Antoinette DeMotta Plato s Response to Epistemological Relativism: A New Reading of the Peritrope Introduction In this paper I will present a new reading of Plato's argument against epistemological relativism, which is found in his Theaetetus dialogue. Under my reading Plato has Socrates character carefully construct an argument which intentionally fails, and then its failure becomes the main point of this passage. I will argue for this claim by critically examining the two dominant readings of the passage. I first articulate the central argument of Myles Burnyeat s reading of this passage. Then I show that under Burnyeat s interpretation, Protagoras Measure Doctrine which is the epistemological claim being addressed requires an eventual assertion. Burnyeat claims that a judgment can only be qualified as many times as can be comprehended, and then an absolute assertion is implicit. So a qualified version of the judgment about the falsity of Protagoras Doctrine must be eventually asserted absolutely, leading to an apparent self-contradiction for anyone who accepts the Measure Doctrine since they must accept that all judgments are true and here is one
which contradicts that judgment, and it must also be true. I argue that, because of this, Burnyeat s reading requires us to conclude that Plato begs the question against Protagoras. This is because a conclusion which requires a relativist to make an eventual absolute assertion presupposes a realist conception of truth, with which it then evaluates relativism, showing that it falls short. While Timothy Chappell points out this very fact about Burnyeat s reading, his own reading also smacks of question begging. I will show how Chappell s reading first concludes that Plato s strategy is to render Protagoras devoid of assertion making ability by driving Protagoras into self-division, and then holds this conclusion to be harmful to the Measure Doctrine. I will argue that with this move, his reading makes the same mistake as Burnyeat s, since it, too, assumes that being unable to make an absolute assertion is harmful to a relativist. After careful consideration of both Burnyeat and Chappell, I conclude that any reading which relies on either a requirement to, or a failure to assert the relativistic claim are not sufficient in determining the meaning of this passage. My reading first establishes a connection between the metaphysical foundation of Protagoras doctrine which is constructed by Plato earlier in the dialogue and the
argument in question, often refereed to as the peritrope argument. I argue that understanding this connection is imperative to correctly reading the passage under discussion. My reading shows that Plato, when having Socrates build such a metaphysical foundation on which to rest the central claim of the Measure Doctrine knowledge is perception is acknowledging the ultimate source of disagreement between Protagoras and Socrates. He does so by showing the incommensurability of Socrates and Protagoras metaphysical assumptions. I claim that it is not a disagreement which Plato believes can be solved by simply building an argument against the Measure Doctrine itself, but instead he requires us to turn to metaphysics in an attempt to discover which metaphysical system is accurate. Whomever has the accurate metaphysical foundation will be able to answer the question what is knowledge since knowledge, for Plato, can only ever be of what is. I conclude that Plato did not intend Socrates argument to harm Protagoras Doctrine in the way most scholars have assumed. I go on to argue that Plato would recognize the inability of his argumentative method to harm a doctrine which rests on a metaphysical foundation such as the one that is so carefully exposed in the dialogue leading up to the execution of the argument.
This metaphysical model, on which Protagoras Doctrine rests, is one which forbids the possibility of contradiction not only among different individuals but also within one perceiving individual. Plato s argumentative method, on the other hand, gets its power from pointing to such contradictions within one individual. My reading asserts that it is the fictional character Socrates, not Protagoras who is defeated when his argument begs the question against its opponent. This interaction is used by Plato to make a larger point about the implications of Protagoras Doctrine, as well as about the nature of knowledge and the direction of our search for it. Further, I point out a way in which the peritrope argument still harms the Measure Doctrine indirectly by showing that, simply by discussing the truth or falsity of the Measure Doctrine we are, in fact, invalidating such a claim. Socrates argument against the Doctrine doesn t have to be a successful one. Just by the act of arguing he demonstrates that it must be the case that more than simply perception exists, since we are currently using an altogether different faculty to examine the truth or falsity of the Measure Doctrine, and this activity is clearly not an act of perception. Thus, Plato is validated in rejecting a conception of truth which relies on the notion that perception is all that there is of knowledge.
The task of this paper is to present a new reading under which Plato's opposition to epistemological relativism is altered. This reading aims to clear Plato of any question begging charges, and deepen his response to this issue by showing that he recognized the difficulty of arguing against epistemological relativism in a way that does not rely on assuming the existence of absolute truth to do so. I. Myles Burnyeat Myles Burnyeat s reading of this passage was ground-breaking, since it was the first to show the peritrope coming last in a closely knit sequence of three linked arguments 1 which ultimately defeat the Measure Doctrine. Burnyeat notes that up until this point in the text Socrates arguments against the Measure Doctrine have all been carefully qualified. This is crucial because if Plato built an argument ignoring the qualifications in Protagoras claim, as was thought prior to Burnyeat s reading, he would not truly be arguing against the Measure Doctrine. Protagoras claim, that human s are the measures of what is, does not claim that all judgments are true simpliciter, but rather that all judgments are true for the person judging them so. It is only at the crucial 1 Burnyeat (1976) P. 177
last part of the three closely linked arguments that the statements are given in an unqualified way. For Burnyeat, unlike for previous interpreters, this signifies a larger meaning which must be teased out. According to Burnyeat, by the time the peritrope is reached, what Protagoras is forced to accept is that a person who judges the Measure Doctrine to be false is succeeding in judging it to be unqualifiedly false, since they do not accept that humans are the measure of what is. Then, the relativizing qualifiers are inappropriate when stating their judgments, since their judgments are a rejection of the need for qualification. Their judgment since each judgment. or measure is of what is must be true. What is true during this particular instance of measuring or judging is the falsity of the Measure Doctrine itself, and with it comes the removal of the necessity to qualify statements. This judgment, too, must be true for Protagoras, since he still holds that all judgments are true for the person judging them so. In this case, what Protagoras is accepting as true is a judgment about the unqualified falsity of the Measure Doctrine. The judgment he accepts states that not all judgments are true, and this judgment is done without qualifications. So, the conclusion is that Protagoras Doctrine forces whomever accepts it into a self contradiction. If they accept that all judgments are true,
they must also accept that if someone judges the statement all judgments are true itself to be false then that judgment too must be true, with no qualification being necessary. Burnyeat s key assumption here is that an assertion can only be qualified as many times as can be comprehended, and then an absolute assertion is implicit. This is why, when a person judges the Measure Doctrine to be false, it becomes unqualifiedly false instead of only unqualifiedly false for the person judging it so. Otherwise, according to Burnyeat, we would have incomprehensible statements of truth, and would lack the ability to assert anything. Burnyeat s conclusion is that Protagoras is defeated by this argument because it requires him to accept two contradictory judgments at once. It is this conclusion which is meant to be the killing blow. II. Timothy Chappell Timothy Chappell s reading takes Protagoras to be making a reductive analysis of truth, that it is nothing more than truth-for. Chappell claims that Plato is presenting a challenge as he does throughout many of his dialogues where the interlocutor must show the equivalence of two concepts which he is claiming are equal. Here, Protagoras
is claiming that truth is nothing more than truth-for, or appearance-to. It entails a dilemma. Either Protagoras reductive analysis will succeed or it will fail. If it fails, then it does not do what it is claiming to do, and there is more to truth than just truth-for. If it succeeds, then Protagoras cannot object to Plato s dropping of the relativizing qualifiers during the crucial point of the peritrope argument. Since Protagoras himself has agreed that the two terms truth and truth-for are completely identical and therefore interchangeable, we should not see any difference in saying the measure doctrine is false is true for the opponents of Protagoras and the measure doctrine is false is true (simpliciter). If Protagoras does disagree with this interchangeability, then he is admitting that the two concepts truth and truth-for are not identical, and therefore failing to make an adequate reductive analysis. In other words, if the reductive analysis fails, then it fails, and if it succeeds than it also fails, since it brings Protagoras into an awkward situation in which he must admit that truth and truth-for obviously do not mean the same thing when Plato inserts the former into the peritrope to make his point. Chappell concludes his reading by stating that Plato fails to convict Protagoras with self-contradiction. Plato does, however, according to this reading, and per his
original intention, provide a dilemma between self-contradiction and self-division which eventually leads Protagoras relativism into self-defeat. This is accomplished by constantly provoking Protagoras to choose between self-contradiction and self-division. When Plato shows Protagoras that he has a contradiction, the only defense Protagoras has at his disposal is to once again divide himself to preserve his theory that every appearance is true. This self division is simply a defense against an instance where Protagoras must accept two contradictory things, such as the truth of his Doctrine and the falsity of his Doctrine. If Protagoras must accept that the Doctrine is both true and false, it is of no consequence to him since his perceptions may be completely different from one moment to the next. That being so, contradictory truths will emerge but they are not truly contradictory since the self which houses them is not the same when it is divided among each perceptual instance. Eventually, this leads to him becoming a completely non-unified thing, incapable of dialectical discussion, which disallows him from even presenting his Measure Doctrine or participating in any form of conversation whatsoever. Protagoras can no longer speak about the nature of truth because his words have no meaning. All he can do is present descriptions of his sensations. What Plato shows with the peritrope
according to this reading is that in such a world, stating theories of truth and engaging in dialectic is meaningless and impossible. So the point of Plato s argument, according to this interpretation, is that we are left wondering how and why Protagoras is bothering presenting us with his theory in the first place, since he can neither state nor defend it in any way. III. Criticisms of Burnyeat and Chappell Both Burnyeat and Chappell offer invaluable contributions to the discussion of the peritrope. Much of my own reading depends on the work they have done. My task is not to scrap their readings in favor of a whole new approach, but rather to use ideas from both thinkers and then go on to reinterpret what Plato s overall point is. My criticisms of Burnyeat and Chappell require an understanding of how and why Plato has Socrates tie Protagoras Measure Doctrine to the Heraclitean Theory of Flux. The Theory of Flux acts as a metaphysical foundation to the theory of knowledge being discussed. This foundation is simply the metaphysical implications of Protagorean epistemology. I will now briefly summarize the Theory of Flux and its connection to the current discussion.
Perceptions, for Heraclitus, are merely the result of the co-mingling of our passive abilities to perceive which are never the same from one moment to the next together with things that act upon our senses and are capable of being perceived. When the active acts upon the passive, a perception occurs. Perception is all that there is of reality under this model. Thus, when a human measures what is, they are simply experiencing, through the senses, an instance of this interaction. There is no way for the measuring to be false because the process itself determines what is. In the Dialogue, Socrates uses an example of wind to demonstrate. He explains that, under this model, it would be absurd for two people to argue about whether the wind that they both experienced is either cold or not cold. That the wind was cold to one while it was not cold to the other can be explained in a reasonable way. The experience of cold wind or not-cold wind occurs when a passive perceiver and an active thing capable of being perceived collide. Since neither the wind itself, nor the thing which it is acting upon will remain the same from one moment to the next, each instance of their meeting, or what we call perception, will be different. Thus, the same wind can be cold to one and not cold to the other, and both can be correct and yet no contradiction has occurred. Thus, gaining knowledge of what is requires only an ability to perceive, and
every perception must necessarily be true. So under such a metaphysical model, Protagoras would be justified when saying that humans are the measures of what is. My claim is that, given the careful articulation of such a metaphysical foundation, Plato would not then build an argument which blatantly ignores the implications of the foundation. Yet it appears that both Burnyeat and Chappell s interpretations of the peritrope would have him doing just that. What follows are my arguments for why both thinker s interpretations of this passage ultimately show Plato to be begging the question against Protagoras doctrine. Burnyeat has the conclusion that if Protagoras is forced to accept both the truth and falsity of his own Doctrine then he is defeated by Plato. However, keeping in mind the above metaphysical model, we can see that such a conclusion would not harm Protagoras. If judgments about what is differ from one perception to the next due to the fluctuating nature of both perceiver and perceived, then one individual can contradict itself from one perception to the next without any real contradiction occurring. That the Doctrine itself is both true and not true is exactly what is expected from the implications of the Doctrine. To hold this consequence of the Doctrine against Protagoras is to privilege the notion of truth realism, which is to beg the question.
Chappell s reading has a similar problem. He concludes that Protagoras Doctrine requires a perceiver to divide him or herself so radically that they become unable to participate in philosophical conversation, or to even make claims that go beyond a description of that individual perception. This, Chappell assumes, is an unattractive implication of the Doctrine. However, to assume that this conclusion is harmful in any way is to assume that our knowledge of truth must be something greater than our knowledge about the individual perceptions which we experience. This is to presuppose the opposite of Protagoras point, and then hold it against him when he fails to abide by that presupposition. So we must conclude that Chappell s reading, too, requires Plato to be begging the question against Protagoras. IV. A New Reading It is important to begin thinking of the events in this section of the Theaetetus as occurring on two different levels which run parallel to one another. On level one, Socrates is engaging in conversation with Theaetetus, Theodorus, and the ghost of Protagoras. On level two, Plato acts as a kind of puppet master, having his characters act out certain arguments in order to serve a greater overall argument. The arguments
occurring on level one should not be seen as conclusive to Plato s whole message. Only through interpreting certain clues in the dialogue can we come to have an understanding of the complexity of Plato s response to epistemological relativism. Understanding the connection between the metaphysical foundation of Protagoras Doctrine which is constructed by Plato earlier in the dialogue and this section of the dialogue, is imperative to correctly reading the passage under discussion. My reading shows that on level two Plato is acknowledging the ultimate source of disagreement between Protagoras and Socrates. He is showing the incommensurability of Socrates and Protagoras metaphysical assumptions. These assumptions are what lead both to their respective conclusions about what knowledge is. This disagreement is one that cannot can be solved by building an argument against the Measure Doctrine, since Protagoras metaphysical model is one which denies that arguments can shed light on truth. For Protagoras, two people who are disagreeing are actually talking about two different things. Even an instance of one person holding two contradictory beliefs is not in disagreement with himself or herself, since each new perception is a new instance of what is, under this model. Plato is telling us that in order to solve this dispute, we must turn to metaphysics
to discover which metaphysical system is accurate. Whomever has the accurate metaphysical foundation will be able to answer the question what is knowledge since knowledge, for Plato, can only ever be of what is. A large part of what Plato is communicating here is that the discussion about knowledge doesn t even make sense until we know what is. Only then can we see if our beliefs matches up to that, and can therefore be called knowledge. It is clear from the above that Plato did not intend Socrates argument to harm Protagoras Doctrine in the way most scholars have assumed. Plato would recognize the inability of his argumentative method to harm a Doctrine such as Protagoras which rests on a metaphysical foundation that forbids the possibility of contradiction not only among different individuals but also within one perceiving individual. Plato generally has Socrates give arguments that get their power from pointing to contradictions within one individual s beliefs, although he himself claims to know nothing. Here we can see that one level two, Plato is constructing a larger argument by having Socrates character fail to defeat Protagoras on level one. He does so by intentionally having Socrates build an argument which begs the question against its opponent. This interaction is used by Plato to make a larger point. This larger argument
is one that neither Burnyeat nor Chappell acknowledged in their readings. Both have readings which are cohesive, but the interpretations behind those readings are not sufficient for getting at the entirety of Plato s argument against epistemological relativism. Plato s argument has two parts. The first is, as stated above, that Protagoras and Socrates cannot defeat one another since both are operating on entirely different metaphysical assumptions. Protagoras assumptions negate the possibility of being defeated by an accusation of contradiction. Socrates, on the other hand generally approaches situations under the assumption that showing a person their contradictory beliefs is fruitful in the search for truth. Plato is here expressing the idea that metaphysics must precede any claims about knowledge. It also hints at the bleak nature of a radical empiricist metaphysics, and the epistemological and moral implications which can inevitably be derived from such a foundation. The second point being made by Plato on level two shows a way in which the peritrope argument harms the Measure Doctrine. It does so by showing that, simply by discussing the truth or falsity of the Measure Doctrine we are, in fact, invalidating the claim by Theaetetus which started this discussion. This claim is that knowledge is
perception. Socrates argument against the Doctrine doesn t have to be a successful one to defeat Theaetetus claim. Plato is pointing to the act of arguing itself, and we are supposed to conclude that more than simply perception exists, since we are currently using an altogether different faculty to examine the truth or falsity of the Measure Doctrine. We are using our faculty of reasoning, and this activity is clearly not an act of perception. Thus, Plato is validated in rejecting a conception of truth which relies on the notion that perception is all that there is of knowledge. In addition to this, we can at least begin to see an avenue for truth which does not completely rely on our senses, and does not end in such a fatalistic conclusion as Protagoras. Conclusion In this paper I have presented a new reading of Plato's peritrope argument against epistemological relativism. I have shown how Plato has Socrates character carefully construct an argument which intentionally fails, and how its failure becomes the main point of this passage. I have argued for this claim by critically examining the two dominant readings of the passage. Through my examination of the readings of Myles Burnyeat and Timothy
Chappell, I have shown the necessity of reproaching this passage in a way which clears Plato of any question begging charges. I show how both Burnyeat s and Chappell s readings require us conclude that Plato begs the question against Protagoras. Then, I go on to give an alternate reading which does not necessarily reject Burnyeat and Chappell outright, but rather offers us a scenario in which either reading could be salvaged if we assume that the passage is functioning on two levels. I have shown that as long as Plato is seen to be intentionally causing Socrates to build an argument which begs the question, then we can still conclude that Plato s overall point includes a deeper response to epistemological relativism. This overall response must include careful attention to the metaphysical foundation of the Protagorean Measure Doctrine. The foundation is built when Socrates joins the Doctrine to the Heraclitean Theory of Flux. This gives a scenario in which the Measure Doctrine would be an adequate response to the question what is knowledge which drives the Theaetetus. My central argument against the readings of Burnyeat and Chappell involve questioning why Plato would present us with such a tight metaphysical system for Protagorean relativism, only to blatantly ignore the implications of the system when having Socrates build an argument against Protagoras. I conclude that
Plato must be making a more complex point, and that his ultimate response to epistemological relativism is not revealed by the readings of Burnyeat or Chappell. Although either could claim an accurate reading of the peritrope itself, both are guilty of losing sight of the bigger picture into which the argument fits. I conclude that without this larger point, given the metaphysical implications of the Measure Doctrine, any arguments against Protagoras will appear to be question begging. I conclude that this passage is meant to demonstrate the incommensurability of Socrates and Protagoras metaphysical assumptions. Plato s main point is that, until we direct our energies towards a metaphysical investigation, we will not be able to conclusively answer the question what is knowledge.