy in exploiting this weakness of language, and they like to trap other people by getting them to solve riddles that are really just problems arising from language’s inability to express certain things or its tendency to misrepresent certain things. (16a/404)
Socrates says that the best way to understand this problem is to consider an old tale. According to a myth, anything that is said to be consists of one and many, and is limited and unlimited. [The next idea seems to be that for any one thing, we can find its other forms. So if we find something as one, we can find it as many, and also as limited and as unlimited, but I am not sure. And in fact, we should also not just find other instances of that thing, but for some reason we should find all instances. The reasoning might have something to do with the myth. So once we have found every instance of something, we have somehow become assured of its pure formal nature. I am guessing. Later the idea will be that we should find all its instances in order to have adequate knowledge of it. Let me quote. ]
It is a gift of the gods to men, or so it seems to me, hurled down from heaven by some Prometheus along with a most dazzling fire. And the people of old, superior to us and living in closer proximity to the gods, have bequeathed us this tale, that whatever is said to be consists of one and many, having in its nature limit and unlimitedness. Since this is the structure of things, we have to assume that there is in each case always one form for every one of them, and we must search for it, as we will indeed find it there. And once we have grasped it, we must look for two, as the case would have it, or if not, for three or some other number. And we must treat every one of those further unities in the same way, until it is not only established of the original unit that it is one, many and unlimited, but also how many kinds it is. For we must not grant the form of the unlimited to the plurality before we know the exact number of every plurality that lies between the unlimited and the one. Only then is it permitted to release each kind of unity into the unlimited and let it go. The gods, as I said, have left us this legacy of how to inquire and learn | and teach one another. But nowadays the clever ones among us make a one, haphazardly, and a many, faster or slower than they should; they go straight from the one to the unlimited and omit the intermediates. It is these, however, that make all the difference as to whether we are engaged with each other in dialectical or only in eristic discourse.
(16c-17 a / 404-405)
Socrates then gives an example. He says that we know that alphabetic letters are both one and many. There is one letter that can be said many times and by many people. But just knowing the facts there there is one letter sound and many enunciations of it, that is to say, just knowing the letter’s unlimitedness or its unity, is not enough to make us literate. For that we would need as well knowledge of “how many kinds of vocal sounds there are and what their nature is” (17b/405). He gives another example. If our only way to classify pitches was, high, low, and equal [perhaps these are relations between pitches, higher, lower, and equal], then we would not have knowledge of music. For this, we would need to learn “how many intervals there are in high pitch and low pitch, what character they have, by what notes the intervals are defined, and the kinds of combinations they form—all of which our forebears have discovered and left to us, their successors, together with the names of these modes of harmony. And again the motions of the body display other and similar characteristics of this kind, which they say should be measured by numbers and called rhythms and meters” (17d-e/405). As these examples show, the degree to which you lack knowledge in all the sorts of variable elements of some field of study is the degree to which you lack expertise in that area.
For when you have mastered these things in this way, then you have acquired expertise there, and when you have grasped the unity of any of the other things there are, you have become wise about that. The boundless multitude, however, in any and every kind of subject leaves you in boundless | ignorance, and makes you count for nothing and amount to nothing, since you have never worked out the amount and number of anything at all.
(17e/405-406)
At this point Protarchus and Philebus agree with Socrates, but they do not see how the point is relevant to the argument. Socrates will explain how that is so, but first he wants to note a few other things on the matter (18a/406).
Socrates elaborates on his prior discussion by adding that his point there was that if we find some unity, we should not think of it merely in terms of something unlimited but rather we should examine it for its multitude of variable elements. He says it works the other way, and so if we come across some unlimited variety, we should not jump to conclude there is some unity, but rather we should delineate all the varieties first. [I might not be following the distinction, but let us try to look closer here. In the prior case, we begin with a unity, like “letter”. We will eventually say that it is unlimited, but to do so, and to have knowledge of its unlimitedness, we need to examine every variety of letter and every variable involved in vocal sounds and so on. Socrates uses the same example, but now says it works the other way. If we begin with an unlimited, we need again to work through all the varieties before we can say we have a unity and have knowledge of that unity. Although the example is the same, letters, this time it is a mythological illustration. Theuth was first to discover that the vocal sounds are unlimited. He found that there are a limited number of vowels, consonants, and mute letters. He next subdivided these three types down to each particular instantiation. With all of these instantiations in front of him and seeing all this variety in its particularity, he called all of these things “letter”, and he realized that to understand any one instance of letter we need to understand all of them. This study of what links all these letters he called the art of literacy. It is still a bit unclear to me what the difference is in the two examples, as they both involve the same process. Socrates is saying these processes have different beginning and ending points. I am not sure how that works however. The idea seems to be that in the first case, we already know that we are dealing with a unified field of things, and then later we come to grasp its unlimited internal variety. So we know from the beginning that we are investigating letters or vocal sounds. In the second case, we do not know yet that all the things we are studying fall under the same category of thing. But this difference I do not grasp. How does Thoth know what to include in his study if he does not already know the unity that makes all the examined instances belong with each other? I suppose to understand this difference we might think of scientific discovery. Perhaps for example with the discovery of evolution, there was first not a knowledge of the unity of the cases being studied, of the fossils for example, which show variety but nothing to unify that variety. Then by studying them and proposing a theory of what unifies them, Darwin was able to give that unity the name “evolution”. But I am not sure.]
SOCRATES: I will do so when I have gone a little further into the subject matter. Just as someone who has got hold of some unity or other should not, as we were saying, immediately look for the unlimited kind but first look for some number, so the same holds for the reverse case. For if he is forced to start out with the unlimited, then he should not head straight for the one, but should in each case grasp some number that determines every plurality whatever, and from all of those finally reach the one. Let us again make use of letters to explain what this means.
PROTARCHUS: In what way?
SOCRATES: The way some god or god-inspired man discovered that vocal sound is unlimited, as tradition in Egypt claims for a certain deity called Theuth. He was the first to discover that the vowels in that unlimited variety are not one but several, and again that there are others that are not voiced, but make some kind of noise, and that they, too, have a number. As a third kind of letters he established the ones we now call mute. After this he further subdivided the ones without sound or mutes down to every single unit. In the same fashion he also dealt with the vowels and the intermediates, until he had found out the number for each one of them, and then he gave all of them together the name “letter.” And as he realized that none of us could gain any knowledge of a single one of them, taken by itself without understanding them all, he considered that the one link that somehow unifies them all and called it the art of literacy.
(18a-d/406)
Socrates now shows how this relates to their debate regarding which, if either, of pleasure or knowledge is the highest good in life. Socrates notes that we have acknowledged that both pleasure and knowledge are unities in the sense he just explained. He then says that they now need to examine their internal varieties to see in what ways they are unlimited. [I am not exactly sure why they need to know about their unlimitedness in order to settle this debate. Perhaps the idea is not just that they need to establish that they are unlimited but more generally they need a complete knowledge of each field, which requires exploring their internal varieties.]
This is the very point in question to which our preceding discussion obliges us to give an answer: to show how each of them is one | and many, and how instead of becoming unlimited straightaway, each one of them acquires some definite number before it becomes unlimited.
(18a-19a/406-407)
Socrates is thus calling for Protarchus to determine “whether there are kinds of pleasures or not, and how many there are, and of what sort they are. And the same set of questions applies to knowledge” (19b/407, Protarchus speaking). As Socrates explains, “Unless we are able to do this for every kind of unity, similarity, sameness, and their opposite, in the way that our recent discussion has indicated, none of us will ever turn out to be any good at anything” (19b/407).
Protarchus then says that if we cannot do an exhaustive analysis of pleasure and knowledge, then we should at least not be mistaken about them. He next summarizes the debate so far. Protarchus then complains that Socrates is trying to overwhelm them with unreasonable questions that they cannot answer. Protarchus then says that Socrates promised to resolve the issue if Protarchus and Philebus were unable to. Since they are not able to give an exhaustive account of all the varieties of pleasure, Protarchus says that Socrates must decide whether he should do so himself for the sake of settling the debate (20a/407).
Socrates then says that a memory just came to mind, as if sent by the gods, because it can help them in their discussion (20b/407-408). He remembers that he once had a dream where he learned that neither pleasure nor knowledge is the good. [For some reason, they take this realization as true without further examination.] Socrates notes that they can now conclude that pleasure is not the highest good and therefore they have been relieved of the task of determining all its varieties. Furthermore, this lack of a need to understand pleasure will be seen more clearly if they progress in the argument. (20c/408)
Socrates then proceeds through a pair of questions that Protarchus answers. Is the good perfect or not perfect? It is not just perfect; it is in fact the most perfect thing of all. Must the good be sufficient? Certainly it is sufficient. That is the main feature that makes it superior to all else. [I am not sure what is meant here by sufficient. Perhaps it means that the good needs nothing else to account for it or to justify it. I am guessing. From what he says below, it seems that the good is sufficient in that whatever is good does not need to be understood in terms of anything else, and more importantly, it can exist independently of anything else. So if knowledge is the good, we should be able to conceive it without relation to pleasure or anything else, and also were the life of knowledge the good life, then it would not require any pleasure in that life.] (20d/408).
Socrates then states what he thinks is the most important thing about the good, namely, that it is what is most highly sought by anything with some notion of it.
SOCRATES: Now, this point, I take it, is most necessary to assert of the good: that everything that has any notion of it hunts for it and desires to get hold of it and secure it for its very own, caring nothing for anything else except for what is connected with the acquisition of some good.
(20d/408)
Socrates now wants to examine very rigorously (‘put on trial’) the life of pleasure and the life of knowledge to see if they can make some determination (‘reach some verdict’) on them taken independently of the other. His reasoning for thinking of them distinctly is that if either of them is the good, then they would not need anything more in addition to what they already are. [We established already that the good is sufficient.] And furthermore, if either pleasure or the good is found to be lacking something, then it cannot be the good [because again, the good is sufficient and is thus not lacking in anything.] (20e-21a/408).
Socrates then asks Protarchus a series of questions to test both pleasure and knowledge as life pursuits to see if they hold up to being completely sufficient by themselves. Could you (Protarchus) live your whole life by enjoying the greatest pleasures? Yes! Would you need anything else were that so? No. So you would not need knowledge, intelligence, calculation, or things related to them? No, for if I had pleasure, I would have everything I could possible need. And you could live your whole life enjoying the greatest pleasures? Sure, I see no reason why not. But if you only had pleasure, you would lack reason, memory, knowledge, and true opinion, and does this not mean that you would be ignorant even of the fact that you are enjoying this pleasure? Yes, that is true. But if you lack memory, would you not be unable to remember that you ever enjoyed yourself in the past; and if you lacked right judgment, would you not be able to realize that you are enjoying yourself in the present moment; and if you are unable to calculate, would you not be unable to anticipate having any pleasures in the future; and thus, would you not be living more of the life of a dumb animal, like a sea mollusk, rather than of a human being? Yes, life would be like this. Is such a life worth living? I am not sure what to say, I am speechless. (21a-21d/408-409, with Socrates as the questioner and Protarchus as the one replying in each case)
Socrates then turns his questions to the idea of living a life of reason. Socrates wonders
Whether any one of us would choose to live in possession of every kind of intelligence, reason, knowledge, and memory of all things, while having no part, neither large nor small, of pleasure or of pain, living in total insensitivity of anything of that kind.
(21d-e/409)
Protarchus says that this life of pure reason, just like the life of pure pleasure, is not desirable. Socrates then wonders what if we lived a life that mixes the two pursuits, or as Protarchus restates it, “a mixture of pleasure with reason and intelligence” (22a/409). Protarchus replies that “Everybody would certainly prefer this life to either of the other two, without exception” (22a/409). [So now we have three possible lives: one of pleasure, one of intellect, and one of a mixture of both.] Protarchus then notes that they may conclude “of the three lives offered to us, two are not sufficient or worthy of choice for either man or animal” (22a-b/410).
Socrates then sums up: it is clear now that neither the life of pleasure nor the life of knowledge by itself is the good. Furthermore [since we established that creatures seek the good above all things] if anyone choses the life just of knowledge or just of pleasure, it would be a choice made “involuntarily, in opposition to what is by nature truly choiceworthy, from ignorance or some unfortunate necessity” (22b/410).
Socrates then reminds us that Philebus’ argument for a life of pleasure has been shown to be not the good life. Yet, Philebus counters that we also established that Socrates’ argument for a life of knowledge as the good life is likewise wrong. Socrates notes that there is also the matter of divine reason [which could be better than even the combined pleasure/knowledge life. But he is not now interested in pursuing that possibility.] Now Socrates would like to figure out, which, out of the life of pleasure or of knowledge, gets second place to the combined life; that is to say, he wants to know which one deserves more credit for making the combined life be closer to the good. He says, “Thus neither of the two would be the good, but it could be assumed that one or the other of them is its cause” (22d/410). Socrates thinks that knowledge will get the second place.
Protarchus then notes that those who favor pleasure could be very disappointed to learn that it is not the highest good in life, and he encourages Socrates to continue his line of reasoning in that regard, rather than stop now (23a-b/410). Socrates says that this argument to give knowledge the second prize will require a long discussion, as he will need to use a different technique in his argumentation (23b/411).
Socrates suggests that they begin by dividing up all things in the universe into a very small number of categories, on the basis of the idea mentioned before, namely that a god “revealed a division of what is into the unlimited and the limit”. He then takes as the third kind the mixture of the unlimited and the limited. To these three he adds a fourth one, namely, the combination of the first two with the third. Protarchus then asks if we need a fifth kind that provides for their separation. [I am not sure what that means. Is it something which is neither limited nor unlimited? I do not know.] Socrates does not think this fifth kind is necessary at least at the moment (23c-d/411).
Socrates the proposes that they begin by examining just at the first three divisions, looking especially at how the first two, the unlimited and the limited (“what has limit”), are both one and many, starting with how the unlimited is many. [Let me quote as I might not have summarized it well.]
SOCRATES: Let us first take up three of the four, and since we observe that of two of them, both are split up and dispersed into many, let’s make an effort to collect those into a unity again, in order to study how each of them is in fact one and many.
PROTARCHUS: If you could explain all that more clearly, I might be able to follow you.
SOCRATES: What I mean is this: The two kinds are the ones I referred to just now, the unlimited and what has limit. That the unlimited in a way is many I will try to explain now. The treatment of what has limit will have to wait a little longer.
(23e-24a/411)
Socrates now asks, in the case of the hotter and the colder, can we conceive of a limit? Or, rather, is it the case that hotter and colder are more a matter of ‘more and less’? And furthermore, is it not so that were the more and the less principles of hotter and colder, that more and less do not operate as if they were attaining some final state of ultimate hotness and coldness? For, were they to attain some final state, they would no longer be a matter of being hotter or being colder. As we can see, hotter and colder, along with all other cases of more or less, are not static states of affairs with determinate quantitative values. Rather, hotter and colder, along with other sorts of more or less, do not have some determinate value, and they are in flux.
SOCRATES: Attention, then. The matter I am asking you to attend to is difficult and controversial, but attend to it nevertheless. Check first in the case of the hotter and the colder whether you can conceive of a limit, or | whether the ‘more and less’ do not rather reside in these kinds, and while they reside in them do not permit the attainment of any end. For once an end has been reached, they will both have been ended as well.
PROTARCHUS: Quite strongly so, Socrates.
SOCRATES: You have grasped this rather well, Protarchus, and remind me rightly with your pronouncement of ‘strongly’ that it and equally its counterpart ‘gently’ are of the same caliber as the more and less. Wherever they apply, they prevent everything from adopting a definite quantity; by imposing on all actions the qualification ‘stronger’ relative to ‘gentler’ or the reverse, they procure a ‘more and less’ while doing away with all definite quantity. We are saying now, in effect, that if they do not abolish definite quantity, but let quantity and measurement take a foothold in the domain of the more and less, the strong and mild, they will be driven out of their own territory. For once they take on a definite quantity, they would no longer be hotter and colder. The hotter and equally the colder are always in flux and never remain, while definite quantity means standstill and the end of all progression. The upshot of this argument is that the hotter, together with its opposite, turn out to be unlimited.
(24a-b/412, boldface and underline mine)
[Here it might not be immediately obvious what Socrates’/Plato’s reasoning is. I will give my interpretation and justify it. My interpretation of Plato’s reasoning is as follows. Plato does not mean hotter and colder as being comparative relations between different things which are hot or cold. Rather, they are comparisons of one thing to itself, more specifically, of one thing during its change where it can be said to be hotter or colder than it just was. Why? Suppose instead Plato includes in this meaning that one thing can be said to be hotter or colder than some other thing. Were that the case, then it would be conceivable that the two things maintain a constant value, the same temperature, with one taking a higher one than the other. It is still possible that Plato allows for such a comparison while also maintaining a dynamic notion of the difference. For example, it could be that there is some imbalance in their difference that cannot last forever, and so eventually these values will change. Or, perhaps the things of different values are mutually affective and are in a state of tug-of-war, with each one fluctuating in temperature until some resolution is attained. But in both these cases, the way that the temperature difference is understood is still somehow in flux, but in the first case it is a delayed flux, and in the second case it is like an oscillating flux. One way or another, the things in question either become hotter or colder than themselves, and this is the sort of flux that Plato seems to be talking about. Therefore, I believe that hotter and colder in this account are matters of self-comparison rather than of comparison between different things altogether. And given what Plato says about them being in flux, we should not think ‘being hotter’ or ‘being colder’ but rather ‘becoming hotter’ and ‘becoming colder’. Because it is self-comparative, that makes it paradoxical, not just in the idea that something is hotter than itself (thus also colder than itself), but also in the way that temporality is conceived in events of becoming. There needs to be temporally distinguishable moments somehow coinciding simultaneously. Or if that is not allowed, temporally distinct states of affairs that given simultaneously. Deleuze’s very profound insight into this matter, which we will analyze in great detail later, is that states of affairs as they come to be were previously bound up in an inconsistency of states and times that in some way were in effect prior to the determinate chronology that is somehow obtained secondarily. In other words, before Alice determinately became a larger size, there was some situation where it was undecided whether she would grow, shrink, or stay the same size, and in a sense she was all three inconsistent states simultaneously. Also in this situation, we cannot say which is before or after, her being larger or smaller are neither before nor after the other state, before the size is determined for what it will become. Suppose she has grown and thus for one reason or another larger wins. This way, the temporal chronology of moments where in the second moment she is larger than the first one is established after the event of becoming has produced this determination. All of this is profoundly puzzling, but we will try to untie the knots in a future post.]
Socrates then continues under the assumption that other matters of more or less will also be unlimited, and he proceeds to cases of the limited, like ‘the equal’, ‘equality’, ‘double’, and “all that is related as number to number or measure to measure” (25a-b/412).
Plato. Philebus. In Plato: Complete Works, pp.398-456. Edited by John M. Cooper. Translated by Dorothea Frede. Indianapolis/Cambridge: Hackett, 1997.
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