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In the Theatetus how successful is Socrates' refutation of Protagoran Relativism?
The project of the Theaetetus is to unveil Plato's epistemology, and more directly what he takes to be the nature of knowledge. Theaetetus, a student of Theodorous, puts forth the proposition that knowledge is perception, a view that is attributed to Protagoras and is the crux upon which his most famous dictum rests
'Man is the measure of all things of those that are, that they are, and of those that are not, that they are not.'
To say that knowledge is perception is to say that what one perceives is true, so that the objects of perception are indeed knowledge. The dictum marks that each individual perceiver determines through his perceptions the nature of reality. The implication of the Protagorean definition of knowledge is the denial of any transcendental standard of truth, independent of the individual knower, to which the knower is subject. It is also a denial that there is a reality to be known independent of one's own perceptions either nothing exists beyond perception or whatever exists is unknowable. To assess how successful Socrates' refutation is we must first assess how it is achieved, and from this consider whether Protagorean relativism can still be worthy of merit.
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To begin the refutation of Protagoras, Socrates first makes some preliminary objections. The first he construes is that one can not give such a special authority to man, as Protagoras gives by marking that "man is the measure of all things". Upon his theory it has to be the case that what is perceived by any perceiver is the 'measure of all things' for that perceiver. Thus man deserves no special authority, and Socrates uses the example of a pig's perception to press home this point. Protagoras' reply is that this is merely a debating point, however I agree with David Bostock on this that what Socrates has achieved with his first objection is the cornering of Protagoras using his own theory. Thus 'Protagoras himself can not be any better judge of truth than the ignorant audience which he mocks' . This seemingly debating point sets the tone for the major objections to follow, his vehicle for refutation is the use of Protagoras' theory against himself.
The second objection, which Socrates will later mark as again one of a 'Captious' nature concerns actual meaning which underpins perception. Socrates sees that we 'know what words and sentences mean, but we perceive only the words and sentences themselves and not their meaning.' This objection breaks down the Protagorean claim that what is perceived is knowledge as the must be an intermediary force that is discovering the meaning of perceived objects e.g. the mind. This objection is impressive as it can be seen as Socrates almost testing the water as it were, as it is upon this notion of an intermediary factor which he will build his own positive doctrine. Two other objections which Socrates marks which again are of a simplistic and captious nature are that
(i) If perceiving is knowing, then why does not hearing a foreign language lead to our knowledge of it? Or why does not seeing letters mean that one can read?
(ii) That one can know something by remembering it, but memory is not perception.
After these preliminary objections, Socrates allies with Protagoras out of fairness, and proposes a rebuttal of his own objections on behalf of Protagoras. He has Protagoras distinguish between what is true and what is better. While it may not be truer than that of someone else, one person's perception may nonetheless be better, if the majority makes this determination. Thus, if the majority decides that one mode of being (wisdom) is "better" than another mode of being (foolishness), then it is, so long as the majority does not change its collective mind. Thus Socrates establishes that there is a place for teachers- 'experts' like Protagoras- to help students learn to be "wise".
Socrates major objection draws upon his first preliminary one that he invoked. He points out the self-defeating character of an all-inclusive relativism, as proposed by Protagoras if "Man is the measure of all things," as Protagoras asserts, then the statement itself is relative, so that the opposite statement would be equally true if someone thought it be so. This means that in some cases, Protagoras would be wrong when he is right. To use a logical form to express this, where P stands for Protagoras' theory
 Either no-one believes P, or only Protagoras and his followers believe P
 If no-one believes P, then according to P it is not true for anyone
 If most people reject P it is "more false than true"
 According to P even Protagoras must agree that his opponents' belief that P is false, is itself true.
 Therefore not even Protagoras can accept P
Thus Socrates has placed his refutation of Protagorean relativism, yet how succesful is it? Its success should be judged as to what is established by the refutation. Plato has adapted Protagoras' Relativism to fit into his own epistemology. At best we can say that 'man is the measure of what he is at the time perceiving' . In essence Socrates has actually done nothing, for one who propounds a relativist thesis as Protagoras does refutes himself. Indeed if what he says is true then Protagoras can have no claim over our attention. To conclude this is an 'entirely satisfactory refutation of Protagoras' , for in its placement Plato clears the path, when coupled with the refutation of Heraclitus, to expounded his own thesis of knowledge. He adapts Protagoras 'perception' to fit within his own complex epistemology
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