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Plato's Philebus - Selections - Comments

Tr. R. Hackforth. This dialog was also known in classical times by the name "On Pleasure" (Diog. L. iii, 58).


In this dialog Plato again considers the question of "what knowledge is", his notions about which I criticized with regard to his Theaetetus. I wrote that "Plato's assumption is that knowledge is one thing, always the same, that there is an essence of knowledge, rather than a variety of different things that we call 'knowledge'". But in the Philebus Plato shows that he is aware of this criticism -- i.e. that something in his account is fundamentally unclear. He asks in the Philebus the question: How can one be many and many be one? How can knowledge be one thing, but at the same time there be many branches of knowledge, some of which are unalike or even opposite to one another (13e-14a)?

Plato's approach to this question is different here. He does not talk about "Forms" ("Absolutes", "Ideas"). He uses the method of definition-by-division (as he does in his Sophist) to say things about knowledge, rather than try to answer the question of "what knowledge is".

Outline of this page ...

Definition by Division (an example)

The word 'game' might be defined using the method of definition by division. We begin with the common name 'game', or, the class 'game'. Then we divide games into sub-classes (i.e. into types or kinds of games), e.g. {board games, ball games ...}, and then subdivide the sub-class of 'ball games', e.g. {ball games with nets} and {ball games without nets} etc.

If we fully carry this out, we can then point to resemblances (likenesses) and dis-resemblances (un-likenesses) between games. In this way we might explain what we mean by the word 'game'; this is a structured version [classification scheme] of definition-by-examples. (A class name is like an umbrella, and we may try to organize whatever we find lying under it.) But does this really explain the meaning of the word 'game'? No -- because that word has no "meaning", if by 'meaning' we mean 'common nature' or 'essence' of games, because games do not have "something [defining] that is common to all" (PI § 66).

And, no, I do not think that Plato would find Wittgenstein's explanation of meaning of the word 'game' acceptable. He would choose instead to say that, although we have a notion of the Form named by the word 'game', we do not as yet have knowledge of it.

Questions: when Plato suggests a definition for a word, or in his view "a definition of a thing", is he offering an hypothesis (about the essence of some thing)? And can this hypothesis-suggesting go on forever? And if it can, then can we ever definitively say "This is sense, that nonsense"? Maybe the defining common nature of knowledge [or, games] is this, maybe that ... indefinitely.

If we define the word 'game' using the technique of definition-by-division, the question of "what a game is", as of "what knowledge is", doesn't arise. Whether Plato imagines that there is a single Form named 'knowledge' or not -- either way it does not matter what he imagines, because what he imagines does not affect the definition-by-division. [Cf. Philosophy of mathematics is the view from outside mathematics: what anyone imagines about geometric points is of no importance to geometry itself.]

Between man and beast

... aye, and if the beasts had any sense, they would deride those who thought much of anything but fodder! (Epictetus, Discourses ii, 14, tr. Crossley)

Thus Epictetus makes the point succinctly (cf. Philebus 67a-b). The difference between man and pig is that when a pig acts the way a pig acts, it is pleased with itself; but that when a man acts like a pig, he feels ashamed of himself. There is in his nature a longing for something nobler than pleasure. That much, I observe, is evident to experience; but Plato must offer an argument, because there are those who claim that the good (or, happiness) for man is pleasure and nothing else.

My comments that follow quotations from the Philebus are written from the point of view of logic of language, which is I think the fundamental question of philosophy: "What is the meaning of word?" That was certainly Socrates' question, although he of course understood it very differently from Wittgenstein.

Is Pleasure the Good (the excellence proper to him) for Man?

11b - Philebus says that the good for all animate beings consists in enjoyment, pleasure, delight, and whatever can be classed as consonant therewith, whereas our contention is that the good is not that, but that thought, intelligence, memory, and things akin to these, right opinion and true reasoning, prove better and more valuable [profitable] than pleasure [or anything else in the world] for all such beings as can participate in them ... That, I think, Philebus, is that substance of our respective theories, is it not?

If we wished to express this in prose [prosaically], could we say that the life of the mind is more useful for man than the life of eating and drinking and of soft flesh and easy pleasure? Because Xenophon's Socrates has said that the good is the useful, and it would be in most contexts very strange to identify the pleasant with the useful. But is "life of the mind" what Plato has in mind here? Apparently (21d-e).

11d - Well, then, I want us to reach agreement on one further point.... What you and I are now to attempt is to put forward a certain state or condition of the soul which can render the life of every man a happy life. Am I right?

PROTARCHUS: Quite right.

SOCRATES: Then you people put forward the state of enjoyment, whereas we put forward that of intelligence?


12c - ... but as for pleasure, I know that it is a thing of variety ... Of course the mere word 'pleasure' suggests a unity, but surely the Forms it assumes are of [many] sorts and, in a sense, unlike each other.

"... and in a sense unlike each other." A word (a common name) suggests a unity (a common nature) -- but if the word's applications are to things that are unlike, or even opposite to one another, in nature, then how can there be a unity (a common nature)?

Anything an individual enjoys doing or experiencing is a pleasure to that person. Does this make 'pleasure' a concept more similar to 'beauty' or more similar to 'useful' -- i.e. is the word 'pleasure' "a word without a grammar" (i.e. where the rules look nothing like rules, as is the case with 'beautiful'), or a word whose grammar is relative ('useful to someone for something', where 'useful' is objectively defined: a hammer is useful to the carpenter for driving a nail)?

The Form 'geometric shape'

12e-13a - Then again [cf. 11b-12c] the same applies as between figure and figure; taken as a class all figure is one, but of its divisions some are absolutely opposite to each other, while others have countless point of difference, and we can find many other instances of the same thing. [Socrates has already given the example of 'color': black and white are both colors, but nonetheless they are absolute opposites to one another. (12e)]

What, then, is left of Plato's Forms? Recall that in Meno 74d, 72c, Socrates asks for the common nature of 'figure' or 'shape' -- which one can do if "all figure is one":

Tell me then, since you call them by a common name and say that they are all [shapes] ... what is that common nature which you designate as [shape]? What is the quality in which they do not differ, but are all alike ...? (Meno; tr. Jowett)

But what is the common nature of the members of the class 'figure' {square, circle, triangle, irregular polygon ...}? "Taken as a class all figure is one." -- But what is 'one' to mean here? And then, does 'class' = 'Form'? If there is no common nature, then is there a class -- not merely as a matter of convention (language) but in reality as well (Forms) [cf. 60b]?

13a - I am afraid we are going to find pleasures in some cases opposite to pleasures.

13b - What then is the identical element present alike in the bad pleasures and in the good that makes you [Protarchus] use the term 'good' in reference to them all?

13e - When I was asked originally what the good is, I suggested intelligence, knowledge, mind and so on, as being good.

13e-14a - Knowledge taken in its entirety will seem to be a plurality in which this knowledge is unlike that -- even, it may be, this knowledge opposite to that. [Socrates says that he would not be a fit person for this discussion if he took fright and therefore] maintained that knowledge is never unlike knowledge [as Protarchus has claimed that, although pleasures arise from opposite sources, those pleasures in themselves "are not opposites. How could pleasure be opposite to pleasure? Surely nothing in the world could be more completely similar than a thing to itself" (12d-e)], thereby bringing our discussion to an end like a tale that is told ...

Plato does not here give an example of "this knowledge [being] opposite to that [knowledge]". What would be an example of two knowledges being unlike or even opposite to one another?

14b - Let us have the varieties [of pleasure and of knowledge] fairly before us [and let our inspection of them] reveal whether we ought to give the title of the good to pleasure or to intelligence or to some third thing. For I imagine we are not striving merely to secure a victory for my suggestions or for yours; rather we ought both to fight in support of the truth and the whole truth.

14c - For really it is a remarkable thing to say that many are one, and one is many ...

I think the question is: if pleasure is just one thing, then how can there be a variety of pleasures which [are unlike and in some cases opposite to one another: whereas nothing can have a contradictory essence (A and not-A)] display no common nature? However, if they do not display a common nature, then why say that they are one -- for should it not instead by concluded that they are not one?

"Umbrella concepts"

An umbrella may cover many things (a man, his newspaper and his hat and cat e.g.); and is there any reason to suppose that those things have a common nature?

(The "theory of abstraction", that we abstract the common nature that we cannot describe (put into words); -- this theory is not consistent -- nor inconsistent -- with the evidence; in fact it has no connection to the evidence at all. We make an analogy from cases where we can identify a common natures to cases where we cannot -- but it is impossible to inspect both ends of this so-called analogy! (In Case A there is a common nature, but there is nothing analogous to that in Case B, because in Case B there is no "identifiable" common nature: "B is like A, but it is impossible to say in what way" -- That is not an analogy; that is not what we call a 'comparison'.) We simply say: Well, we do it in some cases and therefore it must be the case that we do it in all. "We abstract the common nature of color"; what does that notion make clearer? Well, it makes nothing clearer; what it does instead is to throw a blanket over the problem, making it appear to disappear. "What is the common nature of numbers?" -- Is that how we explain the meaning of the word 'number'? No, that is not how we learned, nor how we would teach anyone else, how to use the word number. Is the "theory of abstraction" a theory at all -- i.e. does it explain anything or simply give a name to our ignorance, making the problem appear to disappear?)

15a - But suppose you venture to take as your "one" such things as man, ox, the beautiful, the good; then you have the sort of unities that involve you in dispute ... if you subject them to division.

15b - First, whether we ought to believe in the real existence of monads of this sort; secondly, how we are to conceive that each of them, being always one and the same and subject neither to generation nor destruction ...

These "monads" surely are Plato's Forms, and by 'real existence' he means things for which real definitions can be sought. So long as we regard language Plato's way, so long as we regard the question of the one and the many as being a question about "the world", I don't think we can reach a final clarity here. (I do think that Wittgenstein's logic of language does allow us to reach a final clarity. -- Note, I say a final clarity, not the final clarity. If we look at things Wittgenstein's way, then ...)

15c - [Plato says that these two questions have to be properly settled.]

15d - We get this identity of the one and the many cropping up everywhere as a result of the sentences we utter; in every single sentence ever uttered, in the past and in the present, there it is. [But Plato gives no examples.] What we are dealing with is a problem that will assuredly will never cease to exist; this is not its first appearance. Rather it is, in my view, something incidental to [i.e. a consequence of] sentences themselves, never to pass, never to fade.

People say again and again that philosophy doesn't really progress, that we are still occupied with the same philosophical problems as were the Greeks. But the people who say this don't understand why it has to be so. It is because our language has remained the same ... (CV p. 15)

According to Wittgenstein, all philosophy is a dysfunction of language. [It appears to be a very general fact of nature that everything functional is also dysfunctional.] I would like to know how Plato would have responded to Wittgenstein's various ideas about language and about philosophy and about language in philosophy. I cannot imagine Plato ever agreeing that "The riddle does not exist", that there is nothing fundamentally [i.e. at it very foundations] puzzling about our life, but I also cannot imagine the argument/s with which he would attempt to refute in dialectic that claim of Wittgenstein's.

16b-d - [A method] to which I have always been devoted, though often in the past it has eluded me ... It is a method quite easy to indicate but very far from easy to employ. It is indeed the instrument through which every discovery ever made in the sphere of the arts and sciences has been brought to light. [Then Plato says that the method "came through Prometheus, or one like him, [and] reached mankind together with a fire exceedingly bright". This gift of Prometheus was passed on in the form of a saying:] All things ... consist of a one and a many ...

Would thought -- or rather, speech, language -- be impossible without common names? It would certainly be very different, either very simple, or very complicated indeed with a vast vocabulary. A language of only proper names would not be our language, if it would be a language at all -- for what could be done with it? For example, verbs (e.g. a gesture to come or go) are akin to common names, not proper names, aren't they? It would be a language without classes and sub-divisions -- a way of thinking quite foreign to our own.

The Method of Definition by Division

16d-17a - [Plato describes his method:] ... whatever it be that we are dealing with, to assume a single Form and search for it, for we shall find it there contained; then, if we have laid hold of that, we must go on from one Form to look for two [sub-Forms], if the case admits of there being two, otherwise for three or some other number of Forms. And we must do the same again with each of the "ones" thus reached, until we come to see not merely that the one that we started with is a one and an unlimited many, but also just how many it is.... it is the recognition of those intermediaries [between the one and the unlimited number] that makes all the difference between philosophical and a contentious discussion.

Plato gives no criterion for laying hold of a single Form; we simply make an assumption that there is one -- but apparently not simply based on the presence of a word in our language (12c).

17b - [Plato gives an example of his method in the alphabet:] ... take the letters of your school days as illustrating it.... The sound [we make] is one ... and also an unlimited variety ... And we have no real understanding if we stop short at knowing it simply as an unlimited variety, or simply as one. What makes a man "lettered" is knowing the number and the kinds of sounds. [The case is similar with music.]

Is Plato talking about what we call common names, e.g. 'the letters of the alphabet' does not simply mean 'a', 'b', or 'c' as individuals (as if they were proper names; e.g. 'Mr. A' would not have the same grammar as 'Mr. x' does), but instead as members of the class [Does 'common name' = 'class' or 'category'?] of all letters: {a, b, c, d ... x, y, z}? (We can go further, of course, and distinguish between letters and letter-als, as cf. numbers and numerals, the various shapes of A and a, e.g., thus treating the letter 'a' as a common name.)

17e - ... when you have grasped all this, [you have] gained real understanding, and whatever be the "one" that you have selected for investigating, that is the way to get insight about it.

Is Plato saying something profound here? Can you say of a system of classification that it is "the instrument through which every discovery ever made in the sphere of the arts and sciences has been brought to light" (16c)?

Plato speaks of "intermediates" [Is this related to Wittgenstein's statement about "the importance of finding and inventing intermediate cases" (PI § 122) -- i.e. is what Plato wants a bird's-eye view?], but what would these be? Would this be an example: we do not jump straight from "living being" to "man", but from "living being" to "plant" and "animal", then to "mammal" and "bird" and "reptile" (etc.), naming all the intermediate classes between "living being" and "man"; only then do we finally arrive at "the unlimited variety" (i.e. the members of the class of all mankind {Philebus, Socrates, Protarchus ...})?

Do I understand what Plato is saying? Can you say that you "know yourself" better if you describe all the sub-classes between mankind (the "one") and individual men? Isn't that what children are taught at school -- a system of classification, and is not a system of classification knowledge of your subject? Perhaps in botany, zoology, perhaps in the sciences and in the arts the practice of which requires knowledge. (Wittgenstein at one time wanted a "philosophical grammar" -- i.e. a re-classification of our words into "parts of speech" based on their use in our language.) But I don't know if Plato's method is the one that is actually used.

Is Plato saying something profound here? And if we do not recognize it as such, is that because today his notion is so well established that to us it seems obvious? But of course it wasn't always "obvious". An insight is only obvious after it has been pointed out to us.

At the same time I wonder if a system of classification may not be a hindrance to seeing/looking at things in a new way. For example, the old scheme of "noun, verb, adjective, etc." with 'noun' defined as 'the name of a person, place or thing. That is a classification system may institutionalize a misunderstanding, as in the case of "undefined terms" in geometry. (Isn't knowledge -- i.e. what we think we know -- always limiting in this way?)

The Second half of Plato's method of Definition by Division

18a-b - [But there is another half of Plato's method:] When you have got your "one", you remember, whatever it may be, you must not immediately turn your eyes to the unlimited but to a number [i.e. to the divisions (sub-classes) of your "one"]; now the same applies when it is the unlimited that you are compelled to start with. You must not immediately turn your eyes to the "one", but must discern this or that number [of categories] embracing the multitude, whatever it may be; reaching the one must be the last step of all.

Then, if I understand this, one begins with a "many" e.g. {Philebus, Socrates, Protarchus ...} -- But one must not jump from there to the "one" e.g. of "living being", but instead works one's way up, e.g. from "man" to "mammal" to "animal", in reverse order from the way down (16d-17a).

18b-d - We might take our letters again to illustrate what I mean now. [Then Plato tells the story of "a person in Egypt called Theuth", who is said to have discovered vowels, consonants (I think) and mutes, then divided these groups, vowels e.g. into each of the individual vowels.] [And last] he affixed to the whole collection, as to each single member of it, the name 'letter'. It was because he realized that none of us could ever get to know one of the collection all by itself, in isolation from all the rest, that he conceived of 'letter' as a kind of bond of unity, uniting as it were all these sounds into "one", and so he gave utterance to the expression "art of letters", implying that there was one art that dealt with the sounds.

[Plato's point in describing this method is that now that we are going to consider what pleasure is,] we are not to take the unlimited variety straight away -- [because the "ones" we have selected (i.e. the concepts 'pleasure' and 'knowledge') each possesses a certain number [of subordinate-Forms] before the unlimited variety is reached. [About "intelligence" and "pleasure", we are] to show how each of them is both "one" and "many", and how ... each possesses a certain number ... (18e) [But Plato does not follow through with this plan. Instead:]

19a-b - PROTARCHUS: Philebus, it's no easy problem that Socrates has plunged us into with his curiously roundabout methods.... Socrates, I take it, is now raising the question of kinds of pleasure. Has it different kinds, or has it not, and if it has, how many are there and what are they like? And exactly the same question arises with regard to intelligence.

That would be a classification scheme for the "one" pleasure -- but where is such a scheme to be found, by philosophers, if not in the language that already exists? If logic [dialectic] is here a process of discovery -- i.e. of grammatical investigation -- what does it discover other than facts about our language? And yet, Wittgenstein, had to admit:

The Relation between Concepts and Reality

Indeed, doesn't it seem obvious that the possibility of a language-game is conditioned by certain facts? (OC § 617b)

Then aren't we here indeed investigating the facts that may explain concept formation (PI II, xii, p. 230)? And aren't those facts, not only facts about language, but also about "the world" (reality) in which that language is used?

If the formation of concepts can be explained by facts of nature [i.e. by "the correspondence between concepts and very general facts of nature"], should we not be interested, not in grammar, but rather in that nature which is the basis of grammar? (ibid.)

Plato might respond: Grant me that, and you've granted me all the rest: it is not the grammar of the word 'knowledge' that concerns me but instead the nature of the thing that is named 'knowledge' ... And then what becomes of Wittgenstein's logic of language? Well, we are at a very high level of abstraction here -- i.e. we are stating generalities without particular examples. (And there is that word 'thing' again to spread its dark cloud of vagueness.)

"A high-level truth about smiles" - Obliteration of the distinction between sense and nonsense

J.J.C. Smart says something like: I don't know whether the rule 'A smiling mouth smiles only in a human face' (ibid. § 583) (which Wittgenstein perhaps wrote in the context of Lewis Carroll's Cheshire Cat) belongs to the grammar of the word 'smile'; maybe it is instead a high level truth about smiles (or cats). But will Smart then go on to say that the non-existence of elves is "a high level truth about elves"? If we cannot say that the undefined combination of words 'Do elves exist?' is nonsense -- that is, if we cannot make an objective distinction between sense and nonsense, then philosophy is an idle activity, one where "whatever seems right is going to be right" (ibid. § 258).

19c-20a - PROTARCHUS: You made all of us a free offer of this discussion, in which you yourself, Socrates, were to share, for the purpose of deciding what is the best of all things possessed by man.... What you, I gather, maintain is that there is something which may properly be called a better good than pleasure at all events -- namely, reason, knowledge, understanding, skill, and all that is akin to these things ... [Protarchus again reminds Socrates of his promise. Both Protarchus and Philebus find the method of divisions too difficult, and thus says Protarchus to Socrates:] please make up your mind for yourself whether you must classify the kinds of pleasure and of knowledge or may pass them over -- supposing, that is, that you are able and willing to follow another method and clear up our points of dispute in some other way.

20b - SOCRATES: ... I fancy some god has recalled to my mind something that will help us.... I remember a theory that I heard long ago -- I may have dreamed it -- about pleasure and intelligence, to the effect that neither of them is the good, but that it is something else, different from either and better than both.

20d - [Plato says that the good has three qualities: (1) that it is "perfect", (2) that it is "adequate", and (3) that "every creature that recognizes it goes in pursuit of it".]

20d-21a - Now if we're going to have a critical inspection of the life of pleasure and [of] the life of intelligence, let us see them separately.... Let us have no intelligence in the life of pleasure, and no pleasure in the life of intelligence. For if either of them is the good it must have no need of anything else [Quality no. 2] to be added to it, and if we find that either has such a need, presumably it ceases to be possible for it to be our true good.


21a - Then here's a question for you.... Would you care, Protarchus, to live your whole life in the enjoyment of the greatest pleasures?

21b-c - But if you were without reason, memory, knowledge, and true judgment, you would necessarily, I imagine, in the first place be unaware even whether you were, or were not, enjoying yourself, as you would be destitute of all intelligence.... And surely again, if you had no memory you would necessarily, I imagine, not even remember that you had been enjoying yourself; of the pleasure you encountered at one moment not a vestige of memory would be left at the next.

Therefore, if that account is correct, then pleasure cannot be the good, because pleasure is not "adequate" (20d).

Question: does the cow remember the quality of the hay it ate yesterday? What is pleasure for a cow? (This suggests forms of life: "Only of a human being and what is like one do we say ..." (PI § 360); Plato gives the example of crustaceans (21c)) What is the difference here between saying that "Plato is making our concept [i.e. the rules for using the word] 'pleasure' clearer to us" and "Plato is making the nature of pleasure clearer to us"? If there is a difference, which statement seems closer to the mark in this case?

The Life of Reason

21d-e - SOCRATES: ... let us turn our attention to the life of reason, and have a look at that.

PROTARCHUS: What is the "life of reason"?

SOCRATES: Imagine one of us choosing to live in the possession of intelligence, thought, knowledge, and a complete memory of everything, but without an atom of pleasure, or indeed of pain, in a condition of utter insensibility to such things.

PROTARCHUS: Neither of these lives [i.e. neither the life of pure pleasure nor the life of pure intelligence] seems desirable to me, Socrates, and unless I'm very much mistaken, nobody else will think them so either.

Then does the life of intelligence show itself to be not "adequate" and therefore not the good? But is not the life of knowledge also the life of virtue -- i.e. if not, what becomes of the "soul", of Plato's "so long as we keep to the body" we cannot know the truth (Phaedo 66b-d) nor be bound to a life of virtue (Cratylus 403e-404a)? Can the soul, once freed of the body, experience pleasure or pain? Should one say that shame is an example of the soul's suffering pain? We have expressions such as "the pleasures of the mind" [cf. Philebus 32c]. -- Is what we are doing here no more than connecting up (and disconnecting) concepts? -- But I don't think that kind of pleasure and pain is what Protarchus has in mind.

22a - PROTARCHUS: Anybody, I imagine, will prefer this mixed life [of pleasure and intelligence] to either of those [alone]. Indeed, I will go further: everybody will.

I wonder if Protarchus was correct. Would I not prefer the "life of reason" -- i.e. intelligence without pleasure -- to my present existence? "When a man reaches a certain age, he no longer has many pleasures ..." (Silone's story, after the earthquake). And the few he has he might well be willing to exchange for virtue. Is the loss of pleasure the only reason why a old man wants to die? Wittgenstein, for one example, me for another. Or is it simply that one becomes disillusioned (not the least with oneself), tired, weary. I don't think it's a question of pleasure at all, but maybe of seeing what the good is for man more clearly at an older age (cf. "It seemed to him at that moment that it would have been quite easy to have been a saint"), that he highest good, the excellence most proper, for man is the life of reason.

22b - SOCRATES: Then surely it is obvious by this time that, if you take these two lives [i.e. one of pleasure alone versus one of intelligence alone], neither of them proves to contain the good. If it did, it would be sufficient ["adequate"] and complete ["perfect"] and desirable for ["sought after by"] all plants and animals that had the capacity of living their lives under such conditions from start to finish, and if any of us preferred something else, he would be mistaking the nature of what is truly desirable ... as the result of ignorance or some sort of unhappy necessity.

22d - For as to the cause that makes this combined life [of pleasure and intelligence] what it is, very likely one of us will say it is reason, and the other pleasure, so that while neither of the two would, on this showing, be the good, one of them might very possibly be that which makes the good what it is.

23c - [Plato is now going to argue that what "makes this combined life what it is" is reason rather than pleasure.] Let us try to be very careful with what starting point we take [i.e. with which divisions of the "one" we choose].... Of all that now exists in the universe let us make a twofold division, or rather, if you don't mind, a threefold.

PROTARCHUS: Of what principle, may I ask?

SOCRATES: We might apply part of what we were saying a while ago.... We said, I fancy, that God had revealed two constituents of things: the unlimited and the limit. [The allusion to a god here is significant, because Plato is not going to argue that human reason (e.g. his own) is the good but that "the true, divine reason" is (22c).]

23c-d - Then let us take these [i.e. "the limited" and "the limit"] as two of our classes, and, as the third, something arising out of the mixture of them both .... [Indeed, Plato adds a fourth class, however: that which is the cause of the mixing of them with each other.]

24a-d - [Plato gives the example of the words 'hotter' and 'colder' and says that these kinds of things have "more" and "less" actually resident in them -- i.e. that they are not limited: it can always be hotter or colder] ... this pair is always without bounds [i.e. unlimited], and being boundless means, I take it, that they must be absolutely unlimited.... Once you give definite quantity to "hotter" and "colder" they cease to be; "hotter" never stops where it is but is always going a point further, and the same applies to "colder", whereas definite quantity is something that is stopped going on and is fixed. It follows therefore from what I say that "hotter", and its opposite with it, must be unlimited.

24e-25a - When we find things becoming "more" or "less" so-and-so ... we ought to reckon them all as belonging to a single kind, namely, that of the unlimited; that will conform to our previous statement ... that we ought to do our best to collect all such things as are torn and split apart and stamp a single character on them.

26c - Now add to ['hotter' and 'colder' the pairs] 'drier' and 'wetter', 'higher' and 'lower', 'quicker' and 'slower', 'greater' and 'smaller', and everything ... belonging to the kind of being which admits of "the more" and "the less".

What is this "stamping" except to define a class-name? And what is the class 'unlimited' other than: all things that require a sliding scale without limits at either end? But are we talking about "things" or concept-words here? Well, are not hot and cold features of reality -- i.e. facts? Perhaps, but the sliding scale -- i.e. the rules for measurement -- are not: they are a conception of the facts (concepts not percepts).

25a-b - Then things that don't admit of these terms, but admit of all the opposite terms like 'equal' and 'equality' in the first place, and then 'double' and any term expressing a ratio of one number to another [-- But doesn't 'ratio' mean 'fraction'? But 3/8 = 6/16 = 12/32 -- i.e. is there not unlimited here as well as limited? --], or one unit of measurement to another, all these things we may set apart and reckon ... as coming under the limit [i.e. as belonging to the class titled 'limited' or 'bounded'].

26d - [This Plato calls "the family of the unlimited", but he says that they omitted to collect the family that shows the character of limit; and "the family of the limit" (25e) is that of 'equal' and 'double' and any other term which puts an end to the conflict of opposites with one another, making them well-proportioned and harmonious, by the introduction of number.]

Plato is doing something like "philosophical grammar" here, a grouping of our words into parts of speech, of which one would be limit-words and another unbounded-words. But what is he making clearer here -- that is not simply clarity in the J.L. Austin sense? Plato is not here pointing out parts of speech as an end in itself, but rather as an element of his argument. In the Philebus Plato is doing -- or trying to do -- philosophy, not linguistics (Austin) nor logic-of-language (Wittgenstein).

25b-26b - Now what description are we going to give to number three, the mixture of these two [i.e. of (1) the unlimited and (2) the limit]?... In the case of sickness does not the right association of these factors bring about health?... And then again, if they are introduced by very severe cold and stifling heat they remove all that is excessive and unlimited, and create measure and balance.... Then it is here that we find the source of fair weather and all other beautiful things, namely in a mixture of the unlimited with that which has limit.

26b - And indeed there are countless more things which I may omit to enumerate, such as beauty and strength along with health, besides a whole host of fair things found in our souls ... [because] the lawlessness and utter wickedness of mankind [is] due to the absence of limit in men's pleasures and appetites, and therefore [the god] established among [men] a law and order that are marked by limit.

26c - PROTARCHUS: You are asserting, I gather, two factors in things -- first the unlimited, second the limit. But I can't altogether grasp what you mean by the third thing that you mention.

SOCRATES: The reason for that ... is that you are confused by the multiplicity of that third kind. And yet a plurality of Forms was presented by the unlimited too, and in spite of that we stamped on them the distinguishing mark of "the more" and its opposite, and so saw them as a unity.

If no one has assigned a name [which we inherit when we learn language] to a multiplicity, we may fail to see in that multiplicity any unity at all (whether that "unity" amounts to a common nature or only to various resemblances); and contrary-wise: if a name has been given to a multiplicity we will mistakenly assume there must be an essence (a common nature) in the multitude.

It is remarkable that we ourselves almost never invent new concepts [A new concept is a new classification scheme]; we use the concepts -- normally quite thoughtlessly, lazily -- that are current currency [CV p. 74], almost never breaking out of the grooves in which our thinking and perceiving run [Z § 349]. We see what our language has taught us to see. Facts [cf. conceptualized percepts, statements of fact], if not theory-laden, are at least concept-laden.

26d - And now as to the third kind, I am reckoning all this progeny of our two factors as a unity, and you may take me to mean a coming-into-being, resulting from those measures that are achieved with the aid of the limit.

26e-27a - We said that besides the three kinds there is a fourth kind to be considered ... Now I expect you regard it as necessary that all things that come to be should come to be because of some cause.

PROTARCHUS: Yes, I do. Without that how could they come to be?

SOCRATES: Well, is there anything more than a verbal difference between a cause and a maker? Wouldn't it to be proper to call that which makes things and that which causes them one and the same?... And further, shall we find that between that which is made and that which comes to be there is, once again, a mere verbal difference?

By his agreement, what does Protarchus agree to? It is not merely that every effect has a cause (which is a tautology, or, rule of grammar), but that every event has a cause (which is a proposition, or, statement of fact, "by no means arbitrary, but subject to contradiction," as Pascal wrote). According to Plato, does every event necessarily have a cause -- but what kind of necessity is this? (It appears to be a Thomist first principle.)

Is it correct or incorrect to say that we believe in the uniformity of nature -- i.e. that things don't "just happen" but happen for reasons [causes] displaying regularity that can be expressed in laws of nature? (Maybe the physicist would not agree with our naive view.)

[In 27a Plato distinguishes between a cause and that of which it is the cause -- i.e. between a cause and its effect: "a cause and that which, as a condition of coming to be, is subservient to a cause".]

27b-c - But now that the four kinds have been discriminated it will do no harm to enumerate them in order, so that we may remember each by itself.... The first, then, I call the unlimited, the second the limit, and the third the being that is come to be by the mixture of these two; as to the fourth, I hope I shall not be at fault in calling it in cause of the mixture and of the coming-to-be?

PROTARCHUS: No indeed.

Plato has with three and four designated (pointed out) two unities found in multiplicities -- neither of which has a common-name (26c). Or in other words, two as yet un-named Forms.

27c-d - Then shall we perhaps be in a better position, now that we have discriminated these kinds of things as we have, to achieve our decision about [what occupies] the first place and the second [place, after the best form of life itself]? For that of course was what we started to dispute about.... Come on then. We laid it down, I think, that victory went to the mixed life of pleasure and intelligence ... [which] is a part of our third kind [i.e. of] all unlimited things bound fast by the limit ... Come along now, what is our next point, and what was our purpose in getting where we have got? Wasn't it that we were trying to find out whether the second prize should go to pleasure or to intelligence?

27e-28a - [Plato says that the character of pleasure is of being unlimited, as is the character of pain. Both are unlimited.] ... hence we must look for something other than the character of being unlimited to explain how an element of good attaches to pleasures. [But Plato drops that topic as "one of unlimited speculation".]

28a - [Plato asks whether, "without sinning against the light", we should reckon intelligence, knowledge and reason to belong to the unlimited class or to the limited (or, bounded) class.]

28c-d - But really it's an easy question. For all the wise agree ... that in reason we have king of heaven and earth. And I fancy they are right. But I should like us, if you don't mind, to make a fuller investigation of the kind in question itself.... Are we to say, Protarchus, that the sum of things or what we call this universe [Sophist 233e-234a] is controlled by a power that is irrational and blind, and by mere change, or on the contrary to follow our predecessors in saying that it is governed by reason and a wondrous regulating intelligence?

28e - PROTARCHUS: To maintain that reason orders it all does justice to the spectacle of the ordered universe, of the sun, the moon, the stars, and the revolution of the whole heaven ...

Here, if I am not mistaken, Plato makes the mistake of attributing the character of parts to the character of the whole. There may be laws of physics which apply to some events or processes, but need one regard the "the whole world" as if it were itself an event or process? (And then, there is also the matter of why everything functional is also dysfunctional. If "the world" is very well-governed, it is also very ill-governed. Even in "the ordered universe" the rains that nourish the crops also flood and wash them away.)

30a-b - ... for surely we cannot suppose, Protarchus, that those four kinds, [2] limit, [1] unlimited, [3] combined, and [4] cause, which is present in all things as a fourth kind -- we cannot suppose that this last-named, while on the one hand it furnishes the elements that belong to our bodies with soul ... has nevertheless failed in the case of the elements of the universe [i.e. has failed to give the universe a soul as well as a body, as it has done with man].

PROTARCHUS: No, to suppose that would be utterly unreasonable.

Is that our question here: whether or not it is reasonable ... but in which sense of 'reasonable'? And from 'It is reasonable', does 'It is true' follow?

[30a-b - Plato asks where our bodies could have gotten a soul "if the body of the universe, which has elements the same as our own though still fairer in every respect, were not in fact possessed of a soul", a soul being the "fairest and most precious" thing there is.]

Is Plato's notion here like the doctrinaire proofs of the nature of God based on the principle that "No one gives what he doesn't have"? If God did not have reason, he could not have endowed mankind with it. That principle seems equivalent to Aristotle's "doctrine that what causes or generates something else must be formally identical with its product: only what is hot can generate heat, only a man can beget a man (Physics 257b9, 202a11)" (W.K.C. Guthrie, Plato: the man and his dialogues: earlier period (1975), p. 186). But maybe it isn't, because Aristotle's notion seems to exclude creation: if God must be hot to generate heat, then he must also be cold to generate cold, but that would imply a contradictory essence; therefore, God did not generate heat and cold. When Plato speaks of a "cause" in 30c, what is this cause if not what everyone calls 'God'?

[That does not entail the Scholastic generation "out of nothing", but implicit here is Xenophon's statement about Socrates: "For, like most men, indeed, he believed that the gods are heedful of mankind" (Memorabilia i, 1, 19); and if the gods are "heedful", then they are causes (cf. Sophist 255c-d), and if there is a "world soul" then it is the most heedful thing of all.]

30c - [Plato asks if there is not a cause] which orders and regulates the years, the seasons, and the months, and has every claim to the names of 'wisdom' and 'reason'.... But wisdom and reason cannot come into existence without a soul.

PROTARCHUS: They cannot.

How can ugly parents give birth to a beautiful child? How can an acorn, which has no leaves, give birth to a tree which has? Plato may have answers to such questions; they are not, however, obvious answers. And the meaning (for does not the 'meaning of a notion' include the notion's logical implications?) of Aristotle's notion is not obvious either.

The notion of a "world soul" seems to be dependent on the notion of "the world" -- or universe (a multitude [many] which is also a unity [one]) -- which the Eleatic visitor explains in Sophist 233e-234a; well, is 'the world' nonsense (and if it is, then why does it seem to us that we understand its meaning)? Is Plato not anthropomorphizing the regularity of nature? He sees a pattern or an order and makes an analogy from it to the patterns or orders which are the product of human wisdom and reason. How can the universe give man a soul if it does not possess a soul itself? How can what does not have motion impart motion? Does not a magnet impart motion [to particles of iron] without itself having motion? How can someone who does not love inspire love in another? Cannot such a person be called the cause of that love?

The notion is vague (not at all clear) -- what is the principle here: "Nothing causes in another what it does not possess in itself"? What is the logical [i.e. grammatical] status [i.e. meaning] of that principle -- i.e. what type of possibility-impossibility does it express? It does seems that rationalism, Plato's imagination, is allowed to run wild here.

30d-e - ... reason always rules all things.... mind belongs to the family of what we called the cause of all things.

31a - Then let us have these points in mind about the pair of them, namely that reason was found akin to cause and belonging, we may say, to that kind, whereas pleasure is itself unlimited ...

Reason does not belong to the class of the limit but instead it is the cause of the mixture of the limit with the unlimited. Is not reason what imposes the limit? But Plato only says the reason is "akin" to the cause?

31c - ... both pleasure and pain are natural experiences that occur in the "combined" class.... Let us understand 'combined' as the third of our four classes.

31b - ... we shall never be able properly to examine pleasure apart from pain.

[31d ff. - Plato likens pleasure to the restoration of harmony and pain to the disturbance of harmony.] 32a-b - Now consider whether this statement is satisfactory, which puts the thing in a general formula. When the natural state of a living organism, constituted, as I have maintained, of the unlimited and the limit, is destroyed, that destruction is pain; conversely, when such organisms return to their own true nature, this reversion is invariably pleasure.

Is the natural state of an organism hunger or lack of hunger, thirst or lack of thirst? Desire or lack of desire? Desire does seem to be the human organism's natural state. Recall that in Xenophon Socrates has said that they are most like the gods who have the fewest wants (Xenophon, Memorabilia i, 6, 10; cf. Diog. L. vi, 104). Would Socrates have accepted that a life without pleasure is not worth living (Philebus 21d-e)? I wonder if a life without pleasure, were it also without pain, would not be a "pleasant" life? Is not equilibrium pleasant, particularly in old age?

I want to say: all we are doing here is playing with words: these concepts are fluid and therefore we can manipulate them in most any way that we want: it is a matter of how you want to look at things, of a point of view (as one does when saying that everything a human being does is an act of selfishness -- yes, you can look at the facts that way, characterize them that way, but don't mistake your characterization for a statement about how things "really are". A point of view is not a truth.

32c - [This is somewhat apropos of "pleasures of the soul" (21e).] PROTARCHUS: ... that is a different kind of pleasure and pain, which belongs to the soul itself, apart from the body ...

33b - PROTARCHUS: Certainly it is not to be supposed that the gods feel either pleasure or its opposite.

SOCRATES: No, of course it is not; it would be unseemly for either feeling to arise in them.

But if such a life is not worth living for a man, then what makes the life of the gods' worth living? Do not they live a life of reason alone? Or is that the excellence appropriate to their nature, but not to the nature of man?

35c-d - [Plato concludes that] desire does not belong to the body.... Our discussion then, inasmuch as it has proved that memory is what leads us on to the objects of our desire, has made it plain that it is to the soul that all impulse and desire, and indeed the determining principle of the whole creature, belong.... Then there can be no gainsaying that our bodies cannot possibly feel thirst or hunger or anything of that sort ...

If our bodies could, it would make sense to say that a corpse was hungry or thirsty. But what are such remarks if they are not grammar? It makes sense to say; it does not make sense to say -- how does this add to our knowledge of anything (other than perhaps of the meaning of the language we speak)? A body cannot feel thirst -- what kind of impossibility is this?

36c-d - SOCRATES: Shall we say that these pains and pleasures are true or false? Or that some are true, and others not?

PROTARCHUS: But how, Socrates, can pleasures or pains be false?

SOCRATES: How can fears be true or false, Protarchus? Or expectations, or opinions?

PROTARCHUS: For myself, I should be inclined to allow it in the case of opinions, but not in the other cases.

Pleasure that has the consequence of future pain is nonetheless [still classified as] pleasure; an expectation that an event will occur that does not is nonetheless an expectation. When in English we speak of "false expectations" or "false hopes", the 'false' applies to what is expected or what is hoped for, not to the expectation or hope itself.

Those are grammatical remarks, nothing more, a description of our concepts, or in other words, an account of the rules for using our concept-words (such as 'pleasure' and 'expectation'). But suppose one says, Yes, but on the other hand, grammar [our actual conventions -- as opposed to any fictitious language games we may invent in philosophy -- our forms of life] belongs to our natural history (PI § 415). And so, then, if Plato is clarifying our concepts (the way we use words), is he also clarifying (writing down) our natural history?

But is this anything more than our linguistic natural history? What is the relationship between our language and the world we use language to talk about -- that is, does it follow from our having such and such concepts that those concepts have their foundation in the nature of our world? And, therefore, is Plato telling us something about pleasure, or only about how we use the word 'pleasure'? Is 'pleasure' the name of something (or some collection of things) -- as 'cow' is the name of something? Or is it some other type of name of a "thing"? (I ask this question over and over again, but I find no simple answer to it; it is possible to be interested in a phenomenon from a variety of points of view (ibid. § 108): e.g. How do we use the words 'pleasure' and 'pain'? What is "the nature of human pains and pleasures" [empirical psychology]? The fundamental mistake in philosophy is to allow an investigation to oscillate between a grammatical and an empirical one (ibid. § 392 ["Let me try to see if I can think without words" versus "What do we call 'thinking without words'?"]); that is a sure way of never getting clear about anything.)

37b - SOCRATES: The question then must faced, how it is that whereas we commonly find opinion both true and false, pleasure is true only, and that though [i.e. despite the fact that] in respect of reality holding an opinion and feeling a pleasure are on the same footing [i.e. both are real, or, features of reality]. [In 37b Plato says] The subject feeling pleasure ... will obviously be always in the position of really feeling a pleasure [just as someone who holds an opinion is always in the position of really holding an opinion (37a)].

"... pleasure is true only." -- Plato imagines that with this he is making a statement of fact (or alleged fact) about pleasure. Plato seems to reason that what is real can also be unreal: one can enjoy something or not enjoy it. And he equates what is real with what is true, and what is unreal with what is false. But if he is going to make that "rule of grammar" -- and what else would he be doing except telling us how to talk? --, then he will have to say that someone who does not enjoy himself has false pleasure.

But what Plato suggests is contrary to normal usage, which is that one cannot have a "false toothache" (and therefore neither can one have a "true toothache"; cf. PI §§ 289, 381). You cannot (this is grammatical-logical possibility) be mistaken about whether or not you are experiencing pleasure, but you can be mistaken in your belief (expectation) that such-and-such is going to happen, and you can be mistaken in your belief (opinion) that such-and-such proposition is true or false. (By 'false pleasure' Plato seems to mean what everyone calls 'taking pleasure in what is harmful'.)

"... pleasure is true only." -- This is an example of what Wittgenstein called "an unsuitable form of expression" -- i.e. one that keeps us in a state of confusion (PI § 339). Plato reasoning is an example of following a misleading grammatical analogy.

37e-38a - SOCRATES: Now look here, I fancy we often experience pleasure in association with an opinion that is not right, but false.

PROTARCHUS: Of course, and then, that being so, Socrates, we call the opinion false, but the pleasure itself nobody could ever term false.

Plato-Socrates makes an empirical statement, and then Protarchus makes a grammatical statement. Plato imagines that he is saying something about reality, but he is only making rules of grammar that are contrary to our usual ones; Protarchus reminds him of how we use our language, but instead he also imagines the he is saying something about reality. Is this an example of what Wittgenstein called "obliterating the distinction between factual and conceptual investigations" (Z § 458)? Plato tries to "express by the use of language what ought to be [i.e. must be] embodied in the grammar" (PP iii, p. 312) of the language, but in fact is not.

38-39 - [Plato describes "a man" who "sees objects that come into his view from a distance and indistinctly [and] wants to decide what he sees. Then the next step will be that he puts a question to himself" (38c). And then in 39 Plato compares this ["the book being written in us"] -- he contrasts it with a painting: "A painter, who comes after the writer and paints in the soul pictures" (39b). Protarchus asks how and when this painter paints. "SOCRATES: When we have got those opinions and assertions clear of the act of sight, or other sense, and as it were see in ourselves pictures or images of what we previously opined or asserted. That does happen with us, doesn't it?" (39b-c) "Then are the pictures of true opinions and assertions true, and the pictures of false one false?" "PROTARCHUS: Unquestionably." (39c)]

[Again, a picture which portrays what is not the case (i.e. what is false) is nonetheless a picture. Plato is trying to force a false grammatical account on the reader, but our knowledge of the language we speak rebels against this. (If there is a question of fact here, it is of facts about the grammar of our language, not about the nature of opinions and assertions, although there are such "things".) However, the only sensible reply to Plato is: well, if you want to talk that way; but that is all that you are doing -- i.e. changing the rules [definitions] according to which we talk meaningfully.

39b-41a - SOCRATES: [Plato gives an example of a false pleasure.] People often have visions [painted by the painter, who in this case seems to be imagination running wild or day-dreaming] of securing great quantities of gold, and pleasure upon pleasure in consequence; indeed they behold themselves in the picture immensely delighted with themselves.... Hence we reach the result that false pleasures do exist in men's souls, being really rather a ridiculous imitation of true pleasures, and the same applies to pains.... Then neither can we detect any other sense in which pleasures are bad, save in that they are false.

PROTARCHUS: No, Socrates, what you say is just the opposite of the truth. Surely it is not at all because they are false that we set down pains and pleasures as bad, but because they involve some serious and considerable badness of another sort.

But Plato drops Protarchus's idea as extraneous to his present argument, and says that we must rather "discuss those false pleasures" now. Is Protarchus alluding to "moral good" as opposed to Socrates' "virtue is knowledge" and "the good is what is useful [beneficial]"? He need not be, because a pleasure that has consequences that are not beneficial either in practical matters (including health) or the "care of the soul" are to be adjudged bad (i.e. to be avoided). I do not know why Plato does not want to go in that direction, which seems to be the Socratic and indeed common sense one.

42c - ... we shall discern pleasures and pains in living beings that appear false and are false ...

43c-d - ... let us recognize three sorts of life, the pleasant, the painful, and that which is neither one nor the other.

44a-b - Then are we to take the line that these things are three in number, as we said just now, or that there are only two, pain being an evil for mankind, and release from pain being called pleasant as in itself a good?

44d-e - If we want to see the true nature of any Form, whatever it may be, for example that of hardness, should we understand it best by fixing our attention on the hardest things that are or on those that have a minimum of hardness?

44e-45a - Then if the Form or Kind whose true nature we wanted to see were pleasure, we should have to fix our attention not on minimum pleasures but on such as are said to be the highest and intensest.

PROTARCHUS: Everyone would agree with what you say now.

No, not everyone. Plato assertion here is certainly not true, because if we want to understand the grammar of the word 'pain' (our concept 'pain'), we shall have to consider not only intense and perhaps of short duration pains, but also dull (weak) but perhaps persistent pains. If we want to understand a concept we must examine the whole range; but perhaps Plato is here imagining that a Form necessarily has an essence ("true nature") rather than mere resemblances among its exemplars. Is there an essence of pleasure? Is there an essence of hardness (resistance to pressure) -- i.e. can you say: if we want to understand our concept 'hardness' we shall have to look (or, examine) at it in all its varieties, not in just its most intense (or, maximum) Forms? Plato makes a comparison between two concepts, but it is it persuasive (because is that not all that an analogy can be: If A is like B in such-and-such respects, then A is like B in such-and-such respects -- i.e. there is no additional "therefore")?

45c - We must, as we said, understand the true nature of pleasure, and what account they give who maintain that there is no such thing at all [pleasures simply being the absence of pain in their view].

"... the true nature of pleasure". -- 'What is the nature of pleasure?' versus the question 'How do we use the word 'pleasure'? I wonder if this distinction is ever going to become entirely clear to me. But, on the other hand, there is an important distinction here, because if we ask the latter question, we shall not then make the mistake of asking for the "true nature" of pleasure or for what pleasure "really" is. And to ask such questions is a mistake, a misunderstanding of the logic of our language.

But can't we describe pleasures: can't we say many things about the nature of pleasure (both as a matter of insight [common observation, familiarity] and as a matter of experimental psychology)? Certainly, but what we cannot say is what "pleasure really is" because that [i.e. 'what pleasure really and truly is'] is a nonsensical (i.e. undefined) combination of words.

Are we saying that 'pleasure' is the name of something, or of many somethings -- i.e. is the word 'pleasure' a name (or does it have some other use in our language?) It is a class- or category- or common-name, surely? And if it is not the name of something or of some things (phenomena), then how can we ask what the nature of pleasure is? "We are investing not the phenomenon [or phenomena] of pleasure, but the concept 'pleasure' and that means the use of a word" (cf. PI § 383). ["It is not a something, but not a nothing either ...". When we turn to philosophy as a guide to living, we should not forget the lessons of logic-of-language that we have learned.]

45d-e - PROTARCHUS: The temperate man, surely, is regularly restrained by the proverbial warning, "Never too much", and heeds it, whereas the senseless profligate is mastered by his extreme pleasure, which ultimately drives him insane ...

"Nothing too much" [or "Nothing in excess"] was inscribed at Delphi, as well as "Know thyself". (Protagoras 343b)

45e - SOCRATES: Right. Then if that (45d-e) is so, clearly the greatest pleasures, and the greatest pains too, occur not when soul and body are good, but when they are bad.

Plato asks: "Now are not our obvious pleasures, which are in fact by common admission the greatest [i.e. most intense], the pleasures of the body?" (45a) Again, but what of Beethoven -- i.e. of the enjoyment of music, or of tragedy and of comedy? Surely these are pleasures of the soul, and they are, I believe, as intense if not more intense than the pleasures of the body (sensuality, which indeed Plato calls a "mixed experience" (46a) of pleasure and pain).

47e - Anger, fear, longing, lamenting, love, and emulation, malice, and so forth -- don't you class these as pains of the soul itself [alone]?

"Know thyself" in the Philebus

48a-d - SOCRATES: [Plato speaks of a mixture of pain and pleasure ("bittersweet" mixture) (46c).] Now ignorance, or the condition we call stupidity, is an ill thing.... That being so, observe the nature of the ridiculous.... Taking it generally it is a certain kind of badness, and it gets its name from a certain state of mind. I may add that it is that species of the genus 'badness' which is differentiated by the opposite of the inscription at Delphi.

PROTARCHUS: You mean, "Know thyself", Socrates?

SOCRATES: I do. Plainly the opposite of that would be for the inscription to read, "By no means know thyself".

48d-49a - If anyone does not know himself, must it not be in one of the three ways [or, classes, or, divisions]?... By far the greatest number [of people] are mistaken as regards the third class of things, namely possessions of the soul. They think themselves superior in virtue, when they are not. [The first class is: mistaken about their wealth (finances); the second class: mistaken about their physical qualities (handsomeness). In all three ways men believe themselves to be in a better condition than they actually are].

49a - And is it not the virtue of wisdom that the mass of men insist on claiming, interminably disputing, and lying about how wise they are?

Augustine: he only errs who thinks he knows what he does not know. And we say this again and again to ourselves in philosophy. And yet forever this is our most common error, the error that Socrates avoided (Plato, Apology 22d-e).

49c - ... ignorance in the strong is hateful and ugly; it is fraught with mischief all around ... but [ignorance in the weak] ranks as the ridiculous ...

Is it wrongful to take pleasure in the misfortunes of our enemies?

49d - SOCRATES: Both pain and pleasure can be wrongful, I imagine?... And to delight in our enemies' misfortunes is neither wrongful nor malicious?

PROTARCHUS: Of course not.

SOCRATES: Whereas to feel delight, instead of pain, when we see friends in misfortune, is wrongful is it not?

If the good man harms no one: one must never return wrong for wrong, bad for bad (Socrates says in Plato's Crito 49b-d, and in Republic 335d-e), then how can Plato say that to delight in one's enemies' misfortunes is not harmful to one's soul? Cf. Gorgias 522c-e. [Compare the condemnation of the view expressed in Philebus 49d found in Matthew 5.43-44, Luke 6.27-28.] The good man does not hate, if 'hate' = 'wish harm to come to another'; to hate is what the evil man does. (Yes, the last proposition is a tautology: it only shows a way our concepts are "grammatically" inter-related. But to point out that inter-relationship is important, and, further, it shows that tautologies are not necessarily idle.)

Plato regards delighting in the misfortunes of our friends as an example of mixing pleasure (laughter) with pain (malice): "for we have been for sometime agreed that malice is a pain in the soul, and that laughter is a pleasure, and both occur simultaneously on the occasions in question" (50a).

50b - ... in the whole tragicomedy of life -- as well as on countless other occasions, pains are mixed with pleasures.

50d - ... the general principle [is that] we constantly come upon the mixture of pleasure with pain.... - 50e - Well, after the mixed pleasures we shall naturally go on in turn -- indeed we can hardly avoid it -- to the unmixed.

51b - [Of the unmixed pleasures Plato names, as examples, the pleasures] that attach to colors that we call beautiful, the figures [by which he means "something straight, or round, and the surfaces and solids which a lathe, or a carpenter's rule and square, produces from the straight and round" (51c)], to most odors, to sounds, and to all experiences in which the want is imperceptible and painless, but its fulfillment is perceptible and pleasant.

52a - Now let us proceed to add to them the pleasures of learning, if we do in fact think that they involve no hunger, that no initial distress is felt owed to a hunger for learning.

And if the pleasure of learning did in fact involve pain (hunger for learning), and was therefore not an unmixed pleasure, would not the pleasures of learning nonetheless be adjudged a good? Contra 45e.

52c - Well, we have reached the point of drawing a satisfactory line between pure pleasures and those that may with fair justification be called impure, and now let us add to our statement that those pleasures that are intense are marked by immoderateness, those that are not by moderation. Pleasures that can go to great lengths or to an intense degree, whether they actually do so often or seldom, let us class as belonging to that "unlimited" kind of which we spoke [23c ff.] ...

Some have said that the [intellectual] pleasures of Euclidean geometry belong to the "unlimited kind", that they are intense and "marked by immoderateness", even by occasional ecstasy.

52e - ... I will suggest a general method for the consideration of anything we call pure -- namely, that we should begin by examining one selected example. [The example Plato chooses is "whiteness". (53a)]

53b-c - I imagine we shall not need numerous examples of the same sort to make a pronouncement about pleasure, but are now in a position to realize that any and every sort of pleasure that is pure of pain will be pleasanter, truer, and fairer than one that is not whatever be their comparative bulk or quantity. [Pure white is found even in a small quantity of white unmixed with any other color rather than in a large bulk of impure (or, mixed) white. 'Pure white' is white "with no portion of any other color in its composition" (53a).]

Again Plato makes an analogy that may be false (i.e. A is not like B is such-and-such way). What if the majority of pleasures are of the "mixed" kind, then will we not understand our concept 'pleasure' better by examining those?

"Pure white" would be the essence of white; however, does it belong to the essence of white, that when white is mixed with red the mixture is pink? Perhaps not, but if you want to know about white, will you not also want to know its effect when mixed with other colors? One might say: but if you want to discover the essence of tin, you do not investigate bronze and pewter; no, you investigate tin in isolation ("pure tin"), not in alloys. But if there is an essence of white and an essence of tin -- is there also an essence of pleasure? This asks for a definition.

But we define -- learn to use and teach others to use -- the word 'pleasure' through examples, not by means of a verbal formula. But isn't that also the way we define the word 'white' -- by pointing to instances? But we do not point to pleasure or pain that way -- i.e. the way we point to white-colored objects. That model of definition breaks down if we try to apply it to an "internal object" such as pleasure and pain are often claimed to be. That is Wittgenstein's "beetle in a box" which might as well be nothing, because there is no criterion for identifying it (PI §§ 293, 304).

However, Plato does not take up that question here. And indeed it is not the intent of his analogy between whiteness and pleasure to say that they are necessarily alike in that way.

54b - [Plato here distinguishes between means and ends (54c), the end being the reason (justification) that the means are employed.]

PROTARCHUS: Are you asking me something of this sort -- "Tell me, Protarchus, do you maintain that ship-building goes on for the sake of ships, rather than that ships are for the sake of ship-building?" -- and so on and so forth?

SOCRATES: That is precisely what I mean, Protarchus.

54c - Then there must be some being with a view to which pleasure comes to be, if it is true that pleasure is becoming.... But where there is this regular relation of means to end, the end falls under the heading of good, while the means ... must find a place under another heading.

Well, I don't know about that. It seems to imply that bad means my be used toward a good end. But if the only right acts are good acts [i.e. if we should only ever do what is good], then that cannot be correct.

When we speak of the pleasures of the body, we speak of "fleeting pleasures" -- and hence we can say that "pleasure is becoming"; however, when we speak of the pleasures of the mind (of learning e.g.), should we say that those are becoming (rather than being)? It must also be observed that we often do things that we find pleasant for their own sake, not as a means to an end -- that is, we often do regard "becoming" as falling under the heading of good. (And some things can only be enjoyed as "becoming" [i.e. not in contemplation of static "being"], music e.g.)

54d - Hence if pleasure is becoming, we should be right in setting it under some other heading than that of good?

55a - ... we should all admit that the opposite of becoming is passing away.... Hence it is an alteration of passing away and becoming [e.g. of thirst quenched by drink, hunger by food (54e), taking pleasure in the relief of pain] that will be chosen by those who choose a life like that in preference to the third life we spoke of, the life that included neither pleasure nor pain, but the purest possible activity of thought.

If pleasure were the good for man, then the best of good men would be the man who felt the most pleasure

55b - [Plato says that if pleasure were the good, then one who felt pleasure would be made better (i.e. good) by experiencing pleasure, whereas one who felt pain would be made evil by feeling pain.] Surely it is untenable [that] it should be pleasure alone that is good, not courage nor temperance nor reason nor any of the goods proper to [the] soul ...

If pleasure were the good, then those who enjoyed the most pleasure would be the best (most good) of human beings. That, however, does not appear to be the case. The question is: "What is the logical-grammarian to say?" What do we mean by 'the good' -- is the good that which makes a person good, 'makes' in the sense of 'if you do this, then you are good', and that is what we mean by 'good'? When Socrates in Xenophon says that "the good = the useful", it is clear what he is saying -- namely, that courage, temperance and reason are more useful [beneficial -- i.e. they do make him more good] to a man than their opposites. But do we mean by a 'good man' one who is useful to himself (and to his companions)?

55c - [Plato says that now having dealt with pleasure what he wants to do is to test reason and knowledge to find their purest Form or to "detect what is really the purest element in them".]

55d - Now we may, I think, divide the knowledge involved in our studies into technical knowledge, and that concerned with education and culture, may we not?

Plato here seems to make a distinction between applied and pure sciences -- i.e. between those done for the sake of some end (such a ship-building) versus those which are not. What distinguishes an art (or, science) is that it makes use of (some form) of measurement, of number, as e.g. in the building of ships and houses. "It employs straight-edge and peg-and-cord, I believe, and compasses and plummet, and an ingenious kind of set-square" (56b-c). The more exact an art is (56c), the less uncertainty it involves (56a), the "more closely [it is] concerned with knowledge ... so that we are justified in regarding [such an art] as the purest" and the other arts as relatively impure (55d). [Euthyphro 7b-c gives counting, weighing, and measuring as examples of sure standards of judgment.] As Plato sought "pure pleasure" (53a), he now seeks "pure knowledge", asking "whether one kind of knowledge is purer than another, just as one pleasure is purer than another" (57a-b).

56d-e - SOCRATES: [But with respect to] numbering or arithmetic, ought we not to distinguish between that of the ordinary man and that of the philosopher?

PROTARCHUS: On what principle, may I ask, is this discrimination of two arithmetics to be based?

SOCRATES: There is an important mark of difference, Protarchus. The ordinary arithmetician, surely, operates with unequal units; his "two" may to be two armies or two cows or two anythings from the smallest thing in the world to be biggest, while the philosopher will have nothing to do with him, unless he consents to make every single instance of this unit precisely equal to every other of its infinite number of instances.

PROTARCHUS: Certainly you are right in speaking of an important distinction among those who concern themselves with number, which justifies the belief that there are two arithmetics.

Physics versus Mathematics

"Pure arithmetic" would be concerned only with the rules of arithmetic, not with their application to things in the world (not with counting water drops e.g., where one water drop plus one water drop does not result in two water drops but instead only in one; here 1 + 1 = 1, and some call (or, classify) that a proposition belonging to physics rather than to mathematics, the difference being that propositions of physics are testable hypotheses, whereas the mathematical proposition '1 + 1 = 2' is not). But what do we mean by 'pure arithmetic' [or, if there is anything so-named, 'pure physics'] -- is it not something like chess?

I do not think that Protagoras, who criticised the geometers by saying e.g. that a "circle does not in actual fact touch a ruler at one point only", would have accepted the notion that there are two geometries, one "pure" and one of this world. But why not? He would not have accepted is that 'pure' = 'not of this world' or 'supra-sensual', the gods (or, what is divine) being something about which he refuses to speculate (Theaetetus 162d-e); he would not have accepted that "pure geometry" is knowledge. Would he not, however, have regarded it as a game played according to strict rules, with no subject matter external to the itself, as in chess?

56e-57a - SOCRATES: Then as between the calculating and measurement employed in building or commerce and the geometry and calculation practiced in philosophy -- well, should we say that there is one sort of each, or should we recognize two sorts?

57b-c - ... did [our discussion] not first mention a certain art under one single name, making us think it was really one art, and then treat it as two, putting questions about the precision and purity of those two to find out whether the art as practiced by the philosopher or by the non-philosopher was the more exact?

57c-d - [Protarchus states that the arts] which involve the effort of the true philosopher are, in their use of measure and number, immensely superior in point of exactness and truth.

The geometry of proofs derived from axioms may be extremely exact, but it may not be true when compared to the world we live in. Only by regarding it as something better-worldly can Plato say that the geometry of the philosopher is "superior in truth" to the geometry of the carpenter.

57e - SOCRATES: But we, Protarchus, are likely to be repudiated by the art of dialectic, if we prefer any other to her [as being "pre-eminently exact"].

If dialectic is knowledge, are there two kinds of dialect, one pure, one applied, the former being more exact and therefore purer than the latter? But what would examples be? Would the latter be "discussion without an account", such as the observations of poets or dramatists (or even the "remarks" of Wittgenstein's, when such remarks are isolated) as opposed to the discussions of the philosopher which consist of a line of reasoning; an account is a justification, and in Plato this takes the form of an argument. The dialectic of the philosopher ought to consist of "conclusive and irrefutable proof" ... but in philosophy the only necessity is logical necessity (and logical possibility is not the same as real possibility) if philosophy takes pure mathematics (arithmetic and geometric proofs) as its model. The dialectic of the philosopher has as its aim, for Plato, "perfect truth" (59a-b) -- i.e. truth not subject to change, but permanent, "the eternal truths" which answer the eternal questions.

58b-d - [Socrates explains to Protarchus that] What I wanted to discover at the present ... was not which art or which form of knowledge is superior to all others in respect of being the greatest or the best or the most serviceable, but which devotes its attention to precision, exactness, and the fullest truth, though it may be small [just as a sample of pure white may be small (53a-b)] and of small profit [use, or, benefit] -- that is what we are looking for at this moment. What you must is consider -- and you won't give offense to Gorgias [if you assign to this other art (procedure) the] property of possessing paramount truth ... -- what you must consider is, whether the art we have in mind may reasonably be said to possess in fullest measure reason and intelligence in their purity, or whether we ought to look for some other art with a better claim.

In 58a-b Protarchus has alluded to Gorgias, who on many occasions has said "that the art of persuasion was greatly superior to all others, for it subjugated all things not by violence but by willing submission, and was far and away the best of all arts ..." In Gorgias 454e ff., rhetoric is characterized as a practice of one who does not know what he is talking about persuading others to "belief without knowledge", to belief in what may well be false. It contrasts with dialectic (philosophy).

58d - But if there is a certain faculty in our souls naturally directed to loving truth and doing all for the sake of truth, let us make a diligent search and say what it is ...

59a - [Socrates asks Protarchus if it does not occur to him that] the majority of arts, as also those who are busy therewith, are in the first place concerned with opinion and pursue their energetic studies in the realm of opinion? And are you aware that those of them who do consider themselves students of reality spend a whole lifetime in studying the universe around us, how it came to be, how it does things, and how things happen to it?... Then the task which such students among us have taken upon themselves has nothing to do with that which always is, but only with what is coming into being, or will come, or has come.

By "the realm of opinion" Plato means the realm of mere appearances. Plato's philosophy, on the other hand, seeks the "the unchanging reality behind the changing appearances" -- that reality is the realm of truth. And that is metaphysics: what is real ("the world of appearances") is not really real but instead something else is. This is Drury's fact and theory distinction: "Reality which lies before us at every moment is replaced by the abstract picture we have ourselves created". And that is what Plato's supra-sensual Forms are: his own creation. On the other hand, Plato believed that only what is permanent (unchanging) can be "paramount truth", and if this permanent something cannot be perceived then, as Parmenides had taught ["What is unchanging can only be known by reasoning about it: it cannot be perceived"], it must be reasoned to (and the art concerned with reasoning to it is called 'dialectic' or 'philosophy').

Wittgenstein: "Look at the word 'game' as a tool that has uses in our life" (PI §§ 421, 360). But suppose someone said, I don't want to look at games that way. Games are a feature of reality, are they not? And I want to know what their common nature -- or "Form" (which is eternal, unchangeable) -- is. And, further, if I do not know that, then I do not know what games are. (And I will have to admit my "Socratic ignorance": that I am unable to give an account of what I know to others, and that therefore do not know. Nor do I think I know what I don't know.) Or, if it is that case that there really is no common nature, then neither should there be a common name -- and therefore the word 'game' should be retired/withdrawn from the language. And what applies to 'game' also applies to ethical terms (such as 'piety' discussed in Plato's Euthyphro).

In Plato's view Wittgenstein's investigations belong to the realm of opinion rather than knowledge, just as in Wittgenstein's view Plato's doctrines belong to the realm of fantasy. But one must, I think, ask why Plato asked for common-natures (or Forms); it won't do to say: ah well, that is merely because he did not understand the logic of our language. (Plato's "why" is different from the "why" of Socrates: I do not think you could say that Socrates sought common-natures because he thought they were "paramount truth" but simply because they were, he believed, a requirement of clear thinking, which is of course required if we are to discover the truth. [Socrates' Logic of Language])

And why should a human being be concerned with "that which always is"? Is it not because "here we find no continuing place": we are all going to leave this world, and if our soul does not face oblivion when the body dies but is instead eternal ("immortal", and in that respect unchanging), then it is with eternal things and not with the transitory (changing) things of this world that man should concern himself. (That is said to be the "Medieval view" of life in this world, or as Schweitzer would have said, the world-view of world-and-life-negation. Was Augustine's view also that of Plato's in this context?)

Then there is a way of drawing that is metaphysical. -- "Seen with the eternal as background" [cf. Wittgenstein, Notebooks 7.10.1916] one might say. (CV (1998 rev. ed.) [MS 137 88b: 4.11.1948]

In Tractatus Logico-Philosophicus 6.45, "The world seen sub specie aeterni is [the world seen as a limited whole, and the world seen as a limited whole is [that the world exists is (6.44)]] the mystical" -- and thus "mystical" = "metaphysical", I think. If we do not see Plato in this light, but only in the light of logic-of-language (as essential as that is), we do not see him correctly.

59a-b - [Plato asks if we can] say that any precise and exact truth attaches to things, none of which are at this present, or ever were, or ever will be free from change?

PROTARCHUS: Of course not.

SOCRATES: And how can we ever get a permanent grasp on anything that is entirely devoid of permanence?

PROTARCHUS: Nohow, I imagine.

SOCRATES: It follows then that reason too, and knowledge that gives perfect truth, are foreign to them.

It is Protarchus's "of course not" that perplexes me; I cannot see that Plato has demonstrated it to be true (and in fact, if it is affirmed, it is a false account of the grammar (logic) of our language: we can make precise, exact, and true statements about things that are subject to change). What of the regularity of nature, which Plato was hardly blind to (In 30c he speaks of the order and regularity of "the years, the seasons, and the months" and sees wisdom and reason behind this; cf. Sophist 265c-e), -- would not so-called laws of nature be instances of Plato's Forms, or at least would their nature not be Form-like (akin to Forms)? But would Plato have allowed that there are laws of nature -- i.e. regularities not subject to change (or, essentially unchanging)? Is there any reason to believe that there "must" be permanent laws of nature?

59c - [Plato calls the following a "reasoned declaration".] That we find fixity, purity, truth, and what we have called perfect clarity, either in those things that are always, unchanged, unaltered, and free of all admixture, or in what is most akin to them; everything else must be called inferior and of secondary importance.

59d - And are not 'reason' and 'intelligence' the names that command the greatest respect?... Then these names can be properly established in usage as precisely appropriate to thought whose object is true being.

Plato's Conclusion (in this dialog)

59d-e - [At this point in their discussion, having now stated what the natures of pleasure and of intelligence are,] we have at hand the ingredients, intelligence and pleasure, ready to be mixed, the materials in which, or out of which, we as builders are to build our structure [i.e. to say what is the good life for man] -- that would not be a bad metaphor.

59e-60b - ... I think there is a lot in the proverb about the need for repeating a good thing "once and twice and once again". [Plato's summary (60a-b) follows.] Philebus maintains that pleasure is the proper quest of all living creatures, and that all ought to aim at it; in fact he says that the good for all is pleasure and nothing else, these two terms, 'pleasure' and 'good', being properly applied to one thing, one single existent. Socrates on the other hand maintains that they are not one thing, but two, in fact as in name; "good" and "pleasant" are different from one another, and intelligence has more claim to be ranked as good than pleasure.

61b - Our discussion has made it plain to us, now as at the outset, that we must not look for the good in unmixed life [of either pleasure alone or intelligence alone], but in the mixed. - 61d - To begin with, are we most likely to attain a good result by mixing all pleasure with all intelligence? - 61e - [We should see which are] the truest portions of each before we [make] our mixture ...

62a-b - Now let us imagine a man who understands what justice itself is, and can give an account of it conformable to his knowledge, and who moreover has a like understanding of all else that is.... Will such a man be adequately possessed of knowledge, if he can give his account of the divine circle and the divine sphere themselves [56d ff.], but knows nothing of these human spheres and circles of ours, so that, when he is building a house, the rules that he uses, no less than the circles, are of the other sort?... Are we to throw in along side our other ingredients the art of the false rule and false circle, with all the lack of fixity and purity it involves?

PROTARCHUS: We must, if we are going to find a way home when we want it.

62d - PROTARCHUS: I don't really see, Socrates, what harm one would suffer by taking [into our mixture] all those other sorts of knowledge, providing one has the first sort. [And therefore all types of knowledge are to go into our mixture of knowledge and pleasure.]

62e - SOCRATES: Hence it is time for us to raise the same question about pleasures, whether we are to let them all loose at once ...

63b-c - [Plato says that pleasure can accept all types of knowledge, but that knowledge cannot accept all forms of pleasure. - 63d-64a - For example, the intensest pleasures disturb] "with frenzy the souls in which we [i.e. reason and intelligence (63c)] dwell, and prevent us from ever coming into existence, while as to our offspring, they utterly ruin them in most cases, so careless and forgetful do they make us.... to mix with reason the pleasures that always go with folly and all other manner of evil would surely be the most senseless act for one who desired to see a mixture and fusion as fair and peaceable as might be, so that he might try to learn from it what the good is, in man and in the universe ..."

64d-e - ... any compound, whatever it be, that does not by some means or other exhibit measure and proportion, is the ruin both of its ingredients and, first and foremost, of itself.... So now we find that the good has taken refuge in the character of the beautiful, for the qualities of measure and proportion invariably, I imagine, constitute beauty and excellence.

64e - And of course we said that truth was included among these qualities in the mixture.

65a - Then if we cannot hunt down the good under a single Form, let us secure it by the conjunction of three [-- namely], beauty, proportion ["measuredness" (65b)], and truth, and then, regarding these three as one, let us assert that that may most properly be held to determine the qualities of the mixture, and that because that is good the mixture itself has become so.

But what would it be like if we could "hunt down the good under a single Form"? Plato says that the good is the conjunction or union of three "Forms" beauty, proportion, truth -- and therefore that if anything is good, it is so because it "partakes of" this conjunction or union.

Is 'the good' or 'goodness' a common name which names a common nature? "What is the essence of the good?" -- "If anything possesses each of these three qualities, then it is good." Could we object: We asked you what is the good [in] itself, not which things are good: you have given us the criteria for applying an adjective, whereas it is about the noun that we want to know; surely a Form is named by a noun, not as it were by an adjective? Would Plato reply: I do not know everything; I cannot tell you what the good is in itself [what goodness as such is]. (Xenophon's Socrates does not ask about the "Form" goodness, as if 'goodness' were the name of a thing; for him the word 'good' is, as it is for us -- i.e. in normal usage -- an adjective [not an hypostatized or spirit-like "something"].)

65b - Then let us examine each of our three Forms [i.e. beauty, proportion, truth] separately in relation to pleasure and reason, for we must see to which of the two [i.e. pleasure or reason] we shall assign [i.e. rank] each of them on the ground of closer kinship [to beauty, proportion, truth].... 65a-b - whether it is pleasure or intelligence that is more akin to the highest good, and more valuable with men and gods alike.

65d - [Protarchus says that pleasures are] like children, completely destitute of reason [This is why, "when it is a question of the pleasures of love, which are commonly reckoned to be the greatest, even perjury is forgiven by the gods"]. Reason, on the other hand, if not identical with truth, is of all things the most like it, the truest thing in the world.

65d - PROTARCHUS: I do not think you could discover anything whatsoever more unmeasured [more imprecise, inexact, unmeasurable, unbounded, unlimited] in its character than pleasure and intense enjoyment, nor anything more measured than reason and knowledge.

65e-66a - SOCRATES: Has reason more part in beauty than pleasure, that is to say is reason more beautiful [Note: as well as by 'handsome', the Greek word can also be translated as 'excellent' or 'fine'; cf. the Italian 'bello'] than pleasure, or is the opposite the case?

PROTARCHUS: ... no one can ever possibly have conceived [intelligence and reason] as being or becoming ugly or ever going to be so.... [whereas with the greatest pleasures] we detect in them either an element of the ridiculous or of extreme ugliness, so that we ourselves feel ashamed, and do our best to cover it up and hide it away.

Thus with respect to truth, measuredness (proportion), and beauty -- with respect to all three intelligence is more akin to them than pleasure is, and therefore intelligence is more akin to the good (65a) than pleasure. (Would examples of "measuredness" -- or of tools and concepts exhibiting measuredness -- be the Euthyphro's arithmetic calculation, rulers and scales?)

66a-b - [What takes first place as most akin to the good is] somewhere in the region of measure -- or what is measured or appropriate, or whatever term may be deemed to denote the quality in question.... And the second place lies in the region of what is proportioned and beautiful, and what is perfect and satisfying and so forth -- whatever terms denote that kind of quality. [The third place goes to reason and intelligence. The fourth belongs] to the soul itself, sciences and arts and what may be called right opinions, inasmuch as these are more akin than pleasure to the good.... And as fifth [place], the pleasures which we recognized and discriminated as painless, calling them pure pleasures of the soul itself -- some of them attaching to knowledge, others to sensation.

67a-b - [Thus pleasure will not take] first place, no, not even if all the oxen and horses and every other animal that exists tell us so by their pursuit of pleasure. It is the animals on which the multitude rely [like diviners who rely on birds] ... when they decide that pleasures are of the first importance to our living a good life ... [Most people] suppose that animals' desires are authoritative evidence, rather than those desires that are known to reasoned argument, divining the truth of this and that by the power of the Muse of philosophy.

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