Philebus

Philebus is probably the driest and least stylistically interesting of any of the mature dialogs (ie. from Plato's middle and late period).  While the question it explores is classic Plato -- does the good life have more to do with knowledge or pleasure? -- it pursues it in a strictly analytical fashion to a very precise and rational conclusion.  While we encounter a few sub-questions that bring up more general philosophical issues along the way, the overall structure doggedly pursues the initial question without any hint of myth or rhetoric.  There isn't even a frame story here.  Apparently this was one of the last dialogs Plato wrote.  Perhaps he wanted to leave a systematic and rational summary of the themes that have occupied his late works.  Or maybe he was just in a hurry.  

The argument in the dialog is pretty easy to summarize in outline.  Socrates begins by asking the simple question of whether pleasure or knowledge provides the best guide to living.  But then he immediately goes on to make the contest more complex with two observations about the question.  First he suggests that the right answer might be neither.  Second, he points out that the question itself is too vague -- it's not clear that what we call pleasure or knowledge are one thing.  

This leads to a digression on the general issue of pluralism versus monism.  Socrates 'solves' this age old dilemma by pointing out that everything is both one and many, but that the important thing is to understand how the infinite many can be built from some basic units of identity.  The model he invokes for this is one we've seen several times in his later works (Theaetetus 202e, Sophist 253a, Statesman 277e) -- the alphabet.  Basically, what mediates between the one name we give something like pleasure, and the infinitely many pleasures this encompasses are the basic types of pleasures.  These measure or number the many the same way that letters measure the flow of speech.  

Having tackled the second sub-question, Socrates returns to the first and discovers that neither knowledge or pleasure alone leads to the good life.  After all, would we want to know everything but feel nothing?  And conversely, what good would it do us to feel the most intense pleasures if we didn't know them and weren't even conscious that we were feeling pleasure?  Only the good in itself is good by itself -- is perfect, self-sufficient, and desirable in itself.  This discovery leads Socrates to a metaphysical digression on the 4 kinds of things that make up the universe.  These are:

1. The unlimited -- by which he means any quality defined relatively and capable of continuous increase and decrease without limit.  For example, (in Plato's physics) hot just means "hotter than something colder" and we can of course always find something even hotter.  Pleasure obviously falls into this category.
2. The limited -- by which he means things defined absolutely and which have a number or measure.  The examples he mentions are 'double' and 'equal'.  It's tempting to interpret this category as just all the Forms (except the Good), but Plato doesn't make it completely clear whether Beauty and Courage and Moderation would belong here too, or whether he's just thinking of the 'mathematical' Forms.
3. Mixtures of 1 and 2 -- by which he means things where a limit has been imposed on something unlimited to produce a harmony or proportion in the material.  These mixtures seem to be equivalent to the same 'many' we saw in the first sub-question, but taken as numbered (or lettered, as the case may be).  In other words, the mixtures he's thinking of don't seem to be some random chaos created by Forms mixing with one another and with an unlimited qualitative material.  Instead, a mixture is something where a Form has been imposed on the unlimited to create a measure for it; a mixture is already ordered, proportioned.
4. The cause of the mixtures -- by which he means the final cause or ultimate purpose of the mixtures, not the efficient or mechanistic cause we typically think of today.  The cause is something that allows the limit to measure the unlimited.  It's the thing that generates the ordered mixtures by measuring and applying appropriate limits.  This category is explicitly the Good itself (26c).  Later we'll learn that knowledge and reason fall into this category, because of course the ordered progression of the universe reflects the knowledge and wisdom of the 'world soul'.

If we continue the alphabet metaphor introduced during the discussion of pluralism and monism, it appears that the unlimited maps to speech, the limited to the letters, the mixture to well formed and hence measured speech (ie. writing), and the cause of the mixture to what enables this measurement to happen -- the mind of the author.  You may notice though that these 4 categories sit rather uneasily with the 3 categories introduced earlier.  The unlimited is certainly the many, but since we refer to it as a single category, can also be thought of as one.  Though we might equate the limited with the Forms, it's trickier to identify them with the one, since we were told that somehow the one is also many.  Perhaps the solution to this is simply that each one, each Form, appears many times, though each time identical to itself?  This interpretation would fit well with the alphabet analogy -- 'A' is one thing no matter how many times or in how many ways I wrote it.  That is the nature of a combinatorial measuring or coding system.  The mixtures are then the various combinations of the limits that mediate between the one and the many, precisely numbering the infinite qualitative flux of becoming.  Finally then there must be a measurer who puts this whole system into effect, a fact which Socrates skipped over in his discussion of pluralism and monism.  

At any rate, we then return to a clarified version of the initial question. What we're really asking is what mixture of which aspects of pleasure and knowledge leads towards the Good, which is the unquestioned end that causes all this mixing/measuring/numbering/weaving to happen.  Pleasure and knowledge aren't unitary; they contain different types that we have to distinguish and 'take the measure of'.  And neither one alone will lead to a good life, which can only be produced by whatever mixes the correct proportions of the correct components of each.  Now at least we've uncovered the full problem that was at first inadequately posed and know what type of life we're searching for.  From here, we can continue to ask whether pleasure or knowledge (and which types) stands closer to this ideally good life.  

First, though, Socrates has to conduct parallel analyses of both pleasure and knowledge to discover their types.  Unsurprisingly, this primarily takes the form of uncovering pure pleasure and pure knowledge.  While it's not explicitly described this way, the analyses of the next two sections proceed by the same method of division we saw in the second half of the Statesman.  That is, they are concerned with purifying their respective material by separating off each of the metals that compose an alloy.  Though each of the analyses has some interesting points, they don't make for gripping reading, and I think I will just state the conclusions Socrates reaches.  Pleasure can be divided into two types.  Some, such as hunger and thirst, are mixed with or alternate with pain.  These are the pleasures and pains of a body maintaining its equilibrium through lack, expectation, and temporary satiation.  By contrast, the pleasures of the soul such as learning and contemplating a perfect circle are pure and unmixed with pain.  Likewise, knowledge can be divided into what we would today call the arts and sciences, the latter distinguished by their use of measure and number.  As you would expect, Plato goes on to consider a pure science that deals with number in itself, free of any application, and eventually the purest science of all -- the dialectic -- that must be something like the science of measuring and numbering being itself with words.  So knowledge too has grades of purity that depend on both the object contemplated (pure being vs. applied becoming) and the means employed (art vs. numerical science).  None of this analysis is particularly novel or unpredictable if you are already familiar with Plato's predilection for purity.  

The dialog concludes with Socrates laying out a final ordering of the types of life.  We've already concluded that the best type of (human) life is one that mixes pleasure and knowledge.  However, this life is directed and made possible only by the measuring and ordering Good that selects the materials and supervises their mixture.  The Form of the Good -- composed of Beauty, Truth, and Proportion -- is the cause of the mixture and the reason why it forms a good life.  In a way, the principle of this mixture is beyond life itself, with its coming to be and passing away.  Like we saw in the Statesman, the ideal is a divine image that self-sufficiently contains all the parts in an ordered whole.  All we humans can do is try to imitate the divine proportion by selecting pure elements and weaving them into a harmonious mixture.  So the types of life can finally be fully ranked according to their principle:

1. The Good as divine measure
2. A mixture of pleasure and knowledge according to the recipe provided by the Good.
3. Pure knowledge, reason, and intelligence.
4. Applied knowledge
5. Pure pleasures of the soul
6. etc ...

As you can see, this ranking answers the initial question and defends the life of knowledge as third best, but closer to the ideal than a life of careless physical pleasure.  Here in one of his final works, Plato seems to be updating Socrates' famous maxim from the Apology -- it's the unmeasured life that's not worth living.