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Does Protagoras refute himself?


Protagoras believes that all beliefs are true. Since Protagoras' belief that all beliefs are true is itself a belief, it follows (somewhat trivially, perhaps?) from Protagoras' belief that all beliefs are true that Protagoras' belief is true. But what about the belief that Protagoras' belief is false? Doesn't it follow, by parallel reasoning and not at all trivially. that if all beliefs are true and there is a belief that Protagoras' belief is false, then Protagoras' belief is false?

Protagoras has three alternatives here. First, he may simply agree that this is how things stand. There is indeed as much reason to think that Protagoras' view is true as that it is false; however, this is a position which the author of the Antilogies,(2) the Opposite Arguments', can happily accept. But Protagoras does not take this line.(3)

Or second, Protagoras can deny that there is a belief that Protagoras' belief is false. This move has awkward consequences. Suppose Protagoras is right, and no one truly believes that Protagoras' belief is false. Even so, don't some people believe that they believe that Protagoras' belief is false? (For example, I believe I believe that.) But Protagoras holds that all beliefs are true. So my belief that I believe that Protagoras' belief is false must be true. But if that's true, then it's true that I believe that Protagoras' belief is false; and if that's true, then (by the argument of the first paragraph) Protagoras' belief is false.

Here Protagoras can (if he likes) repeat the denying manoeuvre, and deny that I even believe that I believe that his belief is false. In which case I might retort that, at any rate, I believe that I believe that I believe that Protagoras' belief is false... So we might go on; but the argument seems inconclusive for either side, which is perhaps why Protagoras does not take this second alternative either.(4)

His third alternative is to accept that some people, for instance the present writer, do hold that Protagoras' belief is false; but to make a qualification about what `true' and `false' mean. And this is the route that Protagoras actually takes.

This is his argument. Suppose you say Black is Black and I say Black is White. We seem to be contradicting each other, yet according to Protagoras we can both be right. For our beliefs are (only) relative truths. Relative to what? Relative to us: that, I take it, is the point of his famous slogan (DK B1) that `Man is the measure of all things'. In particular `man' (i.e. any particular human)(5) is a measure of truth about all things. If anything is a truth then it is a truth for someone; conversely, if anything is a belief, then that belief is a truth for the one who holds it. Hence, all beliefs are `true'; but `true' means `true for someone'.

So if I believe that Protagoras' belief is false, this means that Protagoras' belief is false for me. That is, it means that it's true for me that Protagoras' belief is false. But it seems quite all right for me to think this at the same time as Protagoras goes on believing his belief. No contradiction is involved. For Protagoras' belief is true for just as my belief that Protagoras' belief is false is true for me; and just as Protagoras' belief that my belief that Protagoras' belief is false is true for Protagoras too.

Can Protagoras say all of this without running into any sort of incoherence? I think he can. I know of no successful version of the peritrope argument--the claim that Protagoras refutes himself; as I now argue.

First, Plato. Plato correctly states the Protagorean thesis as the view that `What seems true to any person actually is true, to that person to whom it seems true' ([GREEK TEXT NOT REPRODUCIBLE IN ASCII] Theaetetus 170a). But--notoriously--he then goes on to point out the self-refutingness that follows if such a person `agrees with the view of those who think that his belief is false' ([GREEK TEXT NOT REPRODUCIBLE IN ASCII] Theaetetus 171b). This latter remark does not even address Protagoras' thesis, never mind refute it. Protagoras would merely point out that if they think his belief is false, then his belief is false for them, not false, full stop.

Similarly Sextus Empiricus, who takes Protagoras' view to be `that every phantasia is true' (as Barnes translates it).(6) Sextus refutes this allegedly Protagorean claim simply by pointing out that it is a phantasia that not every phantasia is true: so the claim `that every phantasia is true' entails its own falsity. Elegant, but irrelevant, for Protagoras said no such thing as `every phantasia is true'.

As for Aristotle, he seems (on this occasion) even wider of the mark than Sextus and Plato. He apparently takes it that Protagoras' view is that `it is allowed to affirm or deny any predicate of any subject' ([GREEK TEXT NOT REPRODUCIBLE IN ASCII] Metaphysics 1007b22). Plato and Sextus distort Protagoras once over, by treating him as if he had said that all beliefs are true (not just true for their holders). Aristotle apparently distorts him twice over, by taking him to mean that all propositions(7) (not just all beliefs) are true (not just true for their holders). If all propositions were true that would indeed, as Aristotle remarks, make nonsense of human discourse.(8) But Aristotle's remarks about this interesting prospect are simply irrelevant. For Protagoras is not committed to anything like believing that all propositions are true. Whether Aristotle is being ingenuous or disingenuous, he is certainly guilty of ignoratio elenchi.

What about the moderns? Burnyeat has argued(9) that [GREEK TEXT NOT REPRODUCIBLE IN ASCII] should be understood as a doctrine about the thought world of a subject; `true for x' means `true of x's world'. Hence if Protagoras accepts that his doctrine is not true for me, this means that he accepts that his doctrine is not true of my world. But if his doctrine is not true of my world, then it is not true: for his doctrine is supposed to be about anyone's world.

The very fact that unqualified `true's and `not true's are appearing in this argument must, I think, be a sign that something has gone wrong. Surely Protagoras, if he could get his head out of the earth, would reject it. For his doctrine is not, I suggest, `about anyone's world', i.e. about the way things are in anyone's world. It is about (what seems the case to Protagoras about) anyone's truth, i.e. about (what seems the case to Protagoras about) what it is for things to be a certain way in anyone's world. If the way things are in my world is that Protagoras' thesis seems false, then certainly Protagoras' thesis is `false of my world'. But it does not follow that it is false, full stop. And in any case, Protagoras has an account of falsity which says that (it seems to him that) there is no unqualified falsity.

In his later book(10) Burnyeat makes what seems to be a different move against Protagoras: he said that `a commitment to truth absolute is bound up with the very act of assertion'. So "`It is true for me that all truth is relative"' is no help to the relativist because `it is put forward as itself true without qualification'. This seems to me simply to beg the question in favour of objectivism. Why must `It is true for me that all truth is relative' be `put forward as itself true without qualification'? Why can't this just be another relative truth?(11) If `It is true that...' is an operator on sentences that can be reiterated indefinitely many times, I see no reason why the same should not be true of `It is true for me that...'.(12)

As for Bostock,(13) he pinpoints neatly some problems in Burnyeat's account. But he also suggests three lines of argument for the conclusion that Protagoras refutes himself, which themselves seem problematic to me. First, Bostock suggests that we might try getting Protagoras to concede that his doctrine is plausible about perceptions, but less plausible about other [GREEK TEXT NOT REPRODUCIBLE IN ASCII]. But I can find no sign that this distinction is an important or pressing one for the logic of Protagoras' argument, and no sign, either, that Protagoras thinks it such. Second, Bostock suggests that `the doctrine that man is the measure of all things was not actually intended, by Protagoras, to be a doctrine that applies to itself. I see no reason to think that Protagoras must concede this--but I shall return to the point. And third, Bostock points out that even for Protagoras `the good doctor is the one who is right about what course of treatment will lead to a better state of things'--and to claim that here `right' and `better' might not be meant in a straightforwardly objective sense `is surely carrying cynicism too far'. Certainly that claim would be extremely cynical. But it would not be inconsistent; so perhaps the right conclusion is that Protagoras is an extreme cynic, not that he does not seriously believe his own doctrine.

Denyer(14) holds that Protagoras must agree with Plato that people really do disagree with Protagoras (Theaetetus 170c9). But this means that Protagoras must concede--fatally, as Denyer thinks that there is a belief that Protagoras' view is not just false-for-some, but false simpliciter. Why is this concession fatal? Because, says Denyer, `the belief that Protagoras is wrong...purports to be something more than just true for those who happen to accept it' (Denyer, p. 100):

`Those party to [the widespread consensus that Protagoras is wrong] hold... that if the best that can be said for a belief is that it is their belief, then that belief is not true. Now you cannot think such a thing, and also think that the best that can be said for it is that you think it. It would be absurd for me to say "If something is only my opinion, then it is not true; but mind you, this is only my opinion".'

But even if the belief that Protagoras is wrong `purports to be something more than just true for those who happen to accept it', how does that show that that belief is something more than just true for those who happen to accept it? Protagoras does not have to believe that the relativistic nature of appearances must be evident in those appearances. So he does not have to believe, either, that a non-relativistic appearance would be fatal to his doctrine of appearances. That others take it (i) that Protagoras' opinions are not merely false for them but false full stop, and (ii) that there is a gap between something's being true and their believing it to be true (including the case where what they believe true is that there is such a gap)--these are facts which offer no kind of threat to the integrity of Protagoras' position. For the views (i) and (ii) can for him be just two more relative truths; even if they do not look like that to those who hold these views.

A similar remark applies to McDowell, who points out that `it is, arguably, in the spirit of (P) (McDowell's name for what he takes to be Protagoras' claim that "all judgements are true for those who make them") to assume that people are authoritative, not just about the truth of their judgements, but about what judgements they are'.(15) McDowell's point, evidently,(16) is that on certain reasonable assumptions Protagoras could be got to admit that people think that some beliefs are false simpliciter, not merely false for them. But if Protagoras accepts that, then doesn't he concede that there are beliefs (ergo, true beliefs) which use these predicates of other beliefs? And so that his own position is false simpliciter? Once again, the answer to this is `No'. At most all that can be shown by this manoeuvre is that people think they hold beliefs which are true simpliciter. But on Protagoras' terms, that only entails that it is true for them that they hold beliefs which are true simpliciter. Once again, the apparent threat that Protagoras will refute himself is no more than apparent.

However, there is a third variation on Denyer's argument, also suggested by the above remark of McDowell's, and this may still look threatening. This time the idea is to present Protagoras with a dilemma. Suppose that I judge (i) that Protagoras' view is false, full stop, and (ii) that my judgement (i) is an example of an objective truth. Now surely (the argument runs), Protagoras is compelled to say either that (ii) is false in which case (ii) is a counter-example to his theory (because it is false); or else that (ii) is true--in which case (i) is a counter-example to his theory (because [i] is objectively true if [ii] is true).

The dilemma may look worrying. But unfortunately the way out of this problem too is, on reflection, disappointingly obvious. Protagoras can say simply that (ii) is neither objectively false nor objectively true, but simply true for me its holder. But all that follows from that is that it is true for me that (i) is objectively true. And why should Protagoras feel worried about that?

I conclude that no form of the Peritrope argument that I know of is successful against a determined and clear-headed proponent of Protagorean relativism. So what are we to do about this? Since it has not been refuted, must we then accept Protagoras' doctrine?

I think we should not accept it. Not because Protagorean relativism is self-refuting, but because, more simply, we have been given no reason whatever to accept it. Indeed if Protagoras is right, then in the nature of the case we can be given no reason to accept it. For what would be such a reason?

Suppose Protagoras begins trying to persuade us to be Protagorean relativists by saying to us that `Protagorean relativism is true'. By his own account, this means only that Protagorean relativism is true for him. So how am I to construe his remark as being intended to persuade me? Or suppose he goes on to say `You ought to believe Protagorean relativism'. This will be translatable, in his own strict terms, into the remark that it is true for him that Protagorean relativism ought to be true for me; and my response to that remark can perfectly well be `So what?'. Or suppose, even, that he says `Believing Protagorean relativism will be good for you' (cf. Theaetetus 166d). On Protagoras' terms, presumably I should understand this as meaning `It is true for me that things will seem better to you if Protagorean relativism comes to seem true to you'. But then again the same question arises: Why should I be inclined to see this as an argument? Indeed how can I see it as an attempt to give me a reason to accept Protagoras' view as true-for-me? Since all remarks couched in Protagoras' logical idiolect are, ex hypothesi, merely subjective reports, they can tell us something about how things are with Protagoras, but nothing whatever about anything else; and it is unclear why we should be stirred to respond by anything that Protagoras may tell us that is merely a remark about himself.

Here it is interesting to compare the ethical theory emotivism. Notoriously, an emotivist has no reason to treat any moral remark as a move in an argument, since he takes it that any moral remark is at best a subjective report. So likewise, unless we smuggle in an un-Protagorean notion of objective truth, it is impossible to say how we could manage to see any of the remarks that a Protagorean is permitted by his own rules to make as having any sort of rationally persuasive force.

Thus the difficulty with a Protagorean relativist is not to rebut his arguments. It is to see what he says as an argument at all. Protagorean truth is an essentially private affair; your truth need have no sort of connection with or bearing on my truth whatever. So how on earth can Protagoras give us rational (as opposed to merely emotive)(17) arguments to persuade us of his relativism, when the very idea of rational persuasion between two people depends upon the idea that those two people have a notion of truth which they share in as a common possession?(18) If Protagoras is right, then there is an important sense in which it is futile to argue rationally for any position--Protagoras' own position included. But to defend a philosophical position, one of the corollaries of which is that the defence of any philosophical position is pointless: that may be a logically impeccable procedure (as indeed I have argued), but it does seem a curious one pragmatically speaking.

Bostock's conclusion is that `In a sense, one who propounds such a thesis [as Protagoras'] does refute himself'.(19) Though I have argued that there is no sense in which such a person is, strictly, refuting himself by saying what he says, I think that there is a sense in which he is defeating himself by saying it. For as Bostock rightly goes on to say, `if what he says is right he has no claim on our attention'.(20) This is the point that is telling against Protagoras. But--as I have argued--it is a point about self-defeat, not self-refutation.

(1) I am grateful to Thomas Baldwin, David Bostock, Nicholas Denyer, Martin Hollis, Marie McGinn and Antony Price for their criticisms and encouragement of this paper.

(2) See Diels and Kranz, Fragmente der Vorsokratiker (12th. edition, Zurich, 1966; hereafter `DK'), 80 A1, B5-6.

(3) In fact, at least one writer has raised the possibility that Protagoras did take this first alternative (among other entertaining manoeuvres): J. Barnes, The Presocratic Philosophers (London, 1982), pp. 541-53.

(4) Notice an argument, equal and opposite to what I call Protagoras' second alternative, which is suggested by Theaetetus 170e7ff.: that Protagorean relativism fails on its own terms, because, in fact, Protagorean relativism is not true even for Protagoras himself So it does not seem even to Protagoras that how things seem to him is how things are. Presumably Protagoras can retort to this that it does not seem to Protagoras that it does not seem even to Protagoras that how things seem to him is how things are.

(5) For the debate over whether this is what is meant, or whether Protagoras rather meant that the human race (as a whole) was the measure of all things, cp. J. McDowell, Plato: Theaetetus (Clarendon: Oxford, 1973), p. 118 (for the former view); J. Versenyi, `Protagoras' Man-Measure Fragment', Am. J. Philology 83 (1962), 178-84 (for the latter).

(6) Barnes, Op. cit. n. 3, p.543

(7) Or at any rate, all subject/predicate propositions.

(8) Beside the loss of the laws of contradiction and excluded middle, it would make nonsense of modern formal logic, which would then have only one truth-table, and that a rather odd one. It would also make Aristotelian logic very difficult, since Aristotle defines a syllogism as `a set of propositions given which some other proposition must be true' (Aristotle, Prior Analytics 24b20). If all propositions are true, it is going to be difficult to tell which sets of propositions necessitate the truth of any further proposition; for that further proposition would equally have been true if conjoined with any set of other propositions.

(9) M. F. Burnyeat, `Protagoras and self-refutation in Plato's Theaetetus', Philosophical Review 85 (1976), 172-195.

(10) M. F. Burnyeat, The Theaetetus of Plato (Indianapolis, 1990), p. 30.

(11) Cp. J. Passmore, Philosophical Reasoning (London, 1961), p. 67: `Protagoras is still asserting that "p is true for x" and "p is not true for y"; these propositions he is taking to be true,. True simpliciter? Or true for their utterer?

(12) Nicholas Denyer, in his brilliant Language, Thought & Falsehood in Ancient Greek Philosophy (London, 1991), pp. 90ff., argues the opposite view--that Protagoras' qualifiers (`true for x,, etc.) are not in Protagoras' view `repeatable'. On the basis of Theaetetus 1 60b8-c2 Denyer argues thus: `If the qualifiers were repeatable, then to demand that we insert them on every occasion would be to demand that we enter on an infinite regress' (p. 93). Not so if Protagoras would say merely: (i) that we can insert an appropriate qualifier before any sentence, if we like; and (ii) that we must insert the qualifiers whenever it is necessary to do so to block anti-Protagorean arguments. But this, I suggest, is that Protagoras would say. (Consider the analogy between the objectivist's `it is true that...' and Protagoras; `it is true for x that...'.) So he can hold what Denyer (op. cit. p. 94) says he ought to hold, that the qualifiers are repeatable.

(13) D. J. Bostock, Plato's Theaetetus (Oxford, 1988), pp. 89-95.

(14) Denyer, op. cit. n. 12, pp. 94 100.

(15) McDowell, op. cit. n. 12, p. 171.

(16) As an anonymous referee for CQ has rightly insisted to me.

(17) Cp. Theaetetus 201a: `Orators and lawyers...persuade somehow without teaching, but making the jurors believe whatever they like'. This contrast between (rational) teaching and (non-rational) persuading is (I suggest) exactly the contrast between the ways of making people believe things that are open respectively to a Protagorean relativist, and to an objectivist.

(18) Perhaps this explains why Protagoras kept his homomensura doctrine secret (The. 152c). Perhaps his exoteric and esoteric pupils alike were taught crafty ways of logical argument and persuasion: but only the esoteric pupils were taught the doctrine discussed here. For that doctrine, by undermining the notion of the community of truth, undermines the very idea of strictly logical persuasion.

(19) Bostock, op. cit. n. 13, p. 95.

(20) Bostock, loc. cit. n. 19.
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Author:Chappell, T.D.J.
Publication:The Classical Quarterly
Date:Jul 1, 1995
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