You can read Philebus online in English at the Perseus Project and in Victor Cousin's French at Wikisource.
The characters are Socrates, Protarchus, and Philebus. Protarchus is called the son of Callias, but the Callias in question does not seem to be the famous wealthy one who occasionally appears in other dialogues; that is the only definite marker of who these two young men might be. There is also a crowd of unnamed young men.
The Plot and The Thought
The dialogue opens in the middle of a discussion on pleasure. Socrates has been arguing with Philebus, but Protarchus is now taking over for Philebus, and they agree on the crux of the argument:
Philebus holds that what is good for all creatures is to enjoy themselves (chairein), to be pleased (hedone) and delighted (terpsin), and whatever else goes together with that kind of thing. We contend that not these, but knowing (phronein), understanding (noein), and remembering (memnosthai), and what belongs to them, right opinion (doxan orthan) and true calculations (aletheis logismos), are better than pleasure and more agreeable to all who can attain them; those who can, get the maximum benefit possible from having them, both those now alive and future generations. (11b-c)
They also agree on how to proceed. If it turns out that some kind of life is better than either the life of reason or the life of pleasure, they will look at the question of which of the two is closer to that better life.
One of the points that Socrates will insist upon is that there are in fact many different kinds of pleasures. This lets him raise the question of how one and many are related, linking them with limit and the unlimited (i.e., the indeterminate). The boys have difficulty following how any of this is relevant, but Socrates insists that answering the question they are trying to answer requires understanding how pleasure or knowledge can be both one and many. Protarchus responds that they have no answer to this question, but that this doesn't let Socrates off the hook; if they can't answer it, he has to do it.
Socrates replies that "once upon a time I heard in a dream--or perhaps I was awake" (20b) that there was something superior to both the life of pleasure and the life of knowledge, and that if he can make a case for its existence, he will have shown that pleasure is not the good. So he argues that the good is complete and sufficient, and proposes that they consider two unmixed cases: a life of knowledge (phronesis), etc., with no pleasure, and a life of pleasure (hedone), etc., with no knowledge. He points out, though, that a life of pleasure without knowledge will certainly miss out even in matters of pleasure: it is a life in which one cannot rationally plan for future pleasures and in which one cannot remember past pleasures, the life of a mollusk. Protarchus insists that the life of mere pleasure and the life of mere knowledge both seem equally undesirable, but, of course, this suggests that there is a life better than either, namely, the mixed life of both pleasure and knowledge. Thus neither one alone is complete, sufficient, and choice-worthy as the good itself should be. Thus neither reason nor pleasure get the first place; they are now arguing over second place, and Socrates says that he is sure that pleasure will not even get second place as very good-like rather than the good itself.
He returns to the limit and the unlimited. These are two kinds of things; there is also the mixture of them, as a third; and, Socrates suggests, they need a fourth, the cause of their combination. If we take something like the hotter or the colder, these things admit of more and less by nature, and thus are in some sense unlimited -- if they reach their fulfillment, they are ended: "Whatever seems to us to become 'more and less', or susceptible to 'strong and mild' or to 'too much' and all of that kind, all that we ought to subsume under the genus of the unlimited as its unity" (24e-25a). If we take the unlimited, constantly in flux, and mix it with limit, we get harmony, or proportion, and this is a generation (genesis) of something new. This applies directly to pleasure, which admits of more and less, and which therefore requires a limit in order to be excellent.
Socrates and Protarchus then turn to the cause and agree that "everything that comes to be comes to be through some cause" (26e). Thus any sort of coming to be is understood in terms of four kinds: the unlimited and the limit from which it comes to be, the thing that comes to be, and the cause of its coming to be. Now, the mixed life to which they gave first place is clearly the third kind of thing (the thing that comes to be), being a union of unlimited and limit. The life of pleasure, admitting of more and less, is clearly the unlimited or indeterminate. Reason (nous) is cause because all the wise agree "that reason is our king, both over heaven and earth" (28c). Both Socrates and Protarchus agree that this is true of the world: it is ruled by reason, as seen in the orderly character of the heavens. They also agree that this suggests that there is a world soul, organizing everything in an orderly way, because if wisdom organizes the world everywhere, then there must be some kind of life or active cause that has this wisdom.
Socrates argues that pain is a disruption of the harmony (i.e., mixture of unlimited and limit) of a living creature, and its restoration is pleasure. But there are other kinds of pleasure, like the anticipatory pleasure one has by hope of such restoration. (In either case, however, we
seem to have a link to restoration of some kind, and this immediately suggests that if there were an animal that could not be destroyed, and therefore did not need to be restored, it would have no pleasure or pain, although it could very well have knowledge -- as perhaps with the gods.) In addition, 'pleasure' can sometimes be used to include absence of pain, although other pleasures can be had while simultaneously having pains.
From this point, Socrates argues that pleasures can admit of true or false, just like judgments; that they can seems to follow directly from the fact that some pleasures are themselves anticipations, and anticipations can be wrong. In addition, sickness can sometimes intensify pleasures, whereas in health they are moderate, and the same opposition is found when we consider wild passions like fury or malice, which can intensify pleasures, while virtue moderates them. In addition, pleasure seems to be a process (genesis) rather than being (ousia). All of these suggest that pleasures fail in quite a few ways to be complete and sufficient in the way the good must be, and consistently it does so in ways that compare unfavorably with knowledge (phronesis). Further, if we consider the mixed life and ask what in it most contributes to its value, it seems clear enough that it is order and measure, since without order and measure its worth is corrupted; and the good is clearly allied with the beautiful: "For measure and proportion manifest themselves in all areas as beauty and virtue" (64e). All of these tests or trials give the preference to prudence over pleasure.
Socrates then says they should do a "third libation" (66d), and go over the argument again; Protarchus, of course, replies that they have already done so twice, but Socrates summarizes the argument, concluding that pleasure is not the greatest good, and would not be even if all of the lower animals testified that it were, for, in fact, many people accept their testimony in the same way that diviners accept the testimony of birds, instead of following reasoning "under the guidance of the philosophical muse" (67b). Socrates asks if he can now go, and Protarchus says that there is still a bit more to do, and the dialogue ends.
* Catherine Zuckert in Plato's Philosophers discusses the surely important dramatic fact that Philebus, Protarchus, and the other boys, keep insisting that they will force Socrates to finish:
Although neither the setting nor the characters have any political or historical significance, we are repeatedly reminded in the course of the conversation (16a, 19d-e, 23b, 28c, 50d-e, 67b) that there are many young men present who will force the philosopher to complete the argument. In other words, Socrates is compelled to present this argument because of the power (of the opinion) of the many. The threat to the philosopher is said to be "playful" because it is leveld by "boys" who do not yet have the force of the city or its fathers behind them. The threat is, nevertheless, real. Socrates will not be able to attract youths to a life of philosophy so long as they believe that pleasure is the highest good and, consequently, follow Philebus' example in giving up argument when it appears to involve unnecessary painful effort. (p. 387)
Quotations are from Dorothea Frede's translation in Plato, Completed Works, Cooper & Hutchinson, eds., pp. 398-456.