Aristotle , Protagoras , and Contradiction : Metaphysics Γ 4-6

In both Metaphysics Γ 4 and 5 Aristotle argues that Protagoras is committed to the view that all contradictions are true. Yet Aristotle’s arguments are not transparent, and later, in Γ 6, he provides Protagoras with a way to escape contradictions. In this paper I try to understand Aristotle’s arguments. After examining a number of possible solutions, I conclude that the best way of explaining them is to (a) recognize that Aristotle is discussing a number of Protagorean opponents, and (b) import another of Protagoras’ views, namely the claim that there are always two logoi opposed to one another.


Introduction
Protagoras' famous dictum is: (M) "Man is the measure of all things: of the things which are, that they are, and of the things which are not, that they are not."(Theaetetus, 152A) 1 This seems to be the opening line of his book Truth.2Aristotle, however, never quotes the dictum in full, relying for the most part on shorthand formulations like "all beliefs and appearances are true."3Aristotle clearly takes (M) to be mistaken, and in trying to refute it, he connects it to other, more extreme and thus less plausible claims.But his point is not just to link (M) to these extreme claims and call it refuted.His general aim in this part of Metaphysics Γ is to provide a refutation of those who claim to disagree with the principle of non-contradiction (PNC) and thus to provide support for it. 4This requires a dialectical refutation of those, like some Protagoreans, who claim in words to reject PNC.Aristotle's negative arguments against the Protagoreans are found mainly in three short passages: 1007b18-25 and 1009a5-15 present negative arguments, while a more positive one is found at 1010b1-11a2.This paper focuses solely on the negative arguments. 5ereas Plato discusses Protagoras in the context of a discussion of what knowledge is and develops a Secret Doctrine in part to defend Protagoras from the objection that he is committed to contradictions, Aristotle, in contrast, argues twice that the Protagoreans are committed not just to the contradictory of PNC but to its contrary: (C) All contradictions are true. 6e connection between (M) and (C) is the main idea I wish to explore in this paper.It is a puzzling one, for several reasons.First, it is hard to see how Protagoras could be committed to (C) given another view associated with him.In Plato's Euthydemus, Socrates rehearses an argument to the conclusion that it is impossible to contradict (ouk estin antilegein), a view he tells us Protagoras and his followers used to make great use of (286C).If Protagoras held that it is impossible to contradict, how could he be committed to the view that contradictions are always true? Second, Aristotle's argument that Protagoras is committed to the contrary of PNC is strange because his objective in this part of Metaphysics Γ is to defend PNC.And even if he succeeds in refuting the contrary of PNC, this would offer little support for PNC as a general principle.Before discussing Aristotle's arguments in detail, it will be useful to provide a brief response to these questions.Aristotle's arguments here have often been accused of being not only puzzling but weak.Christopher Kirwan (1993: 90) goes so far as to suggest that the arguments in chapter 4 are purposely weak and might have been collected for pedagogical purposes so that Aristotle's pupils could compare and evaluate them.But much of the power of this impression can be dispelled by remembering that Aristotle's aim in addressing opponents like Protagoras is to defend PNC from dialectical objections, i.e., from people who claim to reject the principle in words.Aristotle's arguments, if successful, therefore do provide strong reasons to accept PNC, in that they remove the dialectical objections people give for rejecting it.
Such people, Aristotle says, require refutation. 7His arguments do not and cannot provide a demonstration of PNC, but from an Aristotelian perspective this is not a weakness.In response to the first puzzle, I shall argue that Protagoras is only committed to (C) on certain interpretations of (M).We shall see below that a different interpretation yields a result free from contradiction.
Aristotle needn't concern himself to reject (M) on this interpretation-not in a dialogue with those who refuse PNC-for on this reading, (M) does not run afoul of PNC.I turn now to Aristotle's discussions of the Protagorean view.I hope to be able provide some insight into Aristotle's general concerns in this part of Metaphysics Γ as well as help us understand Protagoras' position and how it was understood in antiquity.

Γ 5
I begin with the latter passage, from the beginning of chapter 5: From the same view proceeds the logos of Protagoras, and both alike must be either true or false.For on the one hand, if all opinions and appearances are true everything must be at the same time true and false.For many men hold beliefs in which they conflict with one another, and all think those mistaken who have not the same opinions as themselves; so that the same thing must both be and not be.And on the other hand, if this is so, all opinions must be true; for those who are mistaken and those who are right are opposed to one another in their opinions.If then, reality is such as the view in question supposes, all will be right in their beliefs.(1009a5-15, Ross's translation slightly modified) 8 There are two arguments in this passage, one embedded in the other.(This is true also in the passage we will examine from Γ 4, where Aristotle's general conclusion is that the Protagoreans are committed to the claim that all things are one.)Here the idea is that two claims 7 I thus contrast dialectical opponents from the physicists, whose reason for claiming to reject PNC is their observation of nature.See, e.g., 1009a15 ff.I say they claim to reject it because, according to Aristotle, no one can actually disbelieve the principle (1005b24 ff.). 8ἔστι δ᾽ ἀπὸ τῆς αὐτῆς δόξης καὶ ὁ Πρωταγόρου λόγος, καὶ ἀνάγκη ὁµοίως αὐτοὺς ἄµφω ἢ εἶναι ἢ µὴ εἶναι.εἴτε γὰρ τὰ δοκοῦντα πάντα ἐστὶν ἀληθῆ καὶ τὰ φαινόµενα, ἀνάγκη εἶναι πάντα ἅµα ἀληθῆ καὶ ψευδῆ˙ πολλοὶ γὰρ τἀναντία ὑπολαµβάνουσιν ἀλλήλοις, καὶ τοὺς µὴ ταὐτὰ δοξάζοντας ἑαυτοῖς διεψεῦσθαι νοµίζουσιν˙ ὥστ᾽ ἀνάγκη τὸ αὐτὸ εἶναί τε καὶ µὴ εἶναι.καὶ εἰ τοῦτ᾽ ἔστιν, ἀνάγκη τὰ δοκοῦντα εἶναι πάντ᾽ ἀληθῆ˙ τὰ ἀντικείµενα γὰρ δοξάζουσιν ἀλλήλοις οἱ διεψευσµένοι καὶ ἀληθεύοντες.εἰ οὖν ἔχει τὰ ὄντα οὗτως, ἀληθεύσουσι πάντες.
are logically equivalent and that both "proceed from the same way of thinking" (1009a15-16). 9It is the inner argument that concerns us here.Aristotle tries to establish a strong logical connection between two claims: first, Protagoras' logos, given as "all opinions (dokounta) and appearances (phainomena) are true"-henceforth (P)-and, second, the contrary of PNC, "everything (panta) must be at the same time true and false," a version of (C). 10 The logical connection Aristotle argues for is inter-entailment: (P) implies (C), and (C) implies (P).So the conclusion of Aristotle's argument is: all opinions and appearances are true if and only if everything is simultaneously both true and false.
Aristotle is careful to argue for both sides of the entailment, even though the second is trivial.But he is not careful in all aspects of the argument.For instance, in arguing that (P) entails (C), instead of repeating the conclusion that everything is at once true and false he offers instead: "the same thing (τὸ αὐτὸ) must both be and not be."This makes two changes: (a) he has moved from a semantic version of the claim to an ontological one; and (b) 'to auto' ('the same thing') replaces 'panta' ('everything').And in the argument that (C) implies (P), Aristotle has dropped the part of (P) referring to appearances.Now, most of these changes are clearly innocuous.The change from a semantic to an ontological version of (C), though it might have philosophical implications, probably was not considered important by Aristotle.This change continues to the end of the passage, where (C) now is characterized in terms of being (ta onta).
This should not trouble us much, because here as elsewhere in Met.Γ Aristotle is not always careful to distinguish what is true from what is real or has being; or, rather, he speaks in both ways apparently indifferently.PNC itself is presented both in terms of statements (1011b13-15)   and in terms of attributes of things (1005b19-24). 11And in Plato's self-refutation argument (Tht.170-1), he too slides between what is and what is true.However, the other discrepancy is not 9 There is some dispute both over the nature of the two views and what 'same way of thinking' they proceed from.Lee (2005: 120-1) argues that "the same view" is not that everything is both true and false but that being is identical to the sensible world (1010a1-3).See also Wedin (2004: 121-2). 10(P) allows qualifiers like for one, while here Aristotle does not mention them.I discuss this apparent discrepancy in §3 below. 11However, the semantic version has some claim to precedence.For at the end of his defense of PNC, Aristotle says it has been shown that the most certain of all beliefs is that "opposite statements (ἀντικειµένας φάσεις) are not at the same time true."He then goes on to argue that it follows from this that "contraries also cannot belong at the same time to the same thing" (Γ 6, 1011b13-22).Aristotle, therefore, thinks that the ontological claim ought to be derived from the semantic one, and (presumably) not the other way around.easily explained away.Why does Aristotle change "everything must be at the same time true and false" to "the same thing must both be and not be"?This anomaly is not found only here.As we shall see, the same expression is used in Γ 4 in a version of (C): "the same thing will be a trireme and a wall and a man" (1007b21-2).What is the significance, if any, of this change?I return to these questions later in the paper.

(C) → (P)
Let us now turn the argument in detail.I begin with the second half of the argument: that (C) entails (P).It is brief and puzzling: "And on the other hand, if this [the same thing both is and is not] is so, all opinions must be true; for those who are mistaken and those who are right are opposed (ta antikeimena) to one another in their opinions."One reason the argument is puzzling is that the claim that (C) entails (P) is trivial.Aristotle could have said simply that if everything is both true and false, as (C) says, everything is true.And if everything is true, all beliefs are true. 12But rather than arguing in this straightforward way, Aristotle somehow makes use of the fact that people hold opposing opinions.It is hard to see how it is relevant that opinions are often opposed to one another; all we need to get to (P) is to notice that (C) ensures that all beliefs are true.
None of the commentators provides much guidance on this issue, nor in general on the argument that (C) implies (P). 13Does Aristotle mention conflicting beliefs simply for reasons of symmetry: the other half of the argument involves conflicting beliefs, so this one should too? 14If this seems unlikely, we might start to consider the possibility that we have somehow 12 Or, if one prefers an ontological version of (C): since everything both is and is not F, all beliefswhether one says that a thing is F or that it is not F-will be true. 13Alexander of Aphrodisias (302,20-34) reconstructs the argument as follows.When a certain affirmation is true, the negation of that affirmation is an error, and vice versa.This is so because when people have opposing opinions, it is possible for one of them to be in error.But this is impossible if all contradictions are true.On this reconstruction it is unclear what role error and opposition play.Ross (1924), Kirwan  (1993: 106), and Lee (2005: 65) all gloss over the argument with little or no comment. 14Conflicting opinions also come up in the Theaetetus' self-refutation argument of 170-1, but there the crucial role is played by higher-order interpersonal beliefs such as Protagoras believes that Socrates believes that (M) is false.Here the argument must be more general if it is to reach its conclusion that everything is true and false.misunderstood Aristotle's argument.A partial solution might be found by reinterpreting (C) along the lines suggested by the way Aristotle's later versions of the claim, as: (S) The same thing is both F and not-F.
Unless 'the same thing' is generalized to include everything, the argument is no longer trivial.If, for instance, Socrates both is and is not a man, then every belief about whether Socrates is a man will be true.But this change does not help with the issue of conflicting opinions, as the move from (S) to (P) still does not require conflicting opinions.For this reason I do not recommend this change.Still, we do require an explanation for why Aristotle at times speaks of the same thing and at other times everything.This and other puzzling aspects of the argument will have to await an explanation until later.My suggestion, which I shall describe in more detail below, is that in his mention of conflicting beliefs Aristotle is here smuggling in another Protagorean thesis.

(P) → (C)
The other half of Aristotle's argument is, if anything, even more puzzling: "For on the one hand, if all opinions and appearances are true everything must be at the same time true and false.For many men hold beliefs in which they conflict with one another, and all think those mistaken who have not the same opinions as themselves; so that the same thing must both be and not be." At first glance, the argument seems to be the following: (1) All beliefs and appearances are true (2) People often have beliefs which conflict with the beliefs of others (3) Everyone thinks anyone with a different opinion is mistaken Therefore: (4) Everything is both true and false 15 .
The argument as it stands is puzzling.The role played by premise (3) is obscure, and the move to the conclusion requires explanation.As M.K. Lee points out, the argument as presented contains two gaps.First, it seems to assume that for the Protagorean, all truths are believed.That 15 Lee (p.65) adds the premise that those with conflicting beliefs also believe the others are mistaken.This hits on a point important for Plato's version of the argument but seems not to be needed here.is, Aristotle here interprets (M) as claiming not only that all beliefs are true but also that all truths are believed.If there were unbelieved truths, there would be no way to connect the premise that people have conflicting beliefs with the conclusion that everything is both true and false.The other gap is that he assumes that for every belief, there is someone who holds its negation, i.e. that for every belief someone can be found who holds its negation.Lee therefore adds the following two premises to obtain a valid argument: (5) For every belief, there must be someone who disagrees with it and (6) Nothing is true unless someone believes it to be true.
Justifying ( 6) is fairly easy.Protagoras clearly holds that belief is sufficient for truth, but does he also hold that it's necessary?Michael Wedin ("Animadversions," 181-4) argues against this biconditional reading of the measure doctrine because it would require us to say about a case in which the subject has no doxastic attitude at all towards some proposition, that the proposition is nevertheless false for him.This, he claims, goes against the spirit of Protagoras' measure doctrine, which he says, "just is a doctrine about agents' doxastic attitudes" (p.183).And again: "the very idea of someone's being a measure requires that he display some doxastic attitude towards whatever he is the measure of" (p.182).
But despite some resistance among scholars, Protagoras clearly is commited to the biconditional reading of (M), and we don't need Aristotle to tell us this. 16But obligingly, Aristotle is clear both that Protagoras must hold the biconditional that belief is both sufficient and necessary for truth, and also why he must do so.He believes Protagoras is committed to the biconditional because he thinks, correctly, that (M) requires this.Advocates of (M) who argue for the sake of argument "must make everything relative-relative to belief [doxan] and perception so that nothing either has come to be or will come to be without someone's first thinking so [prodoxasantos]" (1011b4-7). 17The issue Aristotle has put his finger on is one that some advocates of what is called the biconditional reading of (M) in the Theaetetus have noticed.
As Mehmet Erginel puts it, rejecting the biconditional reading would be "inconsistent with the notion that man is the measure of all things, for there could be, on this view, a lot of things that 16 Though few scholars discuss the issue in the context of Aristotle, the majority of scholars subscribe to the biconditional reading, at least in the Theaetetus.This includes Burnyeat, Fine, and Lee. 17 See also Met.Θ 3, 1047a4-6.ISSN 1981-9471 -FFLCH/USP  www.revistas.usp.br/filosofiaantigaJ. anc.philos.(Engl.ed.), São Paulo, v.7, n.2.p. 75-99, 2013.DOI: http://dx.doi.org/10.11606/issn.1981-9471.v7i2p75-99  are true in A's world independently of A's belief system, i.e. a lot of things of which A is not the measure" ( 22).The doctrine is a claim about the relation between doxastic attitudes and what is.

Journal of Ancient Philosophy
If we reject the biconditional reading of (M), we are left with the possibility that there are truths in my world which I don't believe and thus which I am not the measure of.In general, there can be no proposition, p, which is true in my world but which I don't believe.As Erginel says, this would be inconsistent with the notion that I am the measure of all things. 18Aristotle is correct that Protagoras is committed to the biconditional reading, and ( 6) is justified.

Some Problems
Before turning to the other main passage and the questions it raises, there is more to be said about the latter chapters of book Γ.We have seen that one of Aristotle's main conclusions appears to be that (M) and thus (P) implies the view that everything is both true and false.But in a later passage, from Γ 6, Aristotle seems to have quite a different view of the matter: If not all things are relative [pros ti], but some are (whatever they are) in themselves, not everything that appears will be true; for that which appears [to phainomenon] appears to someone; so that he who says all things that appear are true, makes all things relative.And, therefore, those who ask for an irresistible argument, and at the same time are willing to take a stand in argument, must guard themselves by saying that the truth is not that what appears is the case, but that what appears is the case for him to whom it appears, and when, and to the sense to which, and under the conditions under which it appears.And if they give an account of their view, but do not give it in this way, they will soon find themselves contradicting themselves.(Γ 6, 1011a17-25, Ross's translation slightly modified) In contrast to the argument discussed above, here Aristotle outlines a way for an advocate of pros ti (relativity) to avoid contradictions: he must add the appropriate qualifiers to all his claims about what appears.His reference to the truth of appearances doctrine indicates that some 18 Wedin addresses this worry (at pp.183-4 n14), saying that the biconditional reading (a) might "provide additional support" for the measure doctrine but would have to be gotten by means of an "extra step".And (b) that, even so, since Protagorean worlds are private worlds, no one can be a measure of all truths, as there are truths in other people's worlds, in which the occupier(s) of those other worlds are the measures of them, not me.Both points are wrong.First, as I have argued, the biconditional reading is simply a consequence of the measure doctrine, not an additional support.If I am the measure of all things, there can be nothing-at least nothing in my world-of which I am not the measure.There cannot exist unbelieved truths or unknown properties or objects.Second, it is true that Protagorean worlds are private in the Theaetetus, at a certain stage of the dialectic.But private worlds are undermined and rejected in the passage just before the self-refutation argument and, as Wedin himself points out elsewhere (2003, 127 n25), appear nowhere in Aristotle's discussion.ISSN 1981-9471 -FFLCH/USP  www.revistas.usp.br/filosofiaantigaJ. anc.philos.(Engl.ed.), São Paulo, v.7, n.2.p. 75-99, 2013.DOI: http://dx.doi.org/10.11606/issn.1981-9471.v7i2p75-99  group of Protagoreans is at issue.Aristotle then goes on to provide his own analysis of the situation:

Journal of Ancient Philosophy
For to those who for the reasons named above say that what appears is true, and therefore that all things are alike false and true, for things do not appear either the same to all men or always the same to the same man, but often have contrary appearances at the same time (for touch says there are two objects when we cross our fingers, while sight says there is one), -to these we shall say, 'yes, but not to the same sense and in the same part of it and in the same way and at the same time,' so that what appears is under these qualifications true. 19(1011a28-b1, Ross) In the Γ 5 passage discussed above, 1009a5-15, Aristotle argues that Protagoras' logos implies that everything is both true and false.Yet here, Aristotle provides them a strategy to avoid contradicting themselves.In the second passage quoted, the advocate of the truth of appearances endorses (or at least is committed to) the move from all appearances are true to "all things are alike false and true" (panth' homoiōs einai pseudē kai alēthē).And as we have seen, this is the very conclusion Aristotle accused the Protagoreans of being committed to earlier, in very similar language (cf.einai panta hama alēthē kai pseudē, 1009a9).In the first passage, by contrast, Aristotle shows them a way to avoid the conclusion.By adding the appropriate qualifiers to all their appearance claims, Aristotle shows them how to avoid the unfortunate consequence and also why, when understood properly, appearances do not really conflict.This discrepancy is difficult to explain.
Why, then, does Aristotle connect Protagoras with contradictions at all?One answer is that Aristotle is attacking an extreme version of the Protagorean claim, one that involves rejection of the PNC. 20But I prefer the following explanation.In the arguments from Γ 4 and 5, Aristotle does not allow the Protagoreans to add qualifiers to their claims.On this reading, advocates of the view will naturally find themselves rejecting PNC and so require a refutation.
We can speculate that there might have existed Protagoreans of this sort, who claimed to deny PNC because of their belief in the truth of appearances.But Aristotle recognizes other ways of understanding the view.What I am suggesting is that the Protagorean view that "what appears is true" is open to a number of different interpretations and origins and that Γ 4-6 presents a number of these.Some of those who accept this view do so for the sake of the argument.Some members of this group do not add qualifiers and are thus subject to dialectical refutation such as we saw in Γ 5 and will see below in Γ 4. In 1011a17-25, quoted above, we learn about another group-this time, of people willing to add qualifiers.This group requires no refutation here because by adding the appropriate qualifiers, they do not reject PNC.Another complicating factor is that Aristotle recognizes two different general types of opponent: those who hold their view for the sake of the argument, and those who have been reasoned into it.The former require dialectical refutation, while the latter need to be shown that their grounds for believing their view are problematic.The last passage quoted, 1011a28-b1, discusses some Protagoreans members of this latter group.They have come to believe Protagoras' view "for the reasons named above"presumably, reasons such as the observation that from the same thing come opposite qualities.
(An example of this is that the same leaf can be at one time red and at another time brown, or not-red.)Aristotle's strategy against this group involves making them familiar with certain distinctions, which will help explain why their Protagorean conclusion does not follow.
To get a historical sense of why there might have been many different 'Protagoreanisms', let's take a quick look back at the Theaetetus.Socrates' original example (Tht.152B) is of the same wind's feeling cold to one person and not cold to another.Here, both the statement (or belief or appearance) that the wind is cold and the statement that it is not cold must count as true. 21Generalize this point and we begin to see why Aristotle thinks there are at least some Protagoreans committed to the view that everything is both true and false.The statement that the wind is cold is true because believed by one person but false because someone else believes that the same wind is not cold.This seems to me to go some way towards explaining the puzzling discrepancy I mentioned earlier: that at times, Aristotle argues that Protagoras' logos implies not that "everything is true and false" but that "the same thing will both be and not be."No doubt this was thought by at least some followers of Protagoras to have been problematic, as it entails the denial of PNC.But the rest of the story is not determined by (M) and can change depending 21 Here I follow a suggestion made by G.B. Kerferd, The Sophistic Movement, p. 92.ISSN 1981-9471 -FFLCH/USP  www.revistas.usp.br/filosofiaantigaJ. anc.philos.(Engl.ed.), São Paulo, v.7, n.2.p. 75-99, 2013.DOI: http://dx.doi.org/10.11606/issn.1981-9471.v7i2p75-99upon the particular advocate of Protagoreanism.Any number of possible solutions might have been used, including those we find in the Secret Doctrine of the Theaetetus and many others.

Journal of Ancient Philosophy
Different groups of Protagoreans will require different strategies. 22is leaves us still with some difficult questions.First, we have still not fully understood why Aristotle at first connects Protagoras to the view that all contradictions are true, or that everything is both true and false, and then later offers a solution to just this problem.Second, we have not seen how Aristotle connects Protagoras to this radical view in the first place, nor exactly what his purpose is.Why is it that Aristotle seems to think Protagoras is committed to the completely general claim that everything both is and is not?How does he move from the plausible idea that disagreement is always possible to the seemingly absurd idea that it is actual?
These issues arise again in what follows.

Γ 4
In Γ 4 Aristotle discusses similar themes: (1) Again, if all contradictories are true of the same subject at the same time, evidently all things will be one.For the same thing will be a trireme, a wall, and a man, if it is possible to affirm or to deny anything of anything, -and this premise must be accepted by those who state the logos of Protagoras.For if any one thinks that a man is not a trireme, evidently he is not a trireme; so that he also is a trireme, if the contradictory is true.(1007b18-25, modified) 23 There are some obvious similarities between this and the Γ 5 passage discussed above.
But there are also some new ideas.One interesting difference is that while the argument of Γ 5 is conducted in terms of belief, this argument is conducted mainly in logico-semantic terms, involving what is affirmed and denied.But Protagoras' logos does play a role, in the familiar claim that belief or appearance (dokei) is sufficient for truth.Another new idea is found in the 22 Lee (pp.71-2) argues that the latter passages I have mentioned show that Aristotle thinks there are two ways for Protagoras to avoid contradictions.One is to relativize all statements; the other is to add 'is true for' to all statements.The former suggestion is for those who argue due to problems in their thinking; the latter applies to those who argue for argument's sake.She interprets the latter suggestion as semantic relativism about truth.However, I see nothing to suggest that these are two different strategies.

Journal of Ancient Philosophy
Pace Kirwan and Wedin, the apparent meaning of "everything will be one" is: there is exactly one object.And there is good reason to think this claim follows from the claim that all contradictories are true of the same object. 24It follows from the idea that all contradictories are true of the same subject at the same time.For, assuming all things have all contrary properties, every possible attribute can be truly ascribed to every object.Thus every object would have every property.By Leibniz's Law, if x and y have all the same properties, x is identical to y.If all things have all the same properties, then everything will be identical, and there will be exactly one object.But here again we need not rely solely on speculation, as Aristotle makes it clear what he means in a later passage: And all things will on this view be one, as has been already said, and man and God and trireme and their contradictories will be the same.For if contradictories can be predicated alike of each subject, one thing will in no wise differ from another; for if it differ, this difference will be something true and peculiar to it.And if one may with truth apply the predicates separately, the above-mentioned result follows none the less.(Γ 4, 1008a23-28, Ross) 25 This passage confirms my suggestion that "everything will be one" means "there will be exactly one object."If we can truly predicate of Socrates both man and not-man, the distinction 24 I will not speculate as to why it is problematic for the Protagoreans to be connected with this extreme claim.But it's interesting to note that in the Theaetetus the Protagoreans and Heracliteans are contrasted with the Parmenideans, whereas here they are connected. 25καὶ πάντα δ᾽ ἂν εἴη ἕν, ὥσπερ καὶ πρότερον εἴρηται, καὶ ταὐτὸν ἔσται καὶ ἄνθρωπος καὶ θεὸς καὶ τριήρης καὶ αἱ ἀντιφάσεις αὐτῶν (εἰ γὰρ ὁµοίως καθ᾽ ἑκάστου, οὐδὲν διοίσει ἕτερον ἑτέρου: εἰ γὰρ διοίσει, τοῦτ᾽ ἔσται ἀληθὲς καὶ ἴδιον): ὁµοίως δὲ καὶ εἰ διαιροῦντα ἐνδέχεται ἀληθεύειν, συµβαίνει τὸ λεχθέν.ISSN 1981-9471 -FFLCH/USP  www.revistas.usp.br/filosofiaantigaJ. anc.philos.(Engl.ed.), São Paulo, v.7, n.2.p. 75-99, 2013.DOI: http://dx.doi.org/10.11606/issn.1981-9471.v7i2p75-99  of belief; it just happens to be that everything is mixed together, indeterminate. 30Even though it would guarantee the truth of all views, it wouldn't be because of the belief that the belief is true.

Journal of Ancient Philosophy
It would be simply in the nature of things.This would make Protagoras' view into a fundamentally ontological rather than an epistemic one.The second reason is that Anaxagorean indefiniteness is said to be a consequence of Protagoras' position, not a support for it.And in order to show that Protagoras is committed to Anaxagorean indefiniteness, we will have to already assume something like universal disagreement.Anaxagorean indefiniteness is quite general, and only an equally general Protagorean thesis could be said to commit one to it.
If Anaxagorean indefiniteness fails to explain Aristotle's arguments, let's continue: (3) But they must predicate of every subject every attribute or the negation of it.For it is absurd if of every subject its own negation is to be predicable, while the negation of something else which cannot be predicated of it is not predicable of it; for instance, if it is true to say of a man that he is not a man, evidently it is also true to say that he is either a trireme or not a trireme.If, then, the affirmative can be predicated, the negative must be predicated too; and if the affirmative is not predicable, the negative, at least, will be more predicable than the negative of the subject itself.If, then, even the latter negative is predicable, the affirmative will be so too.(1007b29-1008a2, Ross modified) 31,32 This passage seems to offer more hope in filling the gap I outlined above.Despite its opening line, the passage intends to show that the Protagoreans must predicate of every subject every attribute and the negation of it.Before trying to reconstruct the argument, we need to take a closer look at the first line, which is one expression of the argument's conclusion.I have modified Ross's translation to better reflect the Greek, though in fact, as I will argue, Ross's 30 But cf.Γ 7, 1012a25 ff.Here Aristotle says that Anaxagoras' idea that all things are mixed "seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true." 31 ἀλλὰ µὴν λεκτέον γ᾽ αὐτοῖς κατὰ παντὸς <παντὸς> τὴν κατάφασιν ἢ τὴν ἀπόφασιν: ἄτοπον γὰρ εἰ ἑκάστῳ ἡ µὲν αὐτοῦ ἀπόφασις ὑπάρξει, ἡ δ᾽ ἑτέρου ὃ µὴ ὑπάρχει αὐτῷ οὐχ ὑπάρξει: λέγω δ᾽ οἷον εἰ ὀληθὲς εἰπεῖν τὸν ἄνθρωπον ὅτι οὐκ ἄνθρωπος, δῆλον ὅτι καὶ ἢ τριήρης ἢ οὐ τριήρης.εἰ µὲν οὖν ἡ κατάφασις, ἀνάγκη καὶ τὴν ἀπόφασιν: εἰ δὲ µὴ ὑπάρχει ἡ κατάφασις, ἥ γε ἀπόφασις ὑπάρξει µᾶλλον ἢ ἡ αὐτοῦ.εἰ οὖν κἀκείνη ὑπάρχει, ὑπάρξει καὶ ἡ τῆς τριήρους: εἰ δ᾽ αὕτη, καὶ ἡ κατάφασις.
32 Wedin (2003, 117), following Kirwan, translates the passage as follows: But certainly [vi] their statements, at any rate, must affirm or deny everything of everything, for [vii] it would be absurd if the denial of itself held good of each thing, but the denial of some other thing, which does not hold good of it, did not hold good of it.I mean [viii] for instance that if it is true to say of a man that he is not a man, plainly [ix] he is also either a warship or not a warship, so [x] if the affirmation holds good of him, so also must its denial; but [xi] if the affirmation does not hold good, at least its denial will hold good of him more readily than his own.So [xii] if even the latter does hold good, that of warship will too; and if it does, its affirmation will too.ISSN 1981-9471 -FFLCH/USP  www.revistas.usp.br/filosofiaantigaJ. anc.philos.(Engl.ed.), São Paulo, v.7, n.2.p. 75-99, 2013.DOI: http://dx.doi.org/10.11606/issn.1981-9471.v7i2p75-99