Is wisdom courage? A critical dissection of Pl. Prot. 349d2-351b2

In Pl. Prot. 349d2-351b2, first Socrates leads Protagoras to acknowledge that wisdom and courage are the same thing, then Protagoras accuses him of having put in his mouth words that he never said. Starting from a new reconstruction of the logic of Socrates’ demonstration, I will show how this is more complex, sophistic, and corresponding to Protagoras’ accusation than what is usually believed.


INTRODUCTION
Socrates' first attempt to prove the identity of wisdom and courage (349e1-350c5) and Protagoras' reply (350c6-351b2) make up what is arguably the most complex passage of Plato's Protagoras as far as argumentation is concerned and has always constituted a formidable challenge for scholars, who have offered the most various assessments of it. 1 I too shall present my interpretation of it here, reconstructing the two parts of this exchange and, after each of them, tackling my main points of divergence with the other commentators. Finally, in the conclusion I will take stock of the dialectical and sophistic value of the two characters' words. § 1 SOCRATES' DEMONSTRATION § 1.

MY RECONSTRUCTION OF SOCRATES' DEMONSTRATION
After a long break, which the two characters devoted to debating the consistency of two Simonidean excerpts (338e6-348c4), the discussion on the relationship in which excellence stands to its parts resumes at 349a6 (καὶ…). Socrates asks Protagoras whether or not he confirms his original idea that no part of excellence is similar to the others, either in itself or in its function ( Ἦ…Σώκρατες, at 330a6-b3). 2 Protagoras' answer is a revision of that position to the following effect: (P1) All the f ive good qualities are similar to each other, except courage. For many of the most unjust, impious, incontinent, and ignorant men are nonetheless extremely courageous (349d2-8); 3 To explain this change, one must remember that up to this point Socrates has proved that justice and piety are either the same or very similar (329b7-332a4) and that temperance is the same as wisdom (332a4-333b5), whereas he has simply tried to demonstrate the identity of justice and temperance (333b7-333c1). Therefore, having proved to be unsuccesful on at least two occasions, Protagoras' initial position needs to be revised as in (P1), which represents both a considerable mitigation of it and a last and desperate attempt at defending it, because courage is the only part of excellence that Socrates has not equated to any other yet.
Socrates seems any thing but worried about (P1) and he promptly responds to it by involving his interlocutor in an extremely elaborate reasoning. His starting move is to elicit the following answers from Protagoras: (P2) The courageous are daring (349e2-3); 4 (P3) Excellence is beautiful in all its parts (349e3-8); 5 (P4) The wise are daring (350a6-b1). 6 Then, Socrates asks Protagoras whether he has ever seen a man who is ignorant -that is to say the opposite of wise -but daring, and Protagoras assents: 7 (P5) Some ignorant men are daring (350b1-4). 8 What interpreters fail to see is that from here to φαίνονται at 350c2, Socrates' plan is to refute (P5) by reducing it ad absurdum. To this goal, he needs two further premises though. To begin with, he asks Protagoras whether: (S1) The ignorant but daring men are courageous (350b4). 9 Protagoras denies it through a concise, and partly implicit, reductio ad absurdum of (S1). The idea is that if (S1) were true, since (P6) The ignora nt but daring men are mad [which is a disgraceful state] (350b5-6), 10 such a blemish would affect courage too (Αἰσχρὸν…ἀνδρεία, at 350b5). But that would contradict (P3), therefore Protagoras answers that: (P7) The ignorant but daring men are not courageous, but mad (350b5-6). 11 This, in turn, counts as the first premise of Socrates' reductio ad absurdum of (P5). The second he obtains through a move that, unlike the whole argument frame, scholars have already pinpointed. They do not agree as to the cunning of this move though, but that emerges clearly from the text. For now Socrates reminds Protagoras of (P2), asking him to confirm that: (S2) The courageous are the daring (350b6-7). 12 Clearly, (S2) does not correspond to (P2), and assenting to the former is not equivalent to confirming the latter. Alas, Protagoras does not realize this and answers in the affirmative (350b7). 13 Socrates' trick, however, is as simple as shrewd, as it consists in inserting a mere 'the' before 'daring' in (P2); pace the debate that has arisen around it, the fact that τοὺς θαρραλέους of (S2) denotes the class of the daring, whereas the sole θαρραλέους of (P2) has a predicative function has been satisfactorily clarified by O'Brien. 14 Socrates has therefore taken a grip on (S2), and at 350c1-2 he can finally reduce (P5) to absurdity through an even more concise and implicit inference than Protagoras' previous reductio. For, seemingly, he just briefly reminds Protagoras of (P7) in interrogative form, 15 but one must not miss the bigger point that this short question f lags up, and which can be paraphrased as the following warning: 'Mind (P7), Protagoras! It is endangered by (P5), if (S2), as we want, is to be the case'. In other words, Socrates alerts Protagoras that since the courageous have been shown to be the daring by (S2), (P5) ends up saying that some ignorant men are both daring and courageous. But that contradicts (P7). Therefore, we must exclude the truth of (P5) and deduce its contradictory, namely: (S3) None of the ignorant men is daring.
Socrates is about to end this intricate demonstration, but in the short space of 350c2-5 he manages to amaze Protagoras and us again, through two -and not one, as is usually maintained -last deductions, the latter of which stems from the conclusion of the former. In the first question, he offers (P4) (350c2-3) 16 and (P2') The daring are courageous (350c3-4), 17 which is implied by (S2), as the premises from which Protagoras can draw a natural conclusion by himself, namely: (S4) The wise are courageous.
Finally, in the second and last question, Socrates does the other way around, not telling Protagoras the premises from which to conclude that: (S5) Wisdom is courage (350c4-5). 18 However, this time Socrates uses the phrase 'by this reasoning' (κατὰ τοῦτον τὸν λόγον, at 350c4), which I take to refer to a reasoning that Socrates has been making for some time and which I identify as the one based on (S2), (S3), and (S4), which are the outcomes of Socrates' three immediately previous questions. To see how this is so, one has just, first, to rephrase (S5) in terms of individuals as: then, one has to conclude from (S7) and (S2) that: (S8) The courageous are wise.
At this point, we notice that (S6) is true by (S8) and (S4). Socrates' demonstration of (S5) therefore proves to be as intricate and tricky as successful, with the result that (P1)'s idea that courage is different from any of the other four good qualities can no longer stand.
To recapitulate, Socrates' demonstration is structured in two branches, a very long one (349e3-350c2) concluding (S8) and a very short one (350c2-4) concluding (S4). (S8) and (S4) are the premises to finally infer, first, (S6), and then (S5), which refutes (P1) (350c4-5). In propositional logic this reads as follows: As a marginal note, three things are worth observing. Firstly, (P2) plays no part in the demonstration. Secondly, Socrates' equation ultimately involves not only courage and wisdom, but also daring. Thirdly, although (S8) is the first proposition to refute (P1)'s idea that some ignorant men are courageous, this same refutation started to be possible already at (P7). For from (P2), by contraposition, one can infer: (P2.1) The non-daring are not courageous.
Then, from (P7) and from (P2.1) it follows that neither the ignorant and daring men, nor their complement class, namely the ignorant and non-daring, are courageous, with the result that none of the ignorant men is courageous, contra (P1). This conclusion is equivalent to (S8), the two being contrapositives, and one may therefore wonder why Socrates does not take this shortcut. However, the sole fact that the courageous are wise cannot do anything about (P1)'s other and bigger idea, that courage is different from the other parts of excellence. To refute this, Socrates needs to prove the biconditionality of wisdom and courage, and if he had taken the above shortcut, he would still have needed to prove (S4) next. The strategy that Socrates devises, by contrast, has the advantage of carrying out the demonstrations of (S8) and (S4) at once, thus ending with a conclusion, (S5), which refutes (P1)'s major point. As for Protagoras, he is clearly the one who comes off worse from this analysis. For he turns out to have contradicted himself, although implicitly, in (P1)'s minor point as early as at (P7). § 1.2 OTHER SCHOLARS' ANALYSES OF SOCRATES' DEMONSTRATION § 1. 2

.1 (P4)
In the portion of the Protagoras under examination in this paper, the comparative and superlative degrees of some adjectives do not seem to me to play any special argumentative role that their positive degree could not express. I rather see this linguistic feature as motivated exclusively by stylistic reasons of variation, coherently with the living language of a dialogue. With reference to οἱ ἐπιστήμονες τῶν μὴ ἐπισταμένων θαρραλεώτεροί εἰσιν at 350a6-7, it literally reads 'the wise are more daring than those who are not wise', but in my (P4) I simplified it as 'the wise are daring'.
By contrast, Stokes laments that comparatives like this θαρραλεώτεροι 'have recently suffered some scholarly neglect'. 19 He observes that if Socrates manages to push Protagoras a step further than this and to persuade him that 'the more knowledgeable one is, the more confident one is, then Socrates will be able to argue that the less knowledgeable one is, the less confident one is'. 20 In Stokes' opinion, 'that will give him the direct proportion he requires: no knowledge, no confidence, and hence,' by (P2.1), 'no bravery', 21 which will be an effective objection to (P1). However, this reasoning involves a converse error, because from '>W → >D' one can derive '<W → <D', but not '¬W → ¬D' (with 'W' standing for 'being wise', and 'D' for 'being daring'). This is sufficient to explain why Socrates does not adopt the strategy that Stokes suggests, which, as the scholar himself acknowledges, 'has to be excogitated from his [sc. 'Plato's'] text by dint of taking seriously the otherwise pointless shifts in degrees of comparison'. 22 Ironically, Stokes even wonders what could excuse 'these sins of omission' 23 by Socrates and Plato, rather than ever questioning his own views.
Shaw focuses on the comparison that Socrates and Protagoras establish between the wise and the ignorant as to their daring. He interprets (P4) as something like 'wisdom causes daring' and (P7) as 'madness, insofar as being ignorance, causes daring'. 24 However -as Shaw himself commentsif both the wise and the ignorant are relatively confident, one might reasonably ask in comparison to whom they are relatively confident; they cannot each be confident compared to the other. 25 Shaw attempts to solve this problem by narrowing down the class of the ignorant through a definition of them as 'those who wrongly think they know', as opposed to 'those in the intermediate state of neither knowing nor thinking that they know', and by concluding that 'the wise and ignorant are both confident in relation to those people'. 26 However, these definitions do not have support in the text, nor does he, in fact, find any.
The very contrast that Shaw spots between (P4) and (P7) and tries to solve is actually just a seeming one due to two personal interpretive choices of his, not necessitated by the text. The first is his identification of madness and ignorance in (P7). 27 Granted, one of the upshots of the discussion at 332a4-333b5 is that 'madness and ignorance share an opposite, variously called "prudence" and "wisdom"', and that since 'opposites are unique […] madness is ignorance'. 28 But hardly can this be sufficient for Plato to use madness and ignorance interchangeably from then on. For nothing similar happens, for example, to the parts of excellence, which, over the dialogue, are showed to be identical. Even weaker is Shaw's reference to two previous occurrences of the adjective μανικός as testifying this alleged identity. 29 For both in τὸ πρῶτον τοῦ ᾄσματος μανικὸν ἂν φανείη at 343c7 and in εἰ μὴ μαίνομαι γε at 349e6 the idea is that certain mistakes are so gross that they seem to be due to madness rather than ignorance. Therefore, it is for the rhetorical success of these phrases that a distinction in the use of madness and ignorance must remain. The same holds true of (P7), which otherwise would be scarcely informative, simply redundantly saying that the ignorant but daring men are ignorant.
The second arbitrary choice made by Shaw concerns his 'new causal reading' of Socrates' argument. Admittedly, judging by Πότερον... ἐπίστανται at 350a2-3, a causal relationship between wisdom and daring does seem to be hinted at in the following (P4). 30 But, firstly, such causality is not relevant to the argumentative effectiveness of (P4), which still plays its role of premise for (S4) even if one takes it at its face value, as I did. Secondly, the text does not suggest causality in any of the other propositions of Socrates' demonstration, and this is even more true of (P7), whose paraphrase by Shaw is also misleading. 31 For a proposition such as 'ignorance causes daring' expresses universal validity and equates to 'the ignorant are daring'. In contrast, (P7) is predicated only of some ignorant men, the same ones who are first referred to in (P5) (note τινας at 350b1).
In sum, what (P4) and (P7) taken together tell us is that among the daring we find all the wise (by (P4)) and part of the ignorant (by (P7)). Supposing, for the sake of argument, one translated this in Shaw's causal jargon, he should say that daring is caused either by wisdom or by a certain kind of ignorance, a conclusion that is as unproblematic as far from Shaw's one. § 1. 2

.2 (P7)
In Οὐκοῦν...εἰσιν at 350b4-6 Vlastos spots the following Camestres syllogism by Protagoras: 'all the brave are noble; no confident men who are not wise are noble; hence no confident men who are not wise are brave'. 32 However, this obscures both Protagoras' reference to madness in ἐπεὶ...εἰσιν at 350b5-6 and, before that, the construction μεντἄν[…]εἴη at 350b5. The latter indicates that Αἰσχρὸν...ἀνδρεία at 350b5 is the apodosis of a future supposition in less vivid form whose implicit protasis is the assumption of (S1), in the typical structure of reductio ad absurdum. 33 Vlastos also thinks that through (P7) Socrates wants to mark off courage from daring 'in the sharpest terms', as opposed to the layman's usual confusion of the two. 34 But, as a matter of fact, (P7) leaves open the possibility that the daring, if wise, are courageous.
Taylor criticizes the way Protagoras arrives at (P7) by observing that: even if the state of being daring but lacking in knowledge is not itself any part of excellence, and a fortiori not courage, it does not follow that those in that state do not possess some other state which is courage. The argument would require the additional premiss that no one who is mad possesses any of the virtues. 35 Actually, no such addition is needed, because Protagoras predicates madness of the daring and ignorant men precisely to justify (note ἐπεί at 350b5) why he considers their state disgraceful, and hence incompatible with any part of excellence by (P3). The only implicit assumption that he seems to be making here -and on which Socrates cannot but agree -is that madness is disgraceful.
Taylor has also difficulty in seeing how (P7) can contribute to the demonstration. 36 The best he can do is to conjecture that from (P7) Socrates fallaciously derives one of the two possible readings that Taylor gives of θαρραλεώτατοι δὲ ὄντες ἀνδρειότατοι at 350c3-4 (my (P2')), namely 'since they are most daring (and wisest), they are therefore most courageous'. 37 The fallacy would hence lie in arguing that since 'the absence of knowledge […] prevents daring from counting as courage, therefore the presence of knowledge is sufficient to make daring into courage'. 38 But the hypothesis of a second piece of poor reasoning on Socrates' part few lines after the problematic (S2) seems unlikely. Furthermore, if that reading of θαρραλεώτατοι…ἀνδρειότατοι was the case, what should we make of ἐκεῖ at the beginning of καὶ…ἀνδρειότατοι; at 350c2-4, then? For it is a demonstrative adverb denoting distance and hinting at something previously said, just as (P4) and (S2), which implies (P2'), are. 39 § 1. 2

.3 (S2)
Only Klosko believes, like me, that Socrates uses (S2) 'to fool Protagoras', in order to obtain 'the illicit conversion' of (P2) into (P2') that his argument requires. 40 By contrast, Vlastos omits (S2) from his reconstruction, 41 arguing that 'Socrates would have been an utter fool' 42 to introduce it, again on the assumption that Socrates wants to keep courage and daring separate. However, this is at odds with Socrates eliciting first (P2), which joins courage and daring, and then (P4), which, if taken in conjunction with (S6), returns (P2) as well.
All the other interpreters have endeavoured to justify the employment of (S2) from an argumentative point of view and/or to free So-crates from the charge of having intentionally played a move that they too admit to be irregular. According to O'Brien, for example, after Socrates hears that 'a man can be courageous and yet unjust, impious, intemperate, and stupid', 43 in (P1), he 'decides that Protagoras is using "courageous" as he, Socrates, would use "daring."' 44 He therefore asks Protagoras whether 'by "courageous" he means "daring," but his question as put ("do you call the courageous daring?") is not logically exact'. 45 By agreeing to it, Protagoras commits himself 'only to the predication: "the courageous are daring"', namely to (P2), which is consistent with the idea that 'some daring men are not courageous' 46 that he then expresses in (P7). This clearly puzzles Socrates, who believes that at 349e2 Protagoras declared that 'the courageous and the daring form coextensive classes'. 47 He hence asks the question again, but this time in the correct form of (S2), and Protagoras confirms his assent. 48 According to O'Brien, 'what follows should be read not as a conclusion of Socrates' own making, as it is commonly understood, but as a review of Protagoras' vulnerable position', 49 and owing to his agreement on (S2), Protagoras would turn out to have been 'doubly inconsistent.' 50 For first, at 350c1-2, Socrates would point out that (S2) is incompatible with (P7). Then, at 350c2-5, he would show how from (P4) and (S2) (S5) follows, which conflicts with (P1). 51 As a result, 'the passage is one of a type also found elsewhere in Plato, in which Socrates refutes an argument by proving that it is not self-consistent.' 52 'The scene' -O'Brien concludes -is 'a philosopher's deliberate illustration of how an inquiry can go wrong.' 53 This interpretation is surely fascinating, but not immune from problems either. Firstly, even granting O'Brien's observation of the metanarrative value that presenting a faulty inquiry would have, the mistakes made by both characters that O'Brien's reconstruction involves are more than those that he openly mentions. For after Socrates' alleged oversight at 349e1-3 (asserting (P2) in place of (S2)), and Protagoras' one at 350b6-7 (mistaking (S2) for (P2)), at 350c4-5 Socrates could not, in point of logic, conclude for (S5) in the way O'Brien indicates. For (P4) is not sufficient, in combination with (S2), to give (S5), but (S4). Furthermore, O'Brien passes in silence over the fact that at 350c9-d1 Protagoras is wrong in saying that he never committed himself to (P2'), because he, as a matter of fact, did so by involuntarily consenting to (S2). This would hence be the fourth instance of bad reasoning in the short space of 349e-350c, if O'Brien's reconstruction was the case. One struggles to see how an argumentation so hopelessly flawed could teach anything, let alone 'by negative example, the value of careful procedure', 54 and how it could go with the generally smooth development of the conversation in the dialogue.
Guthrie argues that Protagoras has no ground to claim that he 'has been tricked into the appearance of admitting' 55 (P2'). For at 349e2-3, 'when asked if he would describe the courageous as confident', Protagoras agreed without making any 'distinction between courage and unthinking confidence', of which he would have not thought 'if Socrates had not put it into his head' at 350c1. 56 However, this analysis unfairly reverses the burden of proof, because Socrates' question πότερον… τι; at 349e2 does not require the addition of such a distinction to be exhaustively answered.
Taylor rules out the possibility that Socrates obtains (S2) 'sophistically', 57 as 'it seems incredible that Plato should wish to represent Socrates as arguing in such a morally and intellectually discreditable fashion'. 58 For this reason, he reads (S2) as a mere restatement of (P2), 59 even bracketing the article τούς before θαρραλέους (350b7) in his translation 60 and cutting, as an exception, 350b6-7 out of his synoptic summary of the whole demonstration. 61 But, firstly, Taylor does not justify his assumption that Socrates cannot reason in a patently invalid and cheating way, which, on the contrary, seems to be falsified precisely in a few passages of this dialogue more than elsewhere. 62 Secondly, it is not clear why Socrates should repeat (P2) at 350b6-7, nor does Taylor explain it.
Shaw does not doubt Socrates' good faith throughout the exchange and openly admits to 'extending maximal interpretive charity' to him with regard to (S2). 63 Charity that seems excessive though, as he argues that Socrates simply made a mistake, but not when introducing (S2) -as one would expect -rather in (P2), which Socrates actually meant as 'all and only the courageous are confident'. 64 As a result, on the one hand at 349e2 'Socrates is at fault for not phrasing his question clearly', 65 on the other Protagoras is 'at fault for failing to notice the misunderstanding when Socrates asks his question more clearly' at 350b6-7. 66 Ultimately, Shaw's interpretation removes any doubt about Socrates' introduction of (S2), but at the price of assuming that not only Protagoras -as is usually maintained -but also Socrates himself confuses (P2) and (S2), though on another, and more unlikely, occasion, namely at the beginning of his own demonstration. It goes without saying that all this further and unnecessarily complicates the already intricate rationale of 349e1-350c5. § 1. 2

.4 (P5), (S3), and (S8)
One may counter that the most manifest contradiction at 350b1-7 is actually the one between (P7) and the immediately following (S2), as Taylor too observes. 67 However, it is hard to think that Socrates aims to drop either (S2) -soon after having obtained it, and even illicitly -or (P7) -and so conceding that some ignorant (and daring) men are courageous (and not mad), which is precisely (P1)'s minor thesis, against which Socrates is arguing. Therefore, out of (P7), (S2), and (P5) the last is the only proposition the loss of which is harmless to Socrates, and, on the contrary, the negation of which enables him to obtain (S3). In my account (S3) is essential to reaching (S8), whereas most scholars have omitted it. 68 Starting from Vlastos, they point out the possible derivation of (S8) from (P2) and (P7) that I, too, mentioned above. 69 But the long portion of text separating (P2) and (P7) (349e3-350b4) makes their combination in an implicit reasoning extremely unlikely. 70 § 1. 2

.5 (P2')
θαρραλεώτατοι δὲ ὄντες ἀνδρειότατοι at 350c3-4 has been read in two ways. Its literal translation (i) Since they are most daring, they are most courageous has been alternatively taken to understand σοφώτατοι at 350c2, and hence to read (ii) Since they are <wisest and> most daring, they are most courageous. I already justified my preference for (i), ref lected in my paraphrase (P2'), with its being in keeping with the idea of looking back to previous premises that is expressed by the ἐκεῖ at 350c2. 71 In contrast, (ii) has no basis in anything that has been established up to this point, and hence Socrates 'has no business to assert it', as Vlastos remarks. 72 However, most scholars prefer (ii) to (i), Vlastos included. 73 He points out that (i) is at odds with a neat distinction between daring and courage, which he deems a 'major objective' of Socrates. 74 But from this point of view, (ii) cannot be a better fit either, as it defines a class of individuals who are precisely both daring and courageous, besides wise. Vlastos also emphasizes how, unlike (i), (ii) allows 'to maintain the symmetry' with (P7), since 'the natural complement to "All Confident men who are not Wise are not Brave" is "All Confident men who are Wise are Brave", […] hardly "All Confident men are Brave"'. 75 However, this advantage is a questionable one, because the move from (P7) to (ii) that such symmetry may induce to make is not logically valid, as we earlier saw, quoting Taylor. 76 At that point we also saw that Taylor gives some credit to the possibility that Socrates does make this fallacious step. 77 Therefore, one cannot fail to notice inconsistency in Taylor's attitude about the possibility that Socrates eristically resorts to invalid reasoning. For Taylor also rejects (i) precisely on the grounds that it corroborates the idea that previously Socrates irregularly introduced (S2), which is something that Taylor considers not befitting to Socrates, as we know. 78 Stokes attempts to justify (ii) as derivable from (P2) and (P7), but this is not the case either, as the conclusion of these premises is not (ii), but its converse, namely 'since they are most courageous, they are <wisest and> most daring'. 79 Christensen acknowledges that (ii) 'does not have any foundation in what Protagoras has said so far', but he also defends it as a possible suggestion that Socrates is here making 'by asking if it perhaps could be the case that those who are confident and knowledgeable are courageous'. 80 But what persuasive, let alone logical, value can an inference -such as the derivation of (S4) -have, if it is based on a purely speculative premise? § 1. 2
By contrast, in Taylor's and Shaw's analyses, as well as in mine, the second question introduces a new argumentative point that, although being logically connected with that of the first question, does not come down to it and is described by (S5). 82 Plato's language itself suggests the preferability of this second interpretive option, because a literal translation of ἡ σοφία ἃν ἀνδρεία εἴη at 350c4-5 is precisely the identity proposition 'wisdom is courage'. In contrast, Klosko and Christensen read 'is' of this statement as elliptical for 'is part of', or 'is a kind of', while Vlastos even puts the statement in the predicative form 'all the wise are brave'. 83 These interpretations are linguistically legitimate, but they overlook the fact that (S4) is of no use against (P1), because it cannot refute either the idea that some ignorant men are courageousfor which (S8) is necessary, as Vlastos himself notices 84 -or, a fortiori, the idea that courage is different from the other parts of excellencefor which (S5) is necessary. Therefore, from this perspective too, a reading of the second question as (S5) proves to be preferable.
Four weaknesses can be noticed in this reply though: 85 (I) From (P2) and (P4) nothing follows, and Protagoras' suggestion of adding (P2') to them does not actually help to get (S5) either, but at best (S4), with (P2) being redundant; (II) Protagoras completely passes over the first branch of Socrates' demonstration thus jumping long portions of the conversation, namely (P3) and Ἤδη... φαίνονται; at 350b1-c2; 86 (III) Protagoras reads Socrates' final question καὶ...εἴη; at 350c4-5 as displaying the conclusion that follows from premises that are expressed in the previous question καὶ...ἀνδρειότατοι; at 350c2-4; 87 (IV) Protagoras is right in saying he has never agreed on (P2'), but, unfortunately for him, he inadvertently accepted (S2), which equates to the conjunction of (P2) and (P2') -as he himself indirectly acknowledges in οὕτω...πάντας at 351a4-6. 88 At this point, Socrates might address Protagoras' reply by raising these four issues, thus saving the hard-fought identity of wisdom and courage and sparing himself the effort of starting a new demonstration. I suggest that the reason why he does not act thus is his concern that, now that Protagoras has showed to be aware of the difference between (P2) and (P2'), he may also be about to spot and disclose Socrates' previous deceitful introduction of (S2) in place of (P2). 89 To prevent this embarrassing situation, Socrates may hence prefer not to trigger Protagoras with any further objection and, rather, to flee from a potentially dangerous battlefield to open up a new and hopefully safer front, as he already did earlier. 90

§ 2.2 OTHER SCHOLARS' ANALYSES OF PROTAGORAS' REPLY AND THEIR PROBLEMS § 2.2.1 The meaning and validity of the reply
Allen believes that faced with a conclusion that follows validly from premises he has himself admitted, Protagoras attacks the truth of the conclusion instead of reexamining the agreements which imply it. 91 This, however, presupposes Allen's unlikely account of (S4) as implicitly inferred from (P1) and (P7), which leaves out, among the rest, Socrates' unwarranted introduction of (S2). 92 Only by neglecting this move -which constitutes a threat precisely to those 'agreements which imply the truth of the conclusion' 93 to which he himself refers -Allen can discard Protagoras' remonstrance about Socrates' illicit conversion of (P2) into (P2') as 'irrelevant'. 94 Wolfsdorf does not see anything wrong in (S2) (he even translates Socrates' question as 'do you speak of the courageous as confident?') 95 and thinks that in Οὐ...πάντες at 350c6-d1 Protagoras is speaking elliptically: by rejecting (P2'), Protagoras would actually protest that 'not all fine confident men are courageous'. 96 But here Protagoras is specifically referring to (P2), 97 at a stage when the concepts of beauty and shame had not entered the discussion yet (it happened soon after, with Socrates' question Φέρε...παρέχεις' at 349e3-5).
Furthermore, no reference to beauty and shame is made throughout Protagoras' reply either. Therefore, the following supplemented translation of ἔπειτα...σοφίαν at 350d3-6 by Wolfsdorf appears excessively conjectural: Socrates has tried to show that since knowledge <versus ignorance> is a form of <fine> confidence <and courage is a form of fine confidence>, it follows that knowledge and courage are identical. 98 That wisdom and courage are forms of beautiful daring can be argued on the basis of Wolfsdorf 's reconstruction of Socrates' whole demonstration ('(1) Courageous men are confident', '(2) Courage, qua part of excellence, is fine', '(4) Some without knowledge are confident', '(5) Ignorant confidence is base'). 99 By contrast, that conclusion is only remotely implied in the text, and not at all by Οἶσθα... εἴη; at 349e8-350c5, although this is the passage that Protagoras loosely sketches out at 350d3-6.
Finally, according to Wolfsdorf, what Protagoras means to show to Socrates in τούτῳ... γίγνεται at 350d5-351b2 is that just as wisdom and strength are different forms of beautiful power, so wisdom and courage are different forms of beautiful daring. 100 And this would be due to the fact that just as courage is engendered by natural constitution and good nurture of the soul, not by knowledge, so strength is engendered by natural constitution and good nurture of the body, not by knowledge. 101 This reading distorts the rationale of οὐ... γίγνεται at 351a1-b2, because Protagoras separates courage and daring (as well as strength and power, in his explanatory parallel) in the belief that it was on the identity of these two concepts -and especially on the fact that the daring are courageous -that Socrates based his demonstration of the identity of courage and wisdom (likewise, in Protagoras' parallel the identity of strength and power is pivotal to that of strength and wisdom). To distinguish courage and daring, Protagoras underscores the diversity of their respective sources and therefore -contra Wolfsdorf -his goal is not to suggest that if wisdom was a source of courage, wisdom and courage would be the same thing. Incidentally, such a reasoning would also be absurd, because any causal relationship involves two numerically distinct objects, in point of logic. 102

§ 2.2.2 Does courage come from wisdom?
The last problem in Wolfsdorf 's reconstruction of Protagoras' reply is that it rules out the possibility that wisdom is a source of courage. However, we saw how from the combination of (P2.1) and (P7) it follows that Protagoras implicitly agreed on a connection between courage and wisdom, more precisely that the courageous are wise, even before Socrates had been able to obtain the equivalent (S8). 103 It therefore stands to reason that the good nurture of souls (εὐτροφία τῶν ψυχῶν at 351b2), which Protagoras depicts -along with their natural endowment (φύσις, at ibidem) -as a source of courage, has to do with wisdom to some extent. 104 Likewise, Bartlett is right both to notice the same epistemic nature in art (τέχνη, at 351a7) and to consider this as a source not only of daring, as the text says, but of courage, too. 105 For given (P3) and (P2) (which is repeated in ὥστε... πάντας at 351a5-6, where it also is emphasized how '"not all the bold are courageous," i.e., some of them are' 106 ), θάρσος...γίγνεται at 351a7-b2 can be legitimately taken to say that courage comes from four sources. Two of them, namely art and spirit (θυμός, at 351b1), are common also to other kinds of daring; 107 the other two, namely the natural endowment and good nurture of souls, belong exclusively to courage. Furthermore, it is not hazardous to think of the two specific sources of courage as logically prior to the two general ones: the spirit and art of the courageous -unlike the spirit and art of the other daring people -are likely to come from, respectively, the natural endowment and the good nurture of the courageous' souls. This priority hierarchy among the four sources of courage manages to save both the 'twofold connection between courage and confidence' 108 that Shaw -and in effect Bartlett too 109 -maintains and the distinction between the sources of courage and those of daring, on the basis of which Protagoras differentiates these two concepts, as we saw. 110 By contrast, Shaw and Bartlett identify only two sources, which -they argue -are called by different names depending on whether one refers to courage or daring. 111 Whatever the number of the sources of courage, another interesting distinction among them is between epistemic (the good nurture of souls and art) and non-epistemic ones (the natural endowment of souls and spirit). 112 Bartlett argues that the latter are sufficient to produce courage, as otherwise it would not be possible that some ignorant people are nonetheless courageous, a case that Protagoras brought forth in (P1) and that Bartlett explains as one of courage stemming from the natural endowment of souls only. 113 However, that Protagoras may have changed his mind in that respect cannot surprise us, as we well know by now that an implicit consequence of (P2.1) and (P7) was precisely that 'none of the ignorant is courageous'. 114 Therefore, I rather take 351a7-b2 to say that courage comes from the conjunction of epistemic and non--epistemic elements. This reading -which is favoured by Russell and Shaw 115 -also agrees better with Plato's stylistic choice of placing an ἀπό before each of the three sources of daring (ἀπὸ τέχνης γίγνεται ἀνθρώποις καὶ ἀπὸ θυμοῦ γε καὶ απὸ μανίας, at 351a7-b1), but only one before the two sources of courage, which thus stand out as a unity (ἀπὸ φύσεως καὶ εὐτροφίας τῶν ψυχῶν, at 351b2). § 2.

'But you did not ask me whether the daring are courageous'
In Οὐ...πάντες at 350c6-d1 Protagoras comments on what he and Socrates established at 349e2-3, and he points out how on that occasion conceded (P2) but not (P2'), so Socrates had no right to say θαρραλεώτατοι δὲ ὄντες ἀνδρειότατοι at 350c3-4. If we think back at the two possible ways to read this sentence, the fact that now Protagoras attacks (i) should further confirm that this formulation, and not (ii), was the correct one. 116 However, rather than starting to question their earlier interpretive choice, scholars prefer to devise far-fetched solutions by which to save both their preference for (ii) and Protagoras' current attack on (i).
Stokes, for example, believes that Protagoras targets (i) and not (ii) because the former is an easier target than the latter. But this unwarrantedly assumes that, just like Stokes, Protagoras too sees more than one way to understand θαρραλεώτατοι…ἀνδρειότατοι. 117 Christensen interprets Protagoras' attack on (i) as a sign that he does not object to (ii), but this is hazardous to say, because we saw how (ii) has no justification in what preceded it, and even considering all the propositions featuring in Plato's demonstration, (ii) can be obtained only from (P4) in conjunction precisely with (P2'), namely (i), or with (S2), from which Protagoras indirectly takes distance in οὕτω...πάντας at 351a4-6. 118 Shaw is critical of Protagoras' objection and suggests that one should 'freely read him as making howlers'. 119 For since Protagoras' remark τοὺς...ὡμολόγησα at 350d1-2, that Socrates never refuted his claim that the courageous are confident […] is plainly laughable […] we may attribute other errors to him, provided it helps to make sense of the passage. 120 However, that remark should be put in the context of the whole 350c6-d2, where Protagoras' rhetorical point seems to be that not only he has never agreed on what Socrates put in his mouth, namely (P2'), but also -and as a flip side -that Socrates has never refuted what Protagoras did assert, namely (P2). Granted, the second part of the observation attacks a straw man, because certainly Socrates did not object to (P2). But precisely for this reason it is ungenerous to describe this as a true mistake. It seems more a redundant defence of Protagoras' own position, perhaps provoked by his anxiety at this delicate moment, when he is supposed to counter Socrates' long and complex demonstration. The severity of Shaw's criticism appears even more striking if one recalls his benevolent assessment of Socrates' introduction of (S2), with the result that the impression that Shaw adopts double standards is strong. 121

§ 2.2.4 Socrates' final silence
Christensen observes that Socrates' silence about Protagoras' reply must be read within the frame of his elenctic method, according to which the interlocutor should realize by himself that he has been refuted, which will happen only at the end of the next discussion (360d-361e). 122 At this stage -Christensen says -Protagoras 'has not identified the premises for Socrates' conclusion and thus misinterprets Socrates' argument'. 123 But since Socrates' argument is irregular, Protagoras has not actually been refuted, and his denunciation of Socrates' illicit use of (P2') seems, on the contrary, to prove his good grasp of Socrates' argumentation. Conversely, at the end of Socrates' second and more convincing demonstration of the identity of wisdom and courage, Protagoras has nothing to retort and simply surrenders to it, at 360e3-5. 124 Shaw, too, is puzzled by the fact that Socrates 'doesn't simply respond to Protagoras by clarifying his argument.' 125 Nevertheless, he agrees with Russell that at 351b3-360e5 Socrates 'replies to a deeper objection' that Protagoras raised to Socrates' first demonstration, namely that 'courage requires not only knowledge, but also φύσις'. 126 As I argued above, I too believe that in ἀνδρεία...γίγνεται at 351b1-2 Protagoras presents the natural endowment and good nurture of souls as non-alternative sources of courage. 127 However, I do not think that those words of Protagoras address any of the points of Socrates' demonstration, as this never touched on the origin of courage. Secondly, I cannot consider Socrates' argument to the effect that knowledge cannot be ruled by spirit, pleasure, pain, love, or fear (τοτὲ μὲν... φόβον, at 352b7-8) as anything more than a step towards the identity of wisdom and courage, which he finally reaches in Ἡ... ἀμαθίᾳ; at 360d4-5. It is true that an implicit corollary of Protagoras' belief in the necessity of both epistemic and non-epistemic sources of courage is that 'knowledge can be ruled by fear and so must be bolstered by spirit'. 128 But if Socrates' argument that knowledge rules man's life had been designed as a rejoinder to that view of Protagoras, Socrates would have likely flagged it up somehow. This occurs, for example, in Ἕν...δέ at 360d8-e2, where Socrates asks Protagoras to confirm that the identity of wisdom and courage that they have finally agreed upon refutes (P1)'s idea that there are ignorant and courageous men.

CONCLUSION
Contrary to what scholars usually maintain, Socrates makes an illicit move when he elicits (S2), a proposition on which his demonstration of the identity of wisdom and courage (349e1-350c5) depends. For Socrates presents (S2) to Protagoras as if it was just a reminder of (P2), to which Protagoras earlier agreed. Besides this eristic aspect, the argument remains, however, a masterpiece of dialectic, whose complexity scholars have not fully appreciated, especially as regards the many passages, often implicit, that lead to (S3) and to (S5). As a matter of fact, when Protagoras accepts (S2), Socrates has already led him to inadvertently contradict (P1), through the combination of (P2.1) and (P7).
In his counter at 350c6-351b2, Protagoras is more right than how scholars usually depict him. For he never agreed to (P2') explicitly, but he did so implicitly, when Socrates fooled him into committing himself to (S2), a move that, therefore, Protagoras comprehensibly forgets he made. Although Protagoras' reply testifies some shortcomings of his in following Socrates' train of thought, it has the merit of not resorting to eristic tricks and of silencing Socrates, who then needs to come up with a new strategy to prove that wisdom is courage.
In showcasing an amazing web of eristic and dialectic, of sophistry and philosophy, in which the two characters swap their traditional roles very naturally, 349d2-351b2 proves to be one of the most succesful and representative passages of the whole Protagoras.