Tuesday, June 22, 2021

Sophist

I first read the Sophist almost exactly two years ago when I was working on the first big Plato section in D&R.  As you might imagine, reading so much more Plato in the interim has given me a different perspective on it.  Not that what I wrote earlier seems totally wrong or anything (and I particularly enjoyed the concluding contrast with W.V.O. Quine).  But now I see the way this dialog fits tightly together with Theaetetus and Parmenides. These four (including the Statesman, which is next on our list) seem to constitute a new phase in Plato's philosophy, one that begins to rethink the classic theory of Forms as it was presented in the earlier quartet (Phaedo, Symposium, Phaedrus, Republic). 

Just how to summarize this shift is something I'm still struggling with.  It's clear that Plato isn't ready to just abandon the theory of Forms.  Perhaps he's modifying it to avoid the accusation that his supreme One-Good in the Republic is really no different than Parmenides' conception of the unchanging and undivided One?  Or perhaps he's simply adding more complexity to the theory by following up on his suggestion in Phaedo that some forms can blend with others, and that our knowledge must encompass not merely the individual forms but their various combinations?  Or perhaps he's struggling with something much deeper, something akin to the later problem of evil -- if the virtuous Forms are all that really has being, if they are the only "things that are", then why are there so many appearances and opinions to confuse our knowledge of them?  Having created a sharp appearance-reality distinction between Forms and their incarnation, it seems difficult to avoid a new question: if the Forms alone are the sum total of reality, then what is the ontological status of an appearance?  What exactly are these "things that are not"?  After all, up to now, it has seemed that the overarching theme in Plato's philosophy has been an attempt to teach us to purify the mixtures we find in the world into their component Forms.  This purification serves a moral purpose by allowing us to recognize and select what's good for us.  But where did this mess come from to begin with!?  If the Forms are so pure, how did we get this mixed up world?  This last interpretation of the shift in Plato's philosophy is probably the most interesting.  Because perhaps, in struggling with this problem, Plato began to understand that the two sides of his philosophy -- reality and appearance, models and copies, Forms and world -- were at risk of becoming indistinguishable (or if distinct, entirely relative and interchangeable).  Perhaps, as Deleuze puts it, Plato began to overturn himself.

Was it not inevitable that Plato should be the first to overturn Platonism, or at least to show the direction such an overturning should take? We are reminded of the grand finale of the Sophist: difference is displaced, division turns back against itself and begins to function in reverse, and, as a result of being applied to simulacra themselves (dreams, shadows, reflections, paintings), shows the impossibility of distinguishing them from originals or from models. The Eleatic Stranger gives a definition of the sophist such that he can no longer be distinguished from Socrates himself: the ironic imitator who proceeds by brief arguments (questions and problems). (D&R 68)

After that long intro, you may not be surprised to hear that, as with Theaetetus, I'm a little unsure how much detail to go into here.  I think the Sophist may be even more complex than Theaetetus, and it also starts to cast Parmenides in a new light.  It practically needs a blog of its own. The simplest summary would be that an "Eleatic Stranger" shows up to take on the role usually played by Socrates and tries to come up with a definition of the sophist that would distinguish him from the philosopher.  He proceeds to employ something he calls "the method of division" (apparently Plato's new name for the dialectic, which we saw in the Republic lacked a precise method), which keeps subdividing descriptions in a sort of genealogical tree until it reaches one that will completely and uniquely describe whatever we want to talk about.  Along the way, some strange stuff happens.  The Sophist starts to appear at many different points along the tree of division that the Visitor sets up.  That fucks up our plan.  Hoping to fix this problem, the Visitor suggests that the sophist must be defined by some sort of expertise in making himself appear to be expert in all sorts of things, which is why his location on the tree is hard to pin down.  This turns out to create an even bigger problem because it implies that there is something like a knowledge of appearances, things which, in the Platonic world, are just illusions that are not even supposed to really be.  Fully half the dialog is then taken up with trying to figure out what an appearance is, if it's something that theoretically is not.  This is obviously very related to the question of false judgement that was posed in Theaetetus.  Through this long digression, the Visitor reaches the conclusion that things that are not still, in some sense, are, and vice versa. In other words, non-being is not the opposite of being (a concept which makes no sense) but something different from being, a form which blends with being in certain ways.  Now that he's established that there is a being of mere appearances, the Visitor creates a new genealogical tree and defines the sophist's exact location on it.   

Now, there are a few things we immediately notice about this summary.  First, since the dialog in TheaetetusSophist, and Statesman is explicitly described as three parts of one epic day of conversation, we cannot fail to notice that this procedure is exactly how the conclusion of Theaetetus would try to define knowledge of the sophist.  The Stranger provides true judgement of who the sophist is, together with an account of what makes him different from the philosopher.  But whereas Socrates' inquiry in Theaetetus ended in a sort of aporia -- defining knowledge as true judgement together with a knowledgeable account of what makes each thing different is circular -- the Visitor's inquiry in the Sophist seems to be totally successful.  Both these conclusions, however, seem strangely designed to undercut themselves.  We saw that actually Theaetetus defined the form of knowledge quite successfully -- as representational -- but stumbled on whether we could determine if a particular bit of knowledge was true or not.  By contrast, while the Stranger delivers a clear cut, neatly packaged definition of the sophist, as Deleuze pointed out above, this definition is exactly how you would describe Socrates.  And this is not the only point in the dialog at which the sophist and the philosopher seem to be doubles of one another (see 226b-232 and 253c-254b below).  It's hard to be sure what's going on here, but particularly with the Sophist, I suspect that Plato is drawing our attention to the problem discussed above.  If, as the dialog explicitly argues, being and non-being (difference) are not opposites, then how can we maintain that the sophist is the opposite of the philosopher?  We know that there is some sort of distinction between them, in fact no distinction could be more important.  But when it comes to identifying a particular case, it seems we'll never be able to say which is which.  

Far from being a merely inconvenient problem, this threatens to entirely unravel the central distinction between appearance and reality, sophist and philosopher.  It's truly a weird moment in the Platonic corpus.  Recall that the Forms are meant to solve a moral problem.  We will find out what's good for us by purifying the world into its Forms.  Eventually we even come to see the Form of the Good itself.  Surely, this should let us completely solve our moral problem and purify all possible actions into good and bad ones, right?  But a strange twist seems to have occurred since the conclusion of the Republic.  Plato mentioned there that the Good was beyond even being.  This left open the question taken up in Parmenides about whether the One-Good is, or is not.  Now though, we might read Parmenides as a prelude to the Sophist, or at least in light of it.  Because now we're told clearly that non-being is not the opposite of being.  In which case, the question in Parmenides could not have been either/or.  Instead, as Deleuze suggested, we are using the two separate hypotheses -- that the One-Good is, and that the One-Good is not -- to reach beyond all hypotheses to some necessary apodictic truth.  While the conclusion of Parmenides is still obscure, it seems that perhaps the truth revealed there is that relations of opposition or contradiction cannot be sufficient or exhaustive.  

... whether one is or is not, it and the others both are and are not, and both appear and do not appear all things in all ways, both in relation to themselves and in relation to each other. (Parmenides 166c)

Perhaps this says that, yes, there is both being and non-being, there is both appearance and reality, and, by implication, there is both good and bad, but that these oppositions co-exist in everything.  Which is to say that they cannot be logically binary oppositions that follow the law of the excluded middle.  We could then read the problems we've encountered in Theaetetus, and now the Sophist as continuing the same line of thought.  These dialogs presume that both appearance and reality exist and are distinct (which I claim is the apodictic conclusion of Parmenides that the Republic (511b) claimed was the highest form of understanding), but deal with the consequences of the fact that this distinction is not an absolute and binary logical cleavage in the world.  In fact, contrary to all our attempts at purification, it seems that these two sides are constantly intermixing and getting confused, to the point where we risk not being able to distinguish true knowledge from false or the philosopher from his evil twin the sophist.  What this is supposed to do to our original moral question is now a huge dilemma.  Perhaps, as the final dialog in this series, the Statesman will take up this question more directly.  Or perhaps it will render my whole line of thinking here irrelevant.

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For reference, here is a longer outline of the dialog:

216-218b -- Frame -- Is the visitor a god disguised as a man?  Not easy to distinguish gods from men or philosophers from sophists and statesmen (216c)

218a-d -- going beyond a verbal explanation of the sophist by the method of division.  An explanation of the exact difference between things (259d) is what constitutes knowledge (conclusion of Theaetetus)

218e-221c -- what is the angler?

221d-232 -- what is the sophist?
221d-226b -- 5 money based definitions -- hunter of rich young men, wholesale, retail, OEM, expert in debate
226b-232 -- a sixth definition as discriminator, purifier of ignorance, educator, philosopher.  Context: This makes the sophist indistinguishable from Socrates and even the Visitor.

232-236d -- how can the sophist be an expert in everything?  Sophist as imitator. Imitation divides into making likenesses and appearances. 

236d-260d -- the being of Non-being -- how can the sophist make things that are not appear to be?  The thesis seems to be that non-being is not the opposite or negation of being but is different from being.  This difference is the source of appearance, error, falsity.  Some Forms blend with others and not everything can be neatly separated.
236b-239b -- how can we even talk about non-being?  It can't be one or many.  It can't ever be referred to as some thing.
239c-241d -- if we can't define falsity as saying non-being, then how can we claim the sophist makes copies of things.  The logic of model and copy doesn't seem to apply if being and non-being are interwoven (240b-c).  Non-being is confusing.
241d-243c -- all Presocratics (including Parmenides) talk about what the world is.  But they don't explain what being is, so we may not be any clearer about it than about non-being.  So what is being?
241d-246 -- Parmenides' equation of being and the One has many problems.  Are these two names for the same thing?  But isn't a name a thing too?  Is the one a whole made of unified parts?  Some of this is hard to follow in the same way as Parmenides.
246b-249e -- battle of materialists and idealists. 
246e-248 -- materialists always end up admitting that something without a body has power/capacity (ability to affect or be affected)
248-249d -- idealists think that true beings are the changeless forms.  But then how can we know being, since knowledge seems to be an affection?  If we can know being, then it cannot be completely static.  But if everything is moving and changing how would there ever be enough stability for knowledge?  Ergo, being cannot be one, nor can it be many forms, nor can it change in every way, but it has to be both changing and unchanging.
249e-250e -- but being is still a third thing in addition to both rest and change.  So we are still confused about what it is.  Maybe the confusion about being and the confusion about non-being are related.
251b-254b -- a critique of the purity of the Forms.  Forms mix.  The philosopher is an expert in how Forms mix
251e-253c -- some forms mix.  If no forms mixed we couldn't even talk about anything being.  If all forms mixed there would be no distinctions at all.  So only some forms mix with some others, just like with the letters.
253c-254b -- the philosopher is an expert in how the forms mix. That is exactly how the dialectic, and the method of division works, by gathering and splitting.  The philosopher is confusing because the realm of being is so bright.  The sophist is confusing because the realm of non-being is so dark.  Context: given the confusion around being and non-being how would we ever distinguish these two, especially since we're about to prove they aren't even opposites?
254c-260d -- Which Forms mix and which do not?  
254d-255e -- starting with motion, rest, and being but being forced to add same and different
256-256e -- change is the same as and is different from: rest, same, different, being 
256e-260d -- Since the different blends with all of them, it gives everything a share of non-being.  Non-being shows up as indefinitely many differences between being and the other forms.  Non-being is difference, not the opposite of being, non-being is itself a form.  The things that are different from every form (not beautiful, not just) also are.  So non-being is chopped up into the relations between forms and thus scattered over all of being. 
259 -- Context: the conclusion seems close to Parmenides, and might be a proof that both reality and appearances are (but also are not).    
259d -- Context: another puzzling passage.  The being of difference means that the not large also is, but it's important to specify in exactly what way something is different from a form, and not to just to make it appear different with just verbal tricks.  But how are we ever going to separate these two?
260 -- now that we know what non-being is, we can ask whether it blends with speech and belief to generate falsity  and deception

260e-264c -- false speech and false belief are possible because you can say something (that is) about something (that is) but something different from the being of the object.  Seems to imply the same representational correspondence of recognition we saw in Theaetetus.  Appearances arise when we come to our beliefs through perception instead of the soul operating on its own.  

264c-END -- now that we know that appearances exist, we can go back to 236d and continue the method of division to define the sophist.
265c-d -- a twist in the method of division has us keep a division on the discarded side.  Divine and human production both contain the making of things themselves and copies of things.  
268b -- Context: the final description of the sophist is again very similar to Socrates. It also takes us back to the disputed 6th definition of the sophist as the educator who purifies you by refuting your belief that you know.  But the discussion of the mixing of the forms has put purification into question.  
Context: The dialog does not conclude with aporia or a myth, but everything is wrapped up in a neat package.  Irony?  Since production divides into human and divine (265b) the implication is that there are also divine sophists.

Saturday, June 5, 2021

Theaetetus

Theaetetus is such a long complex dialog that I'm not sure what level of detail I should go into; a simple outline took up four full pages of my notebook!  However, the question it explores -- what is knowledge? -- is an easy to pose philosophical chestnut.  Theaetetus is structured like the early aporetic dialogs.  Various definitions of knowledge are proposed and rejected, and by the end, we only know that we don't know what knowledge is.  However, this late work packs a lot more content into the mold of the early style.  In fact, in a sense, the aporia here is only illusory.  We may not know exactly how to evaluate whether knowledge is true or not, but we have established that the form of knowledge is recognition.  That is, knowing something is just like recognizing your friend Theaetetus when he passes by on the street.  How do you know that you've correctly recognized something, you ask?  Ah, well ... that we're not so sure about.  But there's no question that knowledge here has the form of a correspondence between two stable identities, essentially, a representation.  Another way to express this would be to say that the aporia of the dialog doesn't apply to knowledge so much as to truth.  We know what knowledge is -- the correspondence of representations that constitutes recognition.  We just don't know whether it's true knowledge or not.  Of course, these two are inextricably interwoven, so there's no way to avoid the circularity at the heart of this theory of knowledge, a fact which presents itself as the final aporia in the dialog.

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Let me attempt a quick synopsis and outline.

1) Theaetetus begins with a brief but unusual frame story.  The conversation related in the dialog is actually being read from a book that Euclides composed from some notes he made about a long ago encounter between Socrates, Theatetus, and Theodorus.  It's not clear to me what this particular framing contributes to the content of the dialog, but like the elaborate multi-level frame of Parmenides, it draws attention to itself.  

2) Socrates is introduced to Theaetetus and asks him to define knowledge.  Theaetetus makes the now classic land-war-in-asia blunder and tries to give examples of knowledge.  At which point Socrates predictably says that he wants to know what knowledge is in itself.  But before he lets Theatetus answer, Socrates launches into a long story about how he is merely a midwife of ideas, just here to help Theaetetus give birth to, and evaluate the viability of, his own concept of knowledge.  In context, I think we are clearly meant to ask how Socrates can know the difference between good and bad ideas.

3) Theaetetus defines knowledge as perception.  The discussion of whether this definition will work takes up roughly the first half of the dialog because Socrates digs deeply into the metaphysical backdrop that might make this definition work.  He links it to Protagoras' famous motto that man is the measure of all things.  Whatever you perceive is knowledge of what is real for you.  The implied relativism is pursued all the way to its end, a world of pure flux in which the very concept of knowledge seems to dissolve.  Unfortunately, if the concept of knowledge disappears, so does our ability to know what's good for us.  Conversely, for morality to exist we must know good from bad.  And if there's one thing we know exists for Plato, it's morality.  Every concept he invents is aimed at helping us differentiate and select the good while discarding the bad.  So, ultimately, the Protagorean universe collapses under its own weight because from within it we cannot consistently contend that it is a better way of looking at things. This relativism is self-defeating.  To top it off, it seems unable to explain how our different senses could converge on a single integrated object, nor how we could ever know about abstract objects (such as numbers) that we cannot perceive.

In the middle of this section there's also a long interlude where Socrates praises the life of a philosopher and contrasts it with that of other men.  While it mostly just repeats the motif of the philosopher ascending to a world beyond the senses that we saw in the middle period dialogs, in this context it stands out like a sore thumb.  How does Socrates know which of these lives is better?  This second literary device points in the same direction as the first one about Socrates' role as midwife.  Both are meant to emphasize that the real test of knowledge is whether it helps us live better by separating good ideas and actions from bad ones.

4)  Since Protagorean relativism and the idea that knowledge is perception self-destruct, Theaetetus tries a new definition.  Maybe knowledge is true judgement.  Before testing this new idea, however, Socrates first wants to know how false judgement is possible.  How can we confuse two things that we know, or confuse something we know with something we don't know, or, mostly strangely, how could we confuse two things we don't know?  These questions may not sound compelling in the abstract, but when Socrates makes his ability to recognize Theaetetus the model for knowing Theaetetus, they propose more of a puzzle.  I mean, it's not like we confuse one friend for another, and what would it even mean to confuse two people you don't know?  Socrates investigates a couple of models of how this could happen.  The first describes the soul as made of some waxy substance that gets stamped with sense impressions.  To know something, to recognize it, is to fit a new impression into an old mold.  This process might go awry because your stubborn soul is made of a wax too hard to remember anything, or because the wax is too soft and the impressions melt away.  Since the wax recording system doesn't work perfectly, false judgement can arise when there is a mismatch between a current perception and an existing mold.  This seems like a plausible mechanism for empirical false judgement, but it cannot explain mathematical false judgements or abstract errors.  If we know the numbers, how can we ever make an error of mathematical calculation?  Similarly, if we know the abstract Forms, how can we ever confuse Beauty with Ugliness?  Socrates proposes a second model to explain how these errors might occur.  Over time, by learning, we collect pieces of knowledge like birds in our personal aviary.  However, if we own a big aviary, we might find it hard to pick out a particular bird we added to our collection some time ago.  You know, they're all just in there flapping around.  It's easy to reach for the finch and grab the parakeet.  This mechanism too sounds plausible, but it has the weird consequence that we don't even know our own knowledge!  We don't know the contents of our own soul and make errors not out of ignorance, but because we know too much.  At this point Socrates lets the question of false judgement remain unsolved, and shifts to briefly give an argument for why knowledge cannot be true judgement alone.  Basically, you can be right for the wrong reasons.  This is the same idea as "true opinion" in Meno.  You may do something that works, you may come to the correct conclusion, but unless you can explain why it works, do you really know it?

5) That question sets up the final section of the dialog, in which Socrates and Theaetetus investigate whether perhaps knowledge is true opinion with an account (logos).  This definition is clearly the closest to our modern scientific understanding that requires reason and logic (alternative translations of logos) before something is considered knowledge.   Socrates proposes three types of accounts that might lead to knowledge.  Merely verbal accounts just dress up your judgement using words.  Today we call it 'bullshit'.  Reductive accounts describe all the elements that compose a thing, for example, all the letters that compose a syllable.  Finally, differentiating accounts distinguish between one thing and everything else in the universe.  This last type is clearly what we need to recognize Theaetetus and distinguish him from Theodorus.  Unfortunately, if knowledge is true judgement plus an account of the differences between the actual judgement and other possible judgements, we have a circularity.  To explain exactly what differentiates Theaetetus from Theodorus, we have to first off know that Theaetetus and Theodorus are different.  But how could we know this without already knowing what differentiates the two?   The dialog ends with this apparent aporia.  In fact though, by discussing false judgement so extensively in section 4, we've succeeded in specifying the form of knowledge as true judgement.  We're only unsure about what type of account will make the judgement true.  And the literary setting immediately refers this circularity or aporia back to the moral question that animates all of Plato's philosophy.  The constant and unquestioned assumption is that good and bad exist and are distinct.  As we saw in the Republic, the Good is the center of the Platonic universe.  Knowledge consists in being able to identify and choose the good when we see it.  Of course, we want to give a reasoned account of our choice that explains how we recognized that X was good.  Any such account though is going to depend on pointing to whatever criteria we already implicitly used in the recognition.  Plato is entirely aware of this circularity.  His dialogs all end in aporia or myth for exactly this reason.  We can only ground this circle with divine help.  We can only recognize the Forms through an epiphany that refers to a time before we were born.  The Good has always been there.  We are always just trying to recognize the memory of its Form when its distorted image appears in the world around us.  

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Hopefully that's enough of an overview for me to use Socrates' characterization of himself as a midwife of ideas (section 2) to explore the larger issue of the dialog more deeply.  While describing Socrates as a gadfly or midwife has become a philosophical cliche, these characterizations actually only occur in one dialog each (Apology and Theaetetus, respectively).  He is much more frequently characterized as a numbing or paralyzing agent who reduces his opponents to confusion by revealing to them that they don't know what they thought they knew (eg. the "broad torpedo fish" of Meno).  The reason for this change of metaphor is pretty obvious in the context of a dialog about knowledge.  It serves to highlight the paradox of Socrates' motto -- how can he know that he doesn't know if he doesn't even know what knowledge is?  Instead of confronting this paradox head on, Plato slyly changes the metaphor only to return to the problem through the back door.  As midwife, Socrates doesn't produce any ideological offspring of his own.  He merely sees to the successful birth of whatever ideas his pregnant patient has within them.  Thus his famed ignorance becomes the barrenness of a woman past child-bearing age.  However, Socrates also points out that a midwife actually still knows quite a lot.  For example, a midwife is best equipped to know when someone is pregnant (149c), and is also the one who knows how to bring on labor and see it through to birth (149d).  A midwife makes the best matchmaker (149e) because she can tell what type of children a couple are likely to have.  And finally, with his particular brand of midwifery, Socrates knows which babies to strangle in the cradle.

SOCRATES: So the work of the midwives is a highly important one; but it is not so important as my own performance. And for this reason, that there is not in midwifery the further complication, that the patients are sometimes delivered of phantoms and sometimes of realities, and that the two are hard to distinguish. If there were, then the midwife's greatest and noblest function would be to distinguish the true from the false offspring— don't you agree?
THEAETETUS: Yes, I do.
SOCRATES: Now my art of midwifery is just like theirs in most respects. The difference is that I attend men and not women, and that I watch over the labor of their souls, not of their bodies. And the most important thing about my art is the ability to apply all possible tests to the offspring, to determine whether the young mind is being delivered of a phantom, that is, an error, or a fertile truth.  (150b)

So Socrates' method of short questions and answers can help you give birth to a fully formed idea.  But this doesn't mean it's a good one.  It could be a mere phantom (note that φάντασμα has a wider range in Greek), error, or "wind-egg".  

I have a suspicion that you (as you think yourself) are pregnant and in labor. So I want you to come to me as to one who is both the son of a midwife and himself skilled in the art; and try to answer the questions I shall ask you as well as you can.  And when I examine what you say, I may perhaps think it is a phantom and not truth, and proceed to take it quietly from you and abandon it. Now if this happens, you mustn't get savage with me, like a mother over her first-born child. Do you know, people have often before now got into such a state with me as to be literally ready to bite when I take away some nonsense or other from them. They never believe that I am doing this in all goodwill; they are so far from realizing that no God can wish evil to man, and that even I don't do this kind of thing out of malice, but because it is not permitted to me to accept a lie and put away truth. (151c)

Socrates returns to this metaphor several times in the dialog to emphasize that the discussion should be a friendly and detached exploration of ideas, not some sort of adversarial combat that hinges on tripping up an opponent.  But it also implies that he not merely helps you give birth to an idea, but also judges its worth.  Socrates knows good ideas from bad.  Plato never asks it explicitly, but the question is obviously how he distinguishes the two if he is so famously ignorant.  

Since the whole dialog shows how knowledge takes the form of recognizing things, particularly recognizing what's good and bad for us, we clearly want to understand the source of Socrates' ability to distinguish good from bad ideas.  And when you read the text carefully and with open eyes, I think the answer is quite obvious -- god.  Socrates' ability as a midwife is repeatedly characterized as a divine gift (149c, 150d, 151d, 210d).  Reading the introduction to Andrea Nightingale's new book has made me more attuned to these moments.  She provides a compelling argument that Plato considered the Forms divine in a quite literal sense.  Every time that Plato speaks of the Forms, or discusses the trajectory of the soul's approach to them, we find some myth or metaphor about soaring up to a divine realm.  She doesn't actually discuss Theaetetus in that book, and this dialog doesn't even mention the theory of Forms explicitly, but the basic idea seems to apply equally well.  After all, here we are basically searching for the Form of knowledge.  The dialog does not reach a satisfactory rational definition of knowledge; as we observed, it ends in aporia like the early dialogs.  However, it essentially shows us what knowledge must be like, what form it must take.  We know by the end that it must be some form of judging correspondence by differentiating things that are like from those that are unlike.  At the very end, this definition founders on the question of how exactly we are to judge a correspondence.  To feel like we know something, we'd like to be able to explain the difference between things, most importantly between good and bad.  Unfortunately, to do this we have to already be able to identify good and bad using some set of distinct traits.  That is, we already need to know what's good and bad.  To effectively function as a midwife, Socrates has somehow overcome this circularity.  But ultimately this ability to distinguish true from false, good from bad, is a divine gift.  Knowledge of any the Forms, in fact, is a sort of divinely inspired epiphany.  Perhaps, as we observed with the Good in Book 7 of the Republic, all we can rationally know, or better, hypothesize, is the existence of the Forms.  To actually get to know them and use them, to see them in the world around us on a day to day basis, to go beyond hypothesis to the apodictic, seems to involve some act of transcendence.  This is the only way we overcome the circularity that dogs each of Plato's definitions of these Forms -- that is, precisely the aporia of the early dialogs.  That overcoming always brings us into the realm of the divine, and marks the point where Plato reaches for the stories and myths in place of arguments that we find in his middle period.  So it seems that paradox or logical circularity is not so much resolved as transcended by a deus ex machina moment, a moment which, not coincidentally, often involves some myth about circularity and the circulation of souls.  There's no way to reason ourselves to this epiphany, but, since it literally defines the form of knowledge, we'll recognize the divine in the world when we see it.  

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This reading of Theaetetus is inspired by and fits well with Deleuze's comments about the dialog in Difference & Repetition.  He sees Theaetetus as inaugurating a long tradition of seeing thinking as nothing more than recognizing an identity.  For reference, here are the relevant passages.

Furthermore, if the unspecified object exists only in so far as it is qualified in a particular way, then conversely, qualification operates only given the supposition of the unspecified object. We will see below how - in an entirely necessary manner - good sense and common sense complete each other in the image of thought: together they constitute the two halves of the doxa. For the moment, it suffices to note the precipitation of the postulates themselves: the image of a naturally upright thought, which knows what it means to think; the pure element of common sense which follows from this 'in principle'; and the model of recognition - or rather, the form of recognition - which follows in turn. Thought is supposed to be naturally upright because it is not a faculty like the others but the unity of all the other faculties which are only modes of the supposed subject, and which it aligns with the form of the Same in the model of recognition. The model of recognition is necessarily included in the image of thought, and whether one considers Plato's Theaetetus, Descartes's Meditations or Kant's Critique of Pure Reason, this model remains sovereign and defines the orientation of the philosophical analysis of what it means to think. (D&R 134)

You can see that he's thinking of the final aporia in Theaetetus when he talks about the "unspecified object" and its qualifications.  Socrates claims that to know things, we should be able to give an account of all the qualities that differentiate one object from another.  However, we already have to somehow recognize that there are two separate objects to be compared.  Which is to say that on some level we already have to know about what distinguishes those objects.  Here's how Plato puts the same idea.

SOCRATES: So, it seems, the answer to the question 'What is knowledge?' will be 'Correct judgment accompanied by knowledge of the differentness'— for this is what we are asked to understand by the 'addition of an account.'
THEAETETUS: Apparently so.
SOCRATES: And it is surely just silly to tell us, when we are trying to discover what knowledge is, that it is correct judgment accompanied by knowledge, whether of differentness or of anything else?  And so, Theaetetus, knowledge is neither perception nor true judgment, nor an account added to true judgment. (210a)

And while the reference Deleuze makes to the "faculties" in that passage is mostly aimed at Kant, we can see some of the same structure already in Theaetetus.  One of the ways in which Socrates refutes the threat of Protagorean relativism which appears when Theaetetus at first tries to define knowledge as perception is to appeal to the way the various senses are integrated by a common subject to produce a common object.

SOCRATES: Now what is it through which you think all these things about them? It is not possible, you see, to grasp what is common to both either through sight or through hearing. Let us consider another thing which will show the truth of what we are saying. Suppose it were possible to inquire whether both are salty or not. You can tell me, of course, with what you would examine them. It would clearly be neither sight nor hearing, but something else.
THEAETETUS: Yes, of course; the power which functions through the tongue.
SOCRATES: Good. Now through what does that power function which reveals to you what is common in the case both of all things and of these two—I mean that which you express by the words 'is' and 'is not' and the other terms used in our questions about them just now? What kind of instruments will you assign for all these? Through what does that which is percipient in us perceive all of them?
THEAETETUS: You mean being and not-being, likeness and unlikeness, same and different; also one, and any other number applied to them. And obviously too your question is about odd and even, and all that is involved with these attributes; and you want to know through what bodily instruments we perceive all these with the soul.
SOCRATES: You follow me exceedingly well, Theaetetus. These are just the things I am asking about.
THEAETETUS: But I couldn't possibly say. All I can tell you is that it doesn't seem to me that for these things there is any special instrument at all, as there is for the others. It seems to me that in investigating the common features of everything the soul functions through itself. (185c)

Finally, here's the long main quote that ends by contrasting the image of thinking as puzzlement presented in Book 7 of The Republic with thinking as recognition in Theaetetus.

Does not error itself testify to the form of a common sense, since one faculty alone cannot be mistaken but two faculties can be, at least from the point of view of their collaboration, when an object of one is confused with another object of the other? What is error if not always false recognition? Whence does it come if not from a false distribution of the elements of representation, from a false evaluation of opposition, analogy, resemblance and identity? Error is only the reverse of a rational orthodoxy, still testifying on behalf of that from which it is distanced - in other words, on behalf of an honesty, a good nature and a good will on the part of the one who is said to be mistaken. Error, therefore, pays homage to the 'truth' to the extent that, lacking a form of its own, it gives the form of the true to the false. It is in this sense that in the Theaetetus, under the sway of an apparently quite different inspiration from that in The Republic, Plato presents simultaneously both a positive model of recognition or common sense, and a negative model of error. Not only does thought appropriate the ideal of an 'orthodoxy', not only does common sense find its object in the categories of opposition, similitude, analogy and identity, but error itself implies this transcendence of a common sense with regard to sensations, and of a soul with regard to all the faculties whose collaboration [syllogismos] in relation to the form of the Same it determines. For if I cannot confuse two things that I perceive or conceive, I can always confuse something I see with something I conceive or remember - when, for example, I slip the present object of my sensation into the engram of another object of my memory - as in the case of 'Good morning Theodorus' when it is Theaetetus who passes by. Error in all its misery, therefore, still testifies to the transcendence of the Cogitatio natura. It is as though error were a kind of failure of good sense within the form of a common sense which remains integral and intact. It thereby confirms the preceding postulates of the dogmatic image as much as it derives from them, proving them by reductio ad absurdum.
    It is true that this proof is completely ineffectual, since it operates in the same element as the postulates themselves. Yet it is perhaps easier to reconcile the Theaetetus and the text from the Republic than it may at first seem. It is not by chance that the Theaetetus is an aporetic dialogue, and the aporia on which it closes is that of difference or diaphora (to the same extent that thought requires that difference transcend 'opinion', opinion requires for itself an immanence of difference). Theaetetus is the first great theory of common sense, of recognition, representation and error as their correlate. However, the aporia of difference exposes its failure from the outset, along with the need to search in a quite different direction for a doctrine of thought: perhaps the one indicated by Book VII of the Republic? ... Always with the reservation that the Theaetetus model continues to act in a subterranean manner, and that the persistent elements of representation still compromise the new vision of the Republic. (D&R 149)

This seems to me a penetrating analysis of Theaetetus along the same lines I was just trying to describe.  In particular, it explains why Socrates spends so much time investigating how false judgement can exist.  Socrates discusses the wax soul, which records an image of what it experiences, and the aviary soul, which captures and stores pieces of knowledge as if they were different birds.  These images explain the possibility of error as either a mismatch between perception and reality (caused by defective wax imaging) or a misidentification of the "bird of knowledge" you meant to pluck from the cage in your head.  Socrates calls false judgement "other-judging" or literally heterodoxy (190e).  It's a case of having "crossed opinions", oblique intersections, instead of having everything line up straight as in orthodoxy.  Knowledge here is literally a matter of keeping your opinions (doxa) straight.  Ignorance, however, isn't something fundamentally different; it's just getting your representations out of alignment, getting your wires crossed.  Ultimately, ignorance is just a failure of memory, a failure of integration across time or between senses.  Ignorance is the forgetting that prevents you from recognizing the Forms behind the things you find in the world.

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Finally, just so I don't lose it, here is my detailed outline of the dialog.
  1. Frame story (142-143c) -- Euclides reads his book about the conversation
  2. Introduction to the question of what is knowledge (143c-151e)
    1. Knowledge is important because wisdom is a type of knowledge (146)
    2. Knowledge of a craft or subject of study ≠ knowledge in itself (147c)
    3. What would be common to all types of knowledge? (148c).  Analogy to what is common between all perfect squares that differentiate them from other numbers.
    4. Socrates as midwife (149-151e) -- the goal of the conversation is to give birth to an idea not to have a contest of refutation.  But some ideas are phantoms and should be abandoned. [How can Socrates tell the difference?]
  3. First definition: Knowledge = Perception (151e-187)
    1. Metaphysical backdrop to Theaetetus' first definition (152-160e)
      1. Protagoras' world of pure movement and change (152a-e)
      2. Everything, including a quality like color, is a product of motion and rest.  Rest = death and motion is an inherent good (153a-154b)
      3. But how does motion and rest create change? How can a thing change its nature depending on context?  Three axioms of change. (154b-155d)
      4. Everything is motion.  There is not being, only becoming.  Subject and object are born simultaneously out of motion.  Even qualities like the Forms are "coming to be" (156-157e)
      5. Equivalence of Heraclitus, Protagoras, and Theaetetus definition (158).  Universal flow = relative measurement = knowledge as perception.  How could false perception even exist in a world of becoming?  How could we distinguish between waking and sleeping, madness and sanity?  'Socrates ill' will experience something totally different from 'Socrates well'.  All is relative.
    2. Criticism of the first definition and its implied metaphysics.  Rebuttal of criticism (161d-183c)
      1. Anything is the measure of everything (161d-162).  Why listen to Protagoras when you can measure for yourself?
      2. If knowing = seeing, then how can knowledge = perception if memory of the unseen exists? (163b-166a).  Socrates says this is a bit of a silly verbal debate (166a) but it foreshadows the theory of the integrative capacity of the wax soul.
      3. Socrates speaks for Protagoras and defends relativism (166a-168d)
        1. Protagoras would not grant the unity of the becoming subject of a memory (166b-d)
        2. Relativism doesn't mean that everyone is equal (167).  In fact, different people experience different things and the purpose of wisdom is to make changes for the better in how we experience them, not to simply represent them 'as they truly are' (a concept which Protagoras does not grant).
        3. Protagoras' thesis boils down to two points (168b) -- all things are in motion, and things are what they seem to be.
      4. Now that they have taken him seriously, Socrates and Theaetetus investigate whether Protagoras was right (169a-172c)
        1. People certainly behave as if they could be wrong, and have some concrete concept of truth and falsity, wisdom and ignorance (170b)
        2. The existence of intersubjective truth seems to disprove the theory (170e)
        3. Protagoras' thesis is self-defeating (171a-b).  He himself grants that those who disagree with his theory are correct (for them)
        4. The perception of truth ≠ the reality of benefit (171e).  Most perceptions are reality, but not everyone can recognize what is good and healthy for themselves.
      5. Interlude on the life of the philosopher and its contrast with ordinary life (172c-177c).  
        1. The philosopher is a free man, not a slave to the limited, combative argument in law courts (172)
        2. The philosopher focuses on another world and is often inept in the normal world (173d-175e).  his head is literally in the sky.
        3. There are two types of people or patterns in nature (175e-177c).  The justice and virtue loving philosopher contrasts with the ignorant and vicious person.  The punishment for evildoing is living forever in a vicious world just like the evildoer (177a).  [How can we know which is better?]
      6. Finishing the refutation of Protagoras (177d-187)
        1. Summary of Protagoras' thesis (177d-179d).  Man is the measure of perception (subjective) but not the measure of benefit (objective).  Individuals are not experts in, or the measure of, what will be good for them in the future.
        2. Protagoras and Heraclitus versus Parmenides (181)
        3. Summary of Protagoras' theory of pure motion (181d-183c).  Everything is becoming.  There is constant quantitative and qualitative motion that gives birth to subjects, objects, and even Forms.  But if all things are in motion, if everything becomes and nothing is, then there is no knowledge at all and everything is 'not in this way' (Mu?) (183b). [In particular this means that there can be no knowledge of better and worse, as Protagoras claimed]
        4. Skipping the discussion of Parmenides (184)
        5. Different modes of perception can land on something in common that must be perceived by the soul, and not through any one particular mode (184b-185e)
        6. Integration, comparison, and abstraction can only be performed by the soul (186-187).  Being and truth and other abstract qualities are beyond perception.  Therefore, knowledge (of 'things that are') ≠ perception.
  4. Second definition: Knowledge = True Judgement (187-201d)
    1. How is false judgement possible? (187e-200d)
      1. How can you confuse one known with another, or a known with an unknown, or one unknown with another? (187e188d)
      2. False judgement can't be judging things which 'are not' because the judgement is of something (188d-189b)
      3. How can false judgement be "other-judging" (heterodoxy) which confuses two things 'that are'?  If judging is like having an internal discussion how could anyone assert that the ugly is the beautiful? (189c-190e)
      4. Maybe you can confuse one thing you know with another.  The wax soul and mismatch between signs and representations (191b-195d)
        1. But in which case could this error creep in? (192). Combinations of knowing, perceiving, and their interaction.
        2. How could we confuse Theaetetus and Theodorus? (193-194c).  We have false knowledge when a current perception is fitted into the wrong wax mold. This can be due to unclear perception.
        3. False knowledge and failures of memory (194d-195d).  The wax in the soul can be either too hard or too soft.
      5. How can you confuse two abstract representations that do not involve perception?  The possibility of mathematical false judgement (195e-200d).  The soul as aviary and the difference between possessing knowledge and having it now.
        1. Learning is putting a bird into your collection, but to know and teach something you have to be able to retrieve the correct bird (198b).  It's possible to accidentally grab the wrong bird.
        2. But now our ignorance would be due to knowing too much! (199d-200d).  And if we say that we collect both birds of knowledge and of ignorance, and then confuse the two, we have the initial problem again at a higher level.  How can we confuse knowledge and ignorance?
    2. We don't understand false judgement, so let's investigate true judgement. (200d-201d).  True judgement alone ≠ knowledge because you can judge something truly for the wrong reasons.  For example, your judgement might be influenced by a canny lawyer.  
  5. Third definition: Knowledge = True Judgement with an account (201d-END)
    1. Accounting for knowable complexes as combinations of unknowable primaries (201d-206c).  The model of letters that only have names and syllables formed by a combination of letters.  A primary form must be simple, indivisible, and have no parts.  A whole is always the sum of its parts.  If we don't know the parts we can't know the whole.  Therefore, it makes no sense to claim that we know the complexes on the basis of unknowable elements
    2. Three types of account (logos) (206c-209)
      1. Verbal accounts are too easy to be considered knowledge (206d)
      2. Reductive accounts (207) involving elements can be accidentally correct without knowledge. Eg. the misspelling of names you are sounding out.
      3. Accounts of differences (208d) tell us why something is distinct from everything else.  Knowing Theaetetus is recognizing what particular features distinguish him from everyone.  This results in a circularity because we already have to know those factors in order to recognize something as distinct.