Knowing and not Knowing in the Theaetetus

1. Irony and Circularity in the First Puzzle

Among the many puzzles and arguments which compose Plato's dialogue Theaetetus, there is one brief passage which stands out for its structural complexity and obscure richness. I am talking about Socrates' first puzzle on false judgment. This brief passage, which takes place from 188a to 188c, well deserves the name of puzzle in so far as it has not only been Theodorus and the young Theaetetus, but many readers after them, who have felt 'puzzled' by the words of Socrates. Among them, I must confess an almost immediate fascination with its many twists and puns. Despite being such a short passage, the structure of Socrates' first Puzzle is extremely complex. In order to carry my analysis, I will divide the puzzle in three major sections. The first section includes the antecedents of the actual puzzle. They are Theaetetus' postulation of the hypothesis that knowledge is true judgment [187b, c] and Socrates' question whether such thing as false judgment is actually possible [187c, d]. Socrates' presentation of the three major principles on which he will build his argument constitutes the second section. These three principles are: (1) "With each thing we either know it or we don't" [188a], (2) "...when a man judges, the objects of his judgments are necessarily either things which he knows or things which he doesn't know" [188a] and (3) "Yet if he knows a thing, it is impossible that he should not know it; or if he does not know it, he cannot know it" [188a, b]. Having stated these three principles, Socrates goes on, in the third and last section [ 188b, c], to build a reductio argument against the hypothesis that there is false judgment. His first step is to suppose that someone judges falsely that X is Y. Next, he applies principle (2) to both X and Y. When someone judges that X is Y, either (a) he knows them both, (b) he knows one but not the other or (c) he doesn't know either. Then, he gives different reasons why each one of the alternatives leads into absurdity. Finally, since these are the only possibilities of judgment, the hypothesis that someone judges falsely is rejected [188c].

The paradox that there cannot be such a thing as falsity is not new to Plato by the time of the Theaetetus. It appeared first in the Euthydemus(283e-284c) and later on the Cratylus (430-431). As a matter of fact, it had already showed up on the Theaetetus during the examination of Protagoras' thesis (170-171) and then again in the second puzzle of falsity from 188c to 189b. Furthermore, it will get a extensive and detailed treatment on the Sophist [from 236e on]. However, by most interpretations, the first puzzle stands alone in its approach in so far as it is the first not to rely on metaphysical questions on being and not-being, but on the relation between knowledge and judgment. All other times, Plato analyses falsity "by way of being and not-being"[Theaetetus 188d]. The reason why falsity is commonly linked to the problem of not-being is because of Socrates' recurring equation of false judgment with judging what is not.[White, Nicholas: "Introduction" to Sophist, Hackett, Indianapolis, 1993. pp. xviii, xix]. This way, the question whether there is such thing as falsity was not distinguished from the question whether it can be judged what is not. Consequently, there were always two questions lurking behind the paradox. First, whether there was such thing as what-is-not, and second, whether it could be an object of judgment. However, it was not until the Sophist, that Plato finally found a satisfactory answer to both questions.

Another singularity of this particular treatment of the paradox is its ironic circularity. It is plain to see that there is a circularity in Socrates' analysis of false judgment by way of knowledge, when it is precisely the quest for knowledge which has lead him to raise such a question. However, it is not a mere vice or error, but something that Socrates was at least conscious of. This becomes explicit later, at 196d, when he says

It is important to notice the ironic tone with which Socrates acknowledges this circularity. We can tell that this is not a circularity in which he has failed, but one which Socrates himself has built around his audience with their own words. By the time of the first puzzle, Socrates had already warned Theodorus "you don't realize what is happening. The arguments never come from me; they always come from the person I am talking to" [§161b]. Socrates takes constant care in distancing himself from the hypothesis and arguments brought up during the dialogue. Notice that, if the argument present in the puzzle were not ironic, Socrates would have proved that it is impossible to judge what is false, which is not only a 'very odd thing' ­as Theaetetus says­ but also one of the reasons why the Protagorean thesis was rejected earlier in the dialogue [179c]. Is it that Socrates is now accepting something that he previously rejected? Is this argument meant to reconsider Protagoras' view? To draw such conclusion would be to ignore the ironic tone of the whole puzzle. Once we have come to realize that we have fallen in Socrates' trap, it is very hard to break the circle he has built around us. It is easy to see that something went wrong, but it is hard to find where and how. It is necessary to trace back our steps one by one until we find where did we slip out of sense. This way, the whole argument could be seen as some sort of reductio argument in which Socrates is not rejecting false judgment, but certain view of knowledge which would entail the absurd conclusion that it is impossible to judge falsely.

If the puzzle is an ironic reductio of the sort I have advanced, the absurd conclusion that there is no false judgment must be a reductio of some or all of the premises upon which it is constructed, but which one? Socrates is rarely explicit about the premises of his argument, and even when he is, his irony warns us of taking his word for it. What seem like conclusions may be actually premises, and what looks like a logical principle may end up being a hypothesis. Hence, it is necessary to look carefully at each assumption made along the way of the puzzle.

2. The puzzling spiral

On this analysis, I divide the assumptions of the puzzle in three major groups corresponding to the aforementioned three sections of the puzzle. On the first section, the only hypothesis advanced is that of knowledge as true belief. It is a divided opinion whether the discussion of false belief is a part of the consideration of Theaetetus' second hypothesis, or if it is a mere digression. Under this perspective, it is not meaningless to ask whether the teachings of the first puzzle must be read within the conceptual frame of knowledge as true belief, or in isolation from the rest of the dialogue. On one side of the fence, we have interpreters who take this puzzle as an integral part of Socrates rejection of Theaetetus' second hypothesis. For them, the absurd conclusion that it is impossible to judge falsely derives directly from the view that knowledge is true judgment. Just like the following puzzles, this first onee is nothing but an argument against Theaetetus' hypothesis [Fine, Gail: "False Belief in the Theaetetus" in Phronesis No. 24, 1979. p.78]. On the other side stand those who see the puzzle as a separate argument independent of any particular hypothesis of what knowledge is. For them, Theaetetus' second hypothesis does not feature as premise of Socrates' argument. Consequently, if the puzzle is a reductio argument, the hypothesis rejected must be looked elsewhere. Finally, there are those who stand in middle ground between one extreme position and the other. These are interpreters who think that the only way to make sense of the puzzle is under the hypothesis of knowledge as true judgment, but still believe that its conclusions are farther reaching. Even the ones who think that the puzzle gives sufficient proof to reject Theaetetus' hypothesis think that the puzzle has much more to tell us about the problems of the relation between knowledge and judgment.

Most interpreters, however, have centered their analysis on the third and final section of the puzzle. There are certainly many problematic issues in those few lines. Mostly, the questions are raised on three major issues: (a) the division in cases (does it exhaust all possible cases of judgment?), (b) the rejection of each of the three possibilities (are they all actually impossible?, how?) and (c) the conclusion (does it follow?). Actually, the questions raised on (a) and on (c) are very closely linked in so far as the valid derivation of the conclusion that all false judgments depends directly on whether the division of the four cases is not exhaustive of all possible cases of judgment. If the three cases considered in (c) takes in consideration only some sort of judgments, then we can not reach such a general conclusion as that absolutely no kind of false judgment is possible[Williams Op. Cit. p.299]. This has been argued by some interpreters who take the threefold division to account only for certain sorts of judgments. This is, for example, the debate between Fine, on the one hand, and McDowell on the other. Fine thinks the three cases considered by Socrates actually exhaust all possible judgments, while McDowell takes cover only positive identity statements between individuals. However, it makes little sense to think that this may be the only slip in the puzzle, in so far as, if it were the only thing wrong with the argument, the only thing we could not derive is that not all sorts of false judgments are impossible, but certainly some sort are. If McDowell is right, for example, the puzzle would still prove that false judgments of the sort considered in (c) are impossible, but this conclusion is as absurd as the most general one. That it is impossible to misidentify individuals is as absurd a conclusion as that there are no false judgment at all.

Nevertheless, there is a more radical way to challenge Socrates' threesome division, besides the one followed by McDowell. It would be to say that it is not even exhaustive when circumscribed to the any particular sort of judgments, in so far as the division is not systematic at all. The apparent system of Socrates' division is just that: apparent. Looked more closely, these are three very different cases. The sense in which Socrates talks about knowing or judging in some cases is not the same that in the other, in such way that, even if they all were proved to be false, nothing general would have been proved still. This kind of interpretation tries to show that some of the three cases "X is Y" is read as an identity statement, and in others as predication. For matters of space, I will not develop this analysis any further, but only point towards the possibility.

On the other hand, most interpretations focus themselves on (b). They are interested on whether the three possibilities can be actually rejected. Since Socrates gives no explicit argument for the rejection of any one of the cases considered, but only several disconnected glimpses of what could have been his train of thought, there is no way of directly proving that his arguments are invalid. Before, we have to reconstruct them. Only then will we be able to judge their validity. I do not exaggerate when I say that, at least on this aspect, all interpretations I have read follow the same path. First, they assume that there must be some implicit premises upon which Socrates bases his reductio argument. Second, they postulate different premises, until they find the weakest set of premises which would derive the desired conclusions. Finally, they true to refute it. Since this is common ground, I will not stand here any longer, even though I will use some of the results of those analysis further down the road.

3. Off the beaten path

Even though most analysis focuses on the third section of the puzzle, and there is some reflection around its relation with Theaetetus second hypothesis, no interpreter I have come across even touches on the second and middle section of the text. Some find it unproblematic [C. J. F. Williams: "referential Opacity and False Belief" in The Philosophical Quarterly, Vol. 22, No. 89, October 1972. pp. 289-302.], while others ignore it completely. Myles Burnyeat's analysis of the puzzle on the "Introduction" of the Hackett edition of Theaetetus is a clear example of this sort of reading. Even though most of his analysis is a step by step, sentence by sentence reading of the dialogue. It surprisingly leaves this second section untouched. Also, John McDowell in his "Identity Mistakes: Plato and the Logical Atomists" [McDowell, John: "Identity Mistakes: Plato and the Logical Atomists"Meeting of the Aristotelian Society, 1970, pp. 181-195] does not even mention the three principles. The main reason why readers pass them by is that they seem to state nothing but logical principles. They seem to say nothing in particular about knowledge or judgment, but in general about the most fundamental rules of logical thinking. Under this view, these three principles are not only insufficient to rule out false belief, but immaterial to the derivation or reduction. Those who take this point of view argue that to us, people of the twentieth century, they may seem obvious, but it was not until Aristotle that the western tradition came to recognize them as basic laws of thought, and that is why Socrates had to enunciate them explicitly before using them as premises of his argument.

If this were so, however, we may wonder, first, why was Socrates so explicit about these seemingly obvious principles here, when elsewhere he fills this and many other of his arguments with much more obscure and specific hidden premises. Second, if such general laws are involved in some way or another in every valid argument, why did Socrates decide to make them explicit in this particular argument and not in the others? What is so special about this occasion? It is reasonable, hence, to question their apparent vacuousness. In this respect, I will take side with Gail Fine in her criticism against F. A. Lewis' [Lewis, F. A.: "Two Paradoxes in the Theaetetus" in J. M. E. Moravcsik, ed.: Patterns in Plato's Thought, Dordrecht, Holland, 1973. p.123] naive view that they are "instances of logical laws" [Fine: Op. Cit. p. 71]. Not so much because I think that they are definitely not instances of logical laws, but because I think this is a question that can be answered so easily.

On a first view, all three principles are about knowledge. Furthermore, they are about the objects of knowledge. The three of them say something about which objects may we know or not know. However, there are substantial differences in the way each one talks about them. On the one hand, the first and third principles are about what kind of entities can be objects of knowledge and not-knowledge. On the other, the second principle is not only about the objects of knowledge, but also about the objects of judgment, in relation to those of knowledge. What is stated is that objects of judgment are included among the objects of knowledge. In acknowledgment of this particularity, I am going to go through this second principle first, and then go to the other two, which make better sense when treated together.

(2) "...when a man judges, the objects of his judgments are necessarily either things which he knows or things which he doesn't know."

At first view, there is a straightforward inference from (1) "with each thing we either know it or we don't" to (2). If principle (1) applies to all things, and the set of things which a man judges is a subset of the set of all things, then (1) should apply to them too. However, we may wonder whether this is true, i.e., whether the objects of someone's judgments are actually among the 'all things' mentioned in (1). To meet this consideration, let's start by asking what are the objects of someone's judgment. This is an important question because, if we want the inference from (1) to (2) to hold, principle (1) should extend at least over the domain of (2). This means that the objects of knowledge should include at least the objects of judgment. What we take to be the objects of knowledge will also tell us something about what the objects of knowledge must be.

The objects of someone's judgment may be (a) the proposition that is asserted by the judgment, (b) what is meant by the terms that occur in it, (c) what is meant only by its subject term or (d) what is meant only by its predicate. In a judgment of the form 'X is Y', the object may be either (a) that X is Y, (b) X and Y, (c) only X or (d) only Y [I am not coming out with these possibilities out of the back of my mind, but from other platonic text sin which the issue of what are the objects of judgment is treated For example, when, presenting the hypothesis of falsity as Allodoxia, Socrates gives as an example of false judgment when "a man judges 'ugly' instead of 'beautiful' or 'beautiful' instead of 'ugly" [189c]. In this case, what is the object of judgment? What are 'ugly' and 'beautiful'? This passage cannot be read as literally saying that we judge 'beautiful' or 'ugly' but that we judge something as either beautiful or ugly as, for example, when we judge that Socrates (who is ugly) is beautiful instead of ugly. In this case, it seems like the object of our judgment is the predicate. When someone judges falsely that X is Y, he is judging Y instead of not Y. All possibilities are suggested one time or another in different texts. However, we are asking not in general what is the object of judgment all through the platonic dialogues, but in his very particular passage]. The most direct way of arriving at an answer to such a question is by looking at the rest of the argument. There are very few clues there, but from his example "Socrates is Theaetetus", we can infer that the correct answer is (b), since he says that he who knows neither Socrates nor Theaetetus cannot judge that Socrates is Theaetetus. Another reason for choosing (b) is that Socrates always talks about the objects of a judgment in plural, even when the judgment is one. Option (b) is the only one which allows this. Choices (a) and (c), on the contrary, would imply that there is only one object for each judgment. Therefore, the most likely alternative is (b). Notice that these objects are not necessarily propositions, which implies that there must be at least some non-propositional content in knowledge. If knowledge were exclusively propositional, but judgment not, the inference from (1) to (2) above would fail.

Having analyzed the hermeneutic perils involved in principle (2), specially in its relation to (1), we can return to the other two principles:

(1) "[It is] true about all things, together or individually, that we must either know them or not know them".

(3) "Yet if he knows a thing, it is impossible that he should not know it; or if he does not know it, he cannot know it."

These could be reformulated the following way:

(1') For any subject A and each object X, either A knows X or A does not know X.

and
(3') For any subject A and each object X, if A knows X then it is impossible that A does not know X, and if A does not know X then it is impossible that A knows X.

Put this way, (1') seems to be nothing but an instance of the principle of the excluded and (3') of the principle of non-contradiction, applied both to judgments of the form 'A knows X'. They say that, for any A and any X, (1') either A knows X or not, but (2') not both. However, there are some entanglements behind their apparent simplicity. First of all, for them to actually state the two aforementioned logical principles, the two possibilities considered should be actual opposites. As they are stated, both (1) and (2) include an explicit negation. The question, however, is what is being negated. If the 'not' of ' A does not know X' negates the whole proposition 'A knows X' then it is true that (1) and (3) are instances the logical laws of excluded middle and non-contradiction. However, it could be that 'A doesn't know X' is not the negation of 'A knows X'. One way this may be so is if there may be some quantification hid in both sentences, whether 'A knows X' means (a) 'A knows everything about X' or (b) 'A knows something about X' (and, then, if some, exactly what?). Then, 'A doesn't know X' may mean different things depending on which meaning of 'A knows X' it is the negation of. For ~(a), it would be "A doesn't know everything about X"; while ~(b) would be "A doesn't know anything about X". Notice that ~(a) is still compatible with (b) even though ~(b) is incompatible both with (a) and with (b).

This means that, if there is some quantification hidden in the meaning of 'A knows X", the interpretations which make (3) a case of non-contradiction would be

(3.1) ( (a) v ~(a) ) "For any A and any X, either A knows everything about X or A doesn't know everything about X"

and

(3.2) ( (b) v ~(b) ) "For any A and any X, either A knows something about X or A doesn't know anything about X"

but neither

(3.3) ( (a) v ~(b) ) "For any A and any X, either A knows everything about X or A doesn't know anything about X"

nor

(3.4) ( (b) v ~ (a) ) "For any A and any X, either A knows something about X or A doesn't know everything about X"

Notice that this fourth possibility is actually true, but in a vacuous sense, since (a) implies (b) and, by contra position, ~(b) implies ~(a). In other words, (3.4) is equivalent to

(3.4') ( (b) v ~ (a) ) For any A and any X, if A knows everything about X, A knows something about X

which is true except for those objects for which there is nothing to know [However, it is doubtful that Socrates considered the possibility of objects for which to know everything about them is the same than knowing nothing about them]. In any case, (3.4) has nothing to do neither with the principle of non-contradiction nor with telling us anything about what knowledge is. The previous translation, (3.3), on the contrary, is not necessarily true and, therefore, actually gives us some positive information of what knowledge may be. It is not obviously true because it is at least logically possible for A to know something about X and not know something else about it, in which case it would be false.

Principle (1), in turn, could also be interpreted in any of the following four ways

(1.1) ~( (a) & ~(a) ) "For any A and any X, it is impossible that A knows everything about X and A doesn't know everything about X"

(1.2) ~( (b) & ~(b) ) "For any A and any X, it is impossible that A knows something about X and A doesn't know anything about X"

(1.3) ~( (a) & ~(b) ) "For any A and any X, it is impossible that A knows everything about X and A doesn't know anything about X"

(1.4) ~( (b) & ~ (a) ) "For any A and any X, it is impossible that A knows something about X but A doesn't know everything about X"

Once again, the first two possibilities are instances of the principle of excluded middle. However, this time, it is the third combination which is vacuous, an the fourth which is problematic. Furthermore, it is so for the very same reasons that the third possibility below, i.e., because it rules out that A knows something about X and not know something else.

We can infer from this breaking down in cases for the first and third principles that: if we interpret knowledge and not knowledge in any of the first two possibilities, the principles are nothing but mere instances of logical laws, just as most lectors have taken them to be; but if we take them under the third or fourth interpretation, they can be either vacuous or unproblematic. If we want to defend the view that they are instances of the logical laws of excluded middle and non-contradiction, the only pertinent question is whether we should interpret them as including (a) universal or (b) existential quantifiers. It is easy to see that if we take knowledge to be (a) knowing everything about something, this would be sufficient to grant the forthcoming conclusion that none cannot judge falsely about what he knows. If this were so, however, the rest of the puzzle would be unecessary and gratuitous. Furthermore, it not only makes false judgement impossible, it has a whole lot more heavy consequences, too. For example, it would imply that to know something is to know everything, period. Some have taken this last drawback as enough reason to reject (a) as interpretation of knowledge in the first puzzle [McDowell: Op. Cit. p. 191]. For them, to know X can only be to know something about X, and the only pertinent question to ask is what something .

On the other side of the fence, those who read these principles as not being instances of logical laws take them to express the view that knowledge is an "an all or nothing, hot or miss affair" [Fine, Op. Cit. pp. 70-89]. Under this interpretation, (3) actually expresses some sort of exclusion of the middle, but not that between knowledge and its negation, but between knowledge and ignorance. The same about (1), which expresses the contradiction not merely between knowing and not knowing, but between knowing and ignoring. This way, both are no longer instances of more general logical principles.

It is now that it becomes important to look back upon the first section of the puzzle, and remember that Socrates is exploring with Theaetetus the hypothesis that knowledge is true judgment. They lay the basis of their interpretation on Theaetetus' hypothesis that knowledge is true judgment. Since there is no middle between truth and falsity, there cannot be middle between true judgment and false judgment either and, therefore, neither between knowledge and ignorance [Given the many similarities and parallelisms between both principles, my coming analysis will deal explicitly with (3) but almost all I say there can be extended easily to cover (1) too]. This position is very similar to that of Gail Fine in her False Belief in the Theaetetus. Nevertheless, it differs from mine in that it does not take interpretation (3.3) as a consequence of Theaetetus hypothesis that knowledge is true judgment, but takes them both to be different features of the same model of knowledge as acquaintance. This model ­which she calls the K model­ is to restrict knowledge to that which Bertrand Russell called knowledge by acquaintance [Fine: Op. Cit. p.70 ]. Knowing an object is having some sort of direct acquaintance with it. Either you have it or you don't. According to her, this is the view of knowledge lurking behind both Theaetetus' hypothesis that knowledge is true judgment and Socrates' view that there is no middle ground between knowledge and ignorance.

At this moment, it will prove useful to notice certain peculiar feature of (3), which is that it appears here not for the first time in the dialogue. We can find Socrates using a very similar premise in a previous arguments [165b] against Theaetetus first hypothesis:

This singular fact may be argued either for or against Socrates trust on the principle. On the one hand, it can be said that his repeated use of it is an indication that he actually believed it tobe true. However, once again, that would be to miss again on Socratic irony. Let's go back to the place where we found the previous text to take a better look at it. It is part of the long treatment Socrates gives to Theaetetus' first hypothesis that knowledge is perception. As a matter of fact, Socrates uses the principle precisely to distinguish knowledge from perception. Socrates' point is that (3) says something about knowledge which doesn't hold for perception and, therefore, expresses a basic difference between them. It says that, unlike perception, knowledge is the sort of thing that cannot be in one way and not in another with respect to the same object.

From this passage, I want to draw your attention to the fact that, in this part of the dialogue, from 165a to 165d, Socrates is not simply questioning Theaetetus on the consequences of his first hypothesis, but giving voice to an imaginary sophist. The 'he' in the previous quotation is "one of the mercenary skirmishers of debate". This refutation of Theaetetus' first hypothesis is not the kind of refutation which he sees as part of his midwifery of ideas job, but mere sophistry. In this sense, it is clear that Socrates is at least suspicious of this argument in such a way as it is not absurd to question his trust on what he says there. Therefore, it is very plausible that Socrates took (3) to be not the instance of a general law of thought, but some problematic view of knowledge. In the same sense, it made sense for Socrates to be explicit about principle (3). If this is true, it may also be possible that the absurd conclusion that false judgment is impossible reduces this very principle, and the view of knowledge expressed on it.

On the other hand, the problem with refusing to read (1) and (3) as mere instances of logical laws is that in both of the last two alternative readings above ­(1.3) and (3.3) or (1.4) and (3.4)­ is that we can read any one of them in the meaningful way only by means of taking the other as vacuous. If we, for example, read (3) as (3.3), we would have to be consistent in our reading of (1), and accept its vacuous meaning (1.3.). The same if we choose to take (1) to mean (1.4), in which case we would have to take (3) as expressing the empty proposition (3.4). Either way, it is impossible to do precisely what Fine wants to do in her interpretation, which is to avoid reading any of the principles of this section as vacuous. Either you make one of them meaningful, or you make the other, but it is impossible to make them both say something. The only way out for Fine is to say that Socrates uses 'know' and 'not-know' in one sense in (1) and another in (3). In (1), knowing X is (b) knowing something about something, and not-knowing X is ~(a) not knowing everything about X, while in (2), knowing X is (a) knowing everything about something, and not-knowing X is ~(b) not knowing anything about X. This escape, however, sounds extremely ad-hoc. On the other hand, however, this may not be such a big problem for Fine's interpretation, since it is also true that either interpretation implies her view that it is impossible for A to know something about X and not know something else. In other words, just as it is impossible to avoid reading one of them as vacuous, it is also impossible to read the other as saying that knowledge is an all-or-nothing question.

Finally, there is another objection to the view that 'A knows X' has a hidden quantifier. Either if we take option (a) or (b) above, it seems that X is no longer the object of knowledge, but something or everything about X. What A knows when A knows X is not X, but something or everything about X. This goes against the analysis of the first section of the puzzle we gave before, which said that the object of knowledge were entities like Socrates or Theaetetus, not something or everything about them. Our argument relied heavily on the example 'Socrates is Theaetetus' about which Socrates says the objects (of judgement and, therefore, of knowledge too) are Socrates and Theaetetus. If to know Socrates or Theaetetus is to know everything about them, then for A to say that 'Socrates is Theaetetus' would mean something like "Everything about Socrates is everything about Theaetetus". In general, any judgment of the form "X is Y" would mean that everything about X is everything about Y. Furthermore, every thing would be identical with everything about it, which is a conclusion as odd as that of the impossibility of falsity. The same if we take knowledge to be knowledge of something. Then, for A to say that 'Socrates is Theaetetus' would mean "something about Socrates is something about Theaetetus". In general, any judgment of the form "X is Y" would mean that something about X is something about Y. Furthermore, every thing would be identical with something about it. Once again, we seem to be talking gibberish.

In resume, each one of the four different ways of interpreting (1) and (3) gives us a very different view of knowledge, and provides a very different framework for working the derivation Socrates wants to construct in the next section of the puzzle. There is no definitive argument for uniquely choosing any of the alternatives. In this paper, I have gone through some of the main virtues and vices of each one of them, showing why different interpreters may feel akin to choosing one interpretation instead of the others. As you can see, I have no answer to the question of which are the hypothesis to be rejected if this puzzle is to be read as a sophisticated and ironic reductio argument. Still, I have succeeded in tracing my steps in the least studied section of the puzzle and finding enough problems and riddles as to suggest that a more comprehensive study of the elements involved in the puzzle may prove to be not only fruitful but necessary.



Axel Arturo Barceló Aspeitia

Autumn 1996