vlastos -unity of virtues in protagora

7/28/2019 Vlastos -Unity of virtues in Protagora

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ARTICLESTHE UNITY OF THE VIRTUES IN THE PROTAGORAS *

GREGORY LASTOS

|YJ[y main task in this paper will be to tackle a problem in theProtagoras whose solution is long overdue?the one posed by thefact that in

statingand

defendinghis doctrine of "the

unityof the

virtues" * Socrates employs formulae which seem hopelessly atodds both with common sense and with the procedural assumptions of his own dialectic. The proportions of this problem areobscured in standard discussions of our passage. Some scholarsact as though they were blissfully unaware of its difficulties. Thegrit in the Platonic text gets washed out of their bland paraphrases of Socrates' views; one who has not worked through theoriginal with stubborn attention to its wording would not knowafter reading them what is the problem I am talking about or even

* For valuable criticisms which have helped me to improve this essayat some points I am indebted to Professor Glenn Morrow and Charles Kahn,and to Terry Irwin and Paul Woodruff, graduate students in the PrincetonProgram of Classical Philosophy.1 The Socratic doctrine is presented as one of the two options betweenwhich Protagoras is required to choose in 329C-330B6, and then again,when the debate resumes after break, in 349B1-D1. The defense is presentedin the form of separate arguments for the unity of four pairs of virtues:(1) Justice and Piety (330B6-331E6);(2) Wisdom and Temperance (332A4-333B6);(3) Temperance and Justice (333B8-334C6);(4) Courage and Wisdom (349D2-350C5).

[I capitalize the names of the virtues and "Virtue" wherever each of theseterms functions as the proper name of an eidos or idea.] I shall havenothing to say of the argument for (3) which is sabotaged by Protagorasand is left incomplete. I shall have occasion to analyze the arguments for(1) and a part of the one for (2). In the case of the one for (4) I shall beable to comment only on its terminal section; analysis of the rest of theargument will not be germane to the matters with which I shall be concerned here (I have offered a sketch of it in Vlastos, 1956, xxxii-xxxv). Norwill I have occasion to work through the sequel to this argument (351ff),where the "Socratic Paradox" is defended (for this see Vlastos, 1969 [B]).[All references to modern books and articles are by author and year ofpublication, as listed in the Bibliography below.]


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416 GREGORY LASTOSthat there is a problem.2 When the perplexities which bedevil theSocratic formulae are recognized the acknowledgement is notalways followed by a resolute effort to untie the knots : 3 one findsscholars excusing themselves from the task by implying, or hinting, that Socrates could not really have meant the outrageous

2 A. E. Taylor [1937, 247-248, 257] is a good example. The troublesome formulations (329C6-330B6 and 349B1-D1) of Socrates' views?thoseI shall be calling the "Unity Thesis" and the "Similarity Thesis"?arereported only in the form of questions put to Protagoras; Socrates' ownstand is reduced without argument first (247) to the innocuous thesis that"the principle of goodness will be exactly the same in whatever relation oflife it is displayed" and then (248) to the unproblematic formula which Ishall be calling the "Biconditionality Thesis." Nothing better in Shorey[1933, 125 and 129, with notes]: all three Theses appear only in the formof non-committal questions. Of Shorey's references to other dialogues onlythe one to Laches 198A is at all helpful; Laches 199c-E would have beenmore to the point, though neither this nor any of the others really explainsthe formulae in the Prt. passage, whose apparent perversity Shorey elects to

ignore. One of them would have surfaced on p. 129, where Shoreyrepresents Socrates as "proceed[ing] to identify courage, too, with wisdom,"if "identify" were not being used with deplorable looseness, as shown by theallusion to the definition of Courage by Nicias in the Laches (194E-195A):there Courage is not "identified" with Wisdom but with a species of it(knowledge of things to be dreaded and dared) ; to identify X with a

species of Y is a far cry from identifying X with Y. [The abbreviations ofthe titles of Platonic works I shall be using throughout this paper are thosein use in the Liddell and Scott Greek-English Lexicon; in any case, theyare self-explanatory.]3 Among the rare exceptions I might mention Gallop [1961], Sa van[1964], and Crombie [1962, 233-235]. I have found Gallop's detailedanalysis of argument (1) particularly helpful, in spite of many disagreements (see notes 12, 31, and 84 below). Crombie comes closest to explaining the true meaning of the "Unity of the Virtues":. . . the various virtue-expressions are so closely interrelated in mean

ing that in so far as any one of them can be properly predicated of agiven thing, there is some sense in which all the others may be also.I dare say that if Crombie had not been content to say "there is some sense"

and leave it at that, but had probed the Platonic text until he found therequired sense, his results would have been much the same as mine. Inthat case, he would not have represented Socrates as holding that "wisdomand temperance are the same thing" (234), without indicating that the

obvious sense of this sentence (that these are the same virtue) and theunavoidable implication of this obvious sense (that the names of thefive virtues are synonyms) constitute propositions which Socrates wouldhave been the first to repudiate and would not have dreamed of trying toprove (as he in fact does not: as I trust will be made clear in this essay,none of Socrates' arguments purport to prove that different virtues are thesame virtue or that their names are synonyms).


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 417

things he says?that he put them up only to test Protagoras andexpose the sophist's powerlessness to diagnose perversities in theSocratic theses and fallacies used in their defense.4 Thesescholars, I trust, would agree that to cast Socrates in such a role

?allowing him, in effect, to fight sophistry with sophistry?is adesperate expedient.5 There would be no need of resorting toit if we could understand the Socratic formulae in a way whichpurges them of their offensive features. I believe we can, and myfirst and major task will be to show how. A spin-off of the undertaking will be a new account of the two notorious sentences inour passage?"Justice is just," "Piety is pious"?with implications for the vexed problem of "self-predication" in Plato.

IA careful reading of the initial posing of the issue to be

debated with Protagoras (329C2-330B6) and of its subsequentrestatement when the debate resumes after a break (349A8-C5)4 Paul Friedl?nder [1964, 19-20, 26-28, and notes] concedes that

Socrates appears to have staked out an indefensible thesis ("an exaggeratedform of unity [of the virtues], unity as strict identity" [19]), but impliesthat in so doing Socrates is indulging "a peculiarly iridescent irony, hard tograsp" (19), and that his arguments are deliberately fallacious: the one forthe unity of Piety and Justice is an "artificially constructed piece of nonsense" (20), the one for the unity of Wisdom and Temperance employs aninference that is a "conscious deception on the part of Socrates?or anexercise in logic for the reader" (20). (Shorey too [1903, n. 117] thinks theargument deliberately fallacious, designed to "trip up" Protagoras.) Amore complex view is taken by R. E. Allen [1970, 82, 93-99]. He says that"the Protagoras maintains a studied ambiguity" on the question whetherthe virtues "are one in definition, or one in that they introduce each otherand cannot be detached"; "it does not choose between the alternatives"(99). He appears to think that the point of the first alternative is polemical:

Socrates "attempts to lead Protagoras to admit hat the virtues are all namesfor the same thing, . . . synonyms" (94) and proceeds to defend that thesiswith arguments each of which "is fallacious, and some of them blatantly andscandalously fallacious" (94)?all this in order to show up the fact that

Protagoras, "although he claims to teach virtue, does not know whatvirtue is" (95).5 It is widely assumed that, for good purposes of his own (pedagogicalor polemical), the Platonic Socrates does not scruple to assert categoricallypropositions which he does not himself believe and to defend them bysophistical arguments. I reject this assumption, holding it to be inconsistentwith what we learn in the Platonic corpus about Socrates' conception of thephilosophic life and about his personal character. I count it a merit of the


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418 GREGORY LASTOSwill show that Socrates employs three distinct formulae, onlythe first of which answers at all closely to the term "Unity ofthe Virtues" which has been commonly used in the scholarlyliterature as a label for the position which Socrates upholds inthe debate. The other two formulae, perfectly distinguishablefrom the first (which I shall call the "Unity" Thesis),6 I shallcall the "Similarity" and "Biconditionality" Theses. I shall discuss the three Theses seriatim. But let me emphasize from thestart that they are not treated in the text as logically disjointtenets, but as successive moments in the elucidation of a singledoctrine. That is how Protagoras himself understands them.

At no point does he try to drive a wedge between them or playoff one against another.7 He accepts them as complementaryexpressions of a theory which he rejects and combats as a whole.

1. The Unity ThesisThe question as it is first put is 8whether or not "Justice,"

"Piety," "Temperance," "Courage," and "Wisdom" are all "names

interpretation I shall be presenting that it does not require Socrates toresort to a single sophistical argument. He does slip into fallacies. But noneof them are deliberate.6 There is some awkwardness in keeping "Unity of the Virtues" as thetraditional label for the whole doctrine (this is so common in the scholarlyliterature that it would be confusing to drop it now) and using the "UnityThesis" to designate the first of its three major articulations. But I have been

unable to hit on a happier label for the first Thesis; "Synonymy" most certainly will not do, for the reason I shall explain.7Which is particularly striking in view of his strenuous (and perfectly understandable) objection (331B8-E4) to the vagueness of the Similarity Thesis, while he never faults the Biconditionality Thesis on this score,rejecting it firmly and unequivocally on first hearing (contrast ou?anco? etc.in 329E5 with the more hesitant, 'Eks?vc?? uoi (paivexai ... in 329D8, inresponse to the Similarity Thesis).8 I omit the first part of the question in 329C5-D1, "whether Virtue isone, and Justice, Temperance, and Piety are parts of it," because on thatpoint there is no difference between Socrates and Protagoras: that the severalvirtues are "parts" of Virtue is standard Socratic doctrine (it is unequivocallyaffirmed and strongly emphasized in Meno 78D8-79E2), and it is implicitlyreaffirmed in the next paragraph: at D4-8 the question is not whether thevarious virtues are, or are not, "parts" of virtue, but what kind of "parts"they are?like the parts of a face, or like the parts of a bar of gold? Thereis just one passage in the whole of the Platonic corpus which might lendcolor to the notion that Socrates holds the (virtually self-refuting) viewthat each of the virtues is not a part, but the whole, of virtue: the argument


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 419of the same (thing) which is one (thing) " (ov?jiaxa too a?xou ?v??ovxo?) . Later on, when the issue is formally restated, Socratesasks: "Do these five names apply to one thing (?rci ?vi 7rp?yuax?eaxiv) ?9 Or is there, for each of these names a separate 10essenceunderlying each (f[ sK?aiop xcov ovou?xcov xo?xcov urcOKeixai xi? ??io?ouata)?a thing having its own individual power (Tipayiia?xov?auxoC)?uvajiiv ?Kaaxov) ?" 1X Socrates takes the first, Protagoras thesecond option. This is most surprising. One would certainly

have expected Socrates to join Protagoras in maintaining thateach of the five names applies to a distinct "thing" or "essence."For to claim that all five "are names of" the same thing would benormally understood as claiming [i] the identity and [ii] thesynonymy of the five virtues: that is how the claim is still beingunderstood by commentators today.12 But to make either ofin La. 197E ff. (An analysis of this argument which, I believe, resolvesthe difficulty will appear in my forthcoming Platonic Studies [Princeton

University Press]).9Given the ambiguity of ovoua (to be explained below, pp. 430-432)?referring expression or descriptive predicate?this question could be readto mean either

(a) 'Do all five names apply referringly to the same thing?', or(b) 'Do all five apply descriptively to the same thing?'

Agreeing to (a) restricts one to a single nominatum. Agreeing to (b)does not, leaving open the possibility that there are several nominata (infact, five: one for each of the five virtues) each of which is named by allfive names. I take the wording to be inconclusive as between the tworeadings, and opt for (b) which, as will be seen, has the sterling meritof saving the hypothesis that there are five virtues.10 So Jowett and Guthrie for ??io?, whose literal sense is "private"(??io? is the standard antonym of koivo?, "common").11 I cut off the last clause of the question in 349B1-6, "no one of whichis such as another," because at that point it spills over into the SimilarityThesis. This is one of several points in the text where the rhetoric displaysthe assumption that the two Theses are variant expressions of the samedoctrine: Socrates passes without explanation from the one to the otherwithin a single period here; he does the same again in B6-C5.12For [i] :Friedl?nder ("unity as strict identity"), quoter in n. 4 above.

Gigon [1946, 139 et passim] represents Socrates as demonstrating "theidentity of the virtues." Gallop [1961, 88-89] represents Socrates as concerned to refute Protagoras' denial of the "identity" of the virtues, andfaults Socrates' argument at 330-331 because it "does not seriously purportto prove the identity of Justice and Holiness, but only their homogeneity,"contrasting this argument with the one about Temperance and Wisdom,"which does, whatever its failings, purport to prove identity." And cf. thequotation from Shorey in n. 2 above sub fin. For [ii] see the citation fromAllen in n. 4 above.


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420 GREGORY LASTOSthese claims would be nothing short of preposterous. Of their"identity" there could be no question. What Socrates says of

Piety in the Euthyphro?that it is a single ?5?a, which recurs selfidentically "in" every pious act (5D1-2) and can be used as a"standard" (rcapa?eiyua) by looking to which we can tell whethera given act is or is not pious (6E3-6)?he would say, mutatis

mutandis, of every one of the other four virtues. How thencould he possibly tolerate, let alone uphold, the notion that each isidentical with each? Could one think of him, for instance, conceding that if Euthyphro were to give him the definiens ofCourage, he could use that as a "standard" by which to judgewhether Euthyphro's prosecution of his father was, or was not,pious? As for claiming that the names of the five virtues were allsynonyms, that would imply that any of those five words can befreely interchanged in any sentence (in a transparent context) 13without changing its sense or truth. Try substituting "Courage"for "Piety" in

(1) "Piety is that eidos in virtue of which all pious actions arepious" (Euthphr. 6D),

or "Justice" for "Piety" in

(2) "Piety is that part of Justice which has to do with service to thegods" (Euthphr. 12E).

The substitutions would falsify (1) and make nonsense of (2) ,14Again if two words are synonyms the definiens of either woulddo for the other. Could one say this of words like "Courage" and"Temperance"?or even of words that were more closely relatedin the mind of the Greeks, "Justice" and "Piety?" Can one

13Free substitutability in opaque contexts?contexts introduced byexpressions like "X thought (or believed, said, etc.) that . . ."?is obviouslynot required by the view that the five words are synonyms.14Note that both results would be prohibitive for Socrates. The sentence in (1) is his; the one in (2) is Euthyphro's, but it has Socrates'explicit approval ("What you have said seems to me admirable," 12E9).It should be obvious that there would be many other sentences, explicating,or commenting on, the intensions of individual virtues, where substitutionof the name of one virtue for that of another would yield falsehood ornonsense.


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THE UNITY OF THEVIRTUES INTHE PROTAGORAS 421imagine Socrates accepting the definiens of "Piety" as that of"Justice," or vice versa? We know that he would not. Consider

what happens in the Euthyphro. The search for the definition ofPiety gets nowhere until Euthyphro is brought at long last to seethat Piety is a "part" of Justice,15 and therewith to see that inorder to reach its definition he must find out which special "part"of Justice Piety happens to be.16 This project, which has Socrates' unmistakable approval,17 would make no sense if thedefiniens of Piety were the same as that of Justice. How thencould Socrates have wished to sponsor the thesis that "Justice" and"Piety" are synonyms?

2. The Similarity ThesisThe question now iswhether or not each of the virtues is like

each of the rest and like Virtue.18 To say this Socrates uses avariety of expressions. I list them in the order of their appearancein the text, using

B and A as stand-ins for names of virtues or for"Virtue":

[1] B and A "do not differ at all (o???v ?icup?pei) . . . except insize" (329D1-2).[2] B is "such as" A (eaxiv to sxepov oiov to 6T6pov, 330A8-B1).1915 No progress had been made?Euthyphro's attempts had produced

only "statues of Daedalus" that kept running away, 11C-D?until Socratestook the lead in the search by introducing this line of thought at 11E4 ff.16The question is so put at 12E1-2.17This is clear from 12E3-4: if Euthyphro would tell Socrates "whichpart of Justice is Piety," Socrates would be able to understand "adequately"(?Kavco?)what Piety is.18The latter point?the similarity of each of the virtues to Virtue (asthe "whole" of which each of the virtues is a "part")?plays no role in theargument. But it is explicit in [1] below?the "parts of gold" analogy in329D6-8 and 349C2-3?and had best be included in generalized statementsof the other formulae as well.19This is by far the most frequently used phrase. It recurs at 330B3-7,330E5-6, 331A2-3, 331B6-7. It is to be distinguished from[7] ? is "such as to be an ,4-ish [thing]" (erjTiv ?ai?TT|C o?ovO?KCtiov?va? [rcpayua] 331A7-8; I put in brackets the part of the

quotation which is expendable: it is dropped in subsequent uses),which is only verbally distinguishable from[8] B is A-ish ((painv ?v ttjv ?iKaioaovrjV ?aiov e?va?, 331B2-3),since [8] is used to affirm the direct and full negation of not-[7]. [7] and

[8] occur in the premise-set from which the proposition expressed by [1],


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422 GREGORY LASTOS[3] The "power" (?uvapi?)20 of B is "such as" that of A (330B1).[4] B is "similar" (?|ioiov) to A (349C3).[5] B is "either the same thing as A or as similar to A as it couldpossibly be" (??toi Ta?rc?v y3 ecjTiv 8iKai?Tr|c ?ai?TrjTt il ?ti

?uoi?toitov, 331B4-5).21[6] B is "almost the same as A" (ax?5?v Tt Ta?rc?v), 333B5-6).

The fluidity of the phraseology 22suggests that Socrates is huntingfor the right words and hasn't quite found them. Nor is thetrouble merely verbal. The best he offers by way of specifyinghow or in what respect(s) the virtues are supposed to be similaris an analogy : they are not related to one another as are the partsof the face but as "the parts of [a bar of] gold, which do not differfrom one another except in size" (329D) ,23 What are we to makeof this? To take the analogy at face-value we would have to take

[2], [4], and [5] is deduced (presumably also the proposition expressedby [3], though there is no further allusion to this part of the thesis in theensuing argument) as should be clear from the text and, in any case, fromthe analysis of the argument to be offered below. A comment on the translation of o?o?: This is the pronoun used to introduce the answer to tco?o?:"What sort of man (71010c) is Achilles??He is the sort of man (o?o?) notto forget an injury." The poets use it to introduce similies: "Such as(o?ov) a star sent by Zeus as an omen," so Athena flashed from Olympusto earth ill. 4, 75) : she descended "like" (i.e. with the speed of) a fallingstar. 20 The "power" (?uvaur?) of a particular virtue is that virtue itself,conceived as a dispositional quality manifesting itself in action. As Prauss[1966] remarks, "The 'dynamis' of rjuxppoauvn or ?iKaioauvn is nothing

but fjGKppove?v or ?ixaiov e?vai"

[76]. (But I cannot follow him in thefar-reaching consequences he spins out of this fact; I see no justificationfor his conclusion that "unlike

'quality', 'attribute', etc.," dynamis precludes "relationship to an underlying substance" (loc. cit.). In Socrates'ontology (and Plato's too, for that matter) the dynamis of Temperance existsonly in the persons who have that dynamis and are logically related to it asis subject to attribute. To say this is not, of course, to impute to Socrates

or Plato the Aristotelian ontology of "underlying substances," but only thepre-analytical notion of individuals who are distinguished from their properties. 21 And cf. Socrates' "astonishment" at the suggestion that "there isonly a slight resemblance [Guthrie] between Justice and Piety" (oxrceouxH?v ti rjuiKpov exeiv ?XXi\Xoiq, 331E6).22 I cannot recall its like in any of Plato's Socratic dialogues.23 No explanation is offered for "differences in size jiey?Oei Kai

afiiKpOTUTi]." I surmise that these refer to differences of genus andspecies: Justice may be thought of as bigger than Piety, since the latter isa "part" of Justice (Euthphr. 11E-12E), though this sort of difference is notmentioned in our passages and plays no role in its reasoning.


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THE UNITY OF THEVIRTUES INTHE PROTAGORAS 423him to mean that the virtues are alike in respect of ail theirqualities?that they are qualitatively undifferentiated dispositions,which appears to be the very thing he says himself at [1] above.Could Socrates really mean that? If he did, his present claimwould be as inept and self-defeating as would have been hisprevious one, that all their names name the same thing, if thathad been meant to say that they are all synonymous. Tohomogenize the virtues would be to wipe out those very markswhich make up their distinctive physiognomies and enable us toclassify particular actions as instances of this or that virtue.Socrates himself must be fully aware of those differences betweenindividual virtues. He must be counting on them to vindicatediverse definitions for diverse virtues. Consider his definition ofCourage: "knowledge of what is to be dreaded or dared." 24How would he go about showing that this is not also the definition of, say, Justice, or, again, of Temperance, except by pointingto the fact that whenever we think of an action as brave we do sobecause, and in so far as, we see it as endurance of danger oraffliction, while ifwe had seen it as giving to another person whatis due him we would have thought of it as just, and if it hadstruck us as evidencing the agent's power to keep his appetites

under the curb of reason we would have called it "temperate?"Note that one and the same act could very well display all three ofthese features: any theory should allow calling a particular act"brave" and "just" and "temperate";25 but this would not gainsaythe fact that in manifesting these three virtues it is expressingrecognizably different moral dispositions,

a fact which we would

24 Santas' (449) felicitous rendering of La. 194E-195A, tt|V tcov ?eivo&vKai &appa?,??)V ?7iiaTf|UT|V, put forward there by Nicias; but that it isacceptable to Socrates (and indeed, as Nicias is made to say, that it derivesfrom Socrates: "I have often heard you say . . .," 194C) is made certain bythe fact that Socrates himself employs it as a premise in a demonstrativeargument, Prt. 360D. The allegation one meets frequently in the scholarlyliterature, that no acceptable definition of a virtue is ever reached in the

Socratic dialogues, is false.25One might be tempted to say that Socrates' own theory wouldrequire that every virtuous action must display all five virtues. But this isnever said in the dialogues, and it is not implied by Socrates' doctrine thathaving any virtue implies having all the virtues: a man who has five distinct dispositions which may be concurrently exercised need not be exercising all five on each occasion on which he exercises one.


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424 GREGORY LASTOSexpect Socrates to grant as readily as would anyone else. Whatsense then could we make of his claim that Courage and Justiceand Temperance are as alike as are two bits of a gold bar?

3. The Biconditionality ThesisNow we are in for a surprise. Instead of another paradox

Socrates now gives us a proposition that is crystal-clear:Which of these two things is the case: That some men partake of one

of these parts of virtue, others of some other part? Or is it the casethat if a man has one he will of necessity have them all? (329E2-4).

The latter option, that of Socrates, is simply that the five virtuesconstitute coextensive classes: those who instantiate any one ofthem, must instantiate every one of them. We can put this intosymbolic form:

(x) (Cx ?-? Jx


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THE UNITY OF THEVIRTUES INTHE PROTAGORAS 425the other virtues; and it is also sufficient, and in the same strongsense, for Socrates is convinced that he can prove on logicalgrounds that a man who is wise will have to be temperate, andbrave, etc.28 So stated, the doctrine in our passage becomes perfectly lucid in itself, and it is instantly recognizable as a cardinalSocratic tenet, integral to the theory that Wisdom is the necessaryand sufficient condition of all moral virtue 29and, what is more,coherent with Socrates' personal conviction that to engage hisfellows in intellectual argument calculated to advance their discernment of moral truth is ipso facto to improve them morally, to

make them better men. The Biconditionality Thesis would beone way of enunciating the rationale of this conception of his rolein life. It would explain why he is so sure that the usualapproach, the ad hoc, piecemeal, inculcation of different virtues,would be futile, and that tomake men moral one must make them

wise, for without Wisdom they can have no other virtue, andwith Wisdom they are bound to have every virtue.

Here then we have three theses. All three purport to expressthe same Socratic doctrine. But while the first two are sopuzzling that we are hard put to see how Socrates would wantto affirm what they seem to affirm, the third is a transparentlyclear expression of a well-known Socratic doctrine.30 This contrast might lead one to go in either of two directions. One mightuse it to discredit the first two theses, writing them off as confused and inconsequential expressions of what Socrates was after.This is the way I took them when writing an Introduction to thisdialogue fifteen years ago.31 But there is another way whose

28 The sufficiency of Knowledge for virtuous action is demonstratedin the final argument in the dialogue, the one for the "power" of knowledge, 352A ff.29 For which see e.g. the section on "Virtue is Knowledge" in Gulley[1968, 83 ff.].30 Though a very limited one : it does not spell out the strategic role ofWisdom as the conceptual link between any two of the other four virtues

?i.e. the fact that any two of them necessarily imply one another onlybecause each has inWisdom its own necessary and sufficient condition.31 [1956, liv.]. Quoting the Biconditionality Thesis, I remarked, "Thisis what the argument is all about," and proceeded to ignore the other twoformulations of the doctrine. There is a sense in which I was justified intaking this line. For one who is exclusively concerned?as I was at thatjuncture?with the substantive issue under debate, the Biconditionality


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 427

Thesis, I shall be arguing that each of the following sentences willbe true:

Justice is wise,Justice is temperate,Justice is courageous,

Justice is pious,Justice is just,Justice is virtuous,

provided each is understood to assert its predicate-term not of theabstract noun, Justice, in the subject-position, but to anyone (oranything) who (which) is just, e.g. provided that "Justice is

wise" is understood to assert that whoever (or whatever) is justis wise. When the sentences are read in this way the truth ofthe first four will follow directly from the Biconditionality Thesis,as I shall proceed to demonstrate (in the paragraph after the

next) ; the sixth will also follow from the same Thesis, as I shallexplain; and the fifth will be a tautology. Those sentences willremain true when their predicate-term is put in substantival form,

Justice isWisdom,Justice is Temperance,Justice is Courage,

Justice is Piety,Justice is Justice,Justice is Virtue,

provided we read each of them as a convertible predication, e.g.read "Justice isWisdom" as the conjunction(Justice is wise) & (Wisdom is just),34

34 That Plato would take "Justice is Wisdom" to be convertible isshown by the way he uses (A) "Wisdom is Courage" in 350C and (B)"Courage is Knowledge [=Wisdom]" in 361B. On (A): If "Wisdom isCourage" were read as non-convertible in 350C (i.e. if it were being understood to predicate "Courage" of Wisdom, but not the converse), it would notbe the contradictory of Protagoras' claim in 349D6-8 that some courageousmen are unwise ("most ignorant"). This claim, reformulated to expressthe relation between the virtues, Courage and Wisdom, rather than betweenmen who have Courage but lack Wisdom (cf. n. 60 below), would have

been(1) Courage is not wise.To deny this proposition what Socrates must assert is precisely that(2) Courage is wise.

Since he uses instead(3) Wisdom is Courageto deny (1), he must be taking (3) to mean not only(4) Wisdom is courageous,

hut also (2). He must thus be reading (3) as the conjunction


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428 GREGORY LASTOSreading both conjuncts in the same way as before.35That Socrates himself would wish us to give this reading tosentences like "Justice is wise" and "Justice isWisdom" is a question I shall face squarely later on (Section HI below). For thepresent I shall assume that he does: everything in the presentsection will be conditionalized on this assumption. What is notin question is the fact that he does use sentences with this grammatical structure. Here are the main examples:

Justice is just,86Justice is pious,37Piety'is pious,38Piety is just,39Virtue is noble,40

Wisdom is Courage,41Justice is Wisdom,Temperance isWisdom,Courage isWisdom.42

The syntax of these sentences may seem peculiar at first blush.Admittedly, it is not too frequent in either English or Greek. It isnonetheless fully in line with good usage in both languages. Wesay things like "Justice is impartial" and "Ignorance is bliss"without strain, with no sense of resorting to contrived or stiltedgrammar; the same would be true in Greek. I shall, therefore,proceed to use without apologies substitution-instances of the"B is A" sentence-form in L, reserving comment for the following

(5) (Wisdom is courageous) and (Courage iswise).In (B) we get confirmation for this conclusion. What he was "trying toshow" in this debate, he now tells Protagoras, is. . . that all things [i.e. all the things they had been talking about, thefive virtues] are Knowledge, both Justice and Temperance

andCourage[are Knowledge] (361B1-2).

In 350C he had said he had proved that "Wisdom is Courage." What henow says he had tried to prove is that "Courage is Knowledge [=Wisdom]."The shift from "Wisdom is Courage" to "Courage isWisdom," made withoutexplanation or argument, would be perfectly explicable if Socrates is taking"Wisdom is Courage" to be convertible, for in that case the two sentences

would be interchangeable.35 I.e., as Pauline predications (cf. n. 33 above). All the numberedsentences in the preceding note are likewise Pauline predications.36 330C.37 331B.38 330D.39 330D.40 341E.41 350C (cf. n. 34 above).42 Cf. the citation from 361B1-2 in n. 34 above.


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 429Section, by which time we shall have a better sense of their scopein our passage. My task now is to substantiate the claim I havemade that L, with the proposed reading, follows from the Biconditionality Thesis. How soPThat Thesis assures us that if a given person, Ar, happens tohave any of the five virtues, he will "of necessity" have all five.So suppose N is just. It will follow at once (and necessarily)that N will be wise. If so, his Justice would have to be wiseJustice.43 It could not be dim-witted, scatter-brained, whimsical,or rote-ridden Justice: it could not be flawed by any defect inrationality that would fault it when measured up against the highstandard of Socratic wisdom; for were that the case, N's wisdomcould not be inferred (and inferred with necessity) from the merefact that he is just, as the Biconditionality Thesis assures us thatit can. So AT,s Justice must be wise: if we accept the Biconditionality Thesis, this follows necessarily. And since what is trueof Vs Justice will also be true of M's and O's and of any otherperson's we happen to pick, it will follow by existential generalization that Justice iswise.44 By the same reasoning we may deducefrom the Biconditionality Thesis that Justice is not only wise, butalso temperate, brave, and pious,45 and we may then similarlydeduce from the same premise that all five virtues are interpredicable, and therefore that the 'B is A" sentence-form in L willbe true for any two distinct virtues, regardless of whether thepredicate-term is put in adjectival or substantival form. TheBiconditionality Thesis will also assure us that "Justice is virtuous"and "Justice is Virtue" are true, since we learn from that thesisthat anyone who is just is bound to have all the virtues and thatwhoever is virtuous is bound to be, among other things, just.46As for "Justice is just" and "Justice is Justice," no proof is needed,since all these sentences are used to express in this context is thetautology that whoever (or whatever) is just is just. What has

43 I.e., the sort of Justice whose instances are all wise: a Paulinepredication is nested in "N's Justice is wise."44 Pauline predication.45 Pauline predications.46 Since to be virtuous at all one would have at least one virtue, whenceit would follow, given the Biconditionality Thesis, that one would have allthe virtues, including Justice.


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430 GREGORY LASTOSbeen proved for Justice may be proved for each of the other virtuesby the identical reasoning, and for Virtue by obvious extension ofthat reasoning. So L has been secured.

But now we may ask: How will L help us make sense ofSocrates' saying that the names of all the virtues are names of thesame thing? Itwould not, taken just by itself. To do the job wemust take into account a further fact which has long been knownbut has never been linked up with our passage in the Protagoras.This is that all through the archaic and classical periods the"name" (ovoua) was expected to perform two radically linguisticfunctions: first, of course, that of the proper name: this is theoriginal, and always the primary, use of ?vopa ; but secondlythat of the common name, that is to say of the qualifying predicateor descriptive expression. Of this dual sense of ovoua manyexamples could be given, but one should suffice, for this gives usall the information we need to crack our present puzzle. Theexample comes from the Phaedo?written later than the Protagoras, to be sure, but entirely suitable for the purpose of illustrating and inherited, long-established, usage.47

In the passage on the clever aixia in that dialogue Socratesspeaks of cases in which

not only the Form itself [say, F], is always entitled to its own name,but also something else [say, G] which is not identical with thatForm, but always has its character [G is always F] when it [G] exists(103E2-5).48

47 There is no difficulty in documenting the antiquity of the use of"name" to designate predicative expressions, no less than referring ones.

Thus it is clear in B 9,1 that Parmenides thinks of "fire" and "night" asnames serving a predicative function, since he speaks of mortals "namingeverything Tire' and 'night'," i.e., so classifying the contents of theirputative universe; and that in B 8, 40-41, not only "being," "not-being,""becoming" and "perishing," but even phrases like "changing place" and"interchanging bright color" count as names: he says that these havebeen posited as names with respect to Being (reading ovouaaxai for whosedefense see Mourelatos [1970, 180 ff.]). The use of "naming" for "stating,specifying" is as old as Homer. Liddell and Scott, Greek English Lexiconcites II. 8, 449, "they named (?vopa?ov) glorious gifts." Cf. Mourelatos[1970, 184] on name as "abbreviated description."48We can make best sense of the phraseology by taking "G" here to

refer to G qua immanent character, rather than qua transcendent Form


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THE UNITY OF THEVIRTUES INTHE PROTAGORAS 431In his example G and F are respectively Three and Odd:

Don't you think that [Three] may always be called both by its ownname and by the name of the Odd, though [the Odd] is not identicalwith Three? (104A5-7).

Since Three is odd, every trio is rightly called (hence, "named")"Odd." And since it is also rightly called "Three," it is entitledto both of these names: "Three" names Three, and "Odd" alsonames Three. Here "names" is evidently used in the two differentsenses I have specified. In

" 'Three' names Three" the "name" isa proper name, a referring expression. In

" 'Odd' names Three"the "name" is a descriptive predicate.49 Plato does not identifythese two functions as different senses of "name" and "naming."Elsewhere he notices the difference between the subject- andpredicate-terms of a sentence like "Theaetetus sits," calling thefirst word an ?vopa, the second a pr\\ia. This is in the Sophist(261Dff.) where his analysis of the syntactical structure of a sentence had advanced in depth. But even there he does not go so faras to say that the pf?|ia is itself an ovo|ia discharging a predicativeinstead of a nominative function.50 To take note of the distinction between referring and predicative expressions he resorts totwo different words, ovojia, pfjpa, instead of saying that the same

(hence the expression "when it exists" which would be puzzling if assertedof a Form). But this does not affect the general point that a given eidos(immanent or transcendent) will always be entitled both to its own "name"

and to the "name" of any eidos which is truly predicable of it.49 Though what it is predicated of is not, strictly speaking, the singularterm Threeness, but the instances of that term: "Three is odd" should be

construed as a Pauline predication (cf. n. 33 above), as in the otherexamples in the passage, where the point is so much clearer: thus in"Snow is cold" (cf. Phdo 103C-D), "cold" would not be predicated of theForm, Snow (which would be absurd), but of its "participants" (cf. RC,n. 83). 50 I italicize "say" because I do think he implies as much: he introduces the ?vo|xa-pfj|ia distinction by saying that he wants to investigatethe combination of names (rcepi xcov ovou?xcov . . . ?7UfJKe\|/G)ue0a . . .eue ?Xkf(koiq auvapu?xxei eue pf|, eue x? p?v ?G?X-ei, x? ?? pf|, 261D2-6),

which implies that the acceptable combination?the one that producessentences, instead of meaningless strings?will always involve both ovouaand pfjpa and still be a combination of names: this shows that ?vopa isbeing used both in a broader sense, which includes pfljia, and in a narrowersense which contrasts with pfjua.


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432 GREGORY LASTOSword, ?voua, can be used in each of these distinct ways. Still lessthen could we expect that he should be making this point in the

Phaedo, though he does realize here that "Odd" names Three ina different way from that in which "Three" names Three: for hespeaks of the latter as calling Three "by its own name" 51in contradistinction to the former; "Odd" is not Three's "own name,"

while "Three" is. But he does not focus attention on this. Whatdoes catch his eye is the fact that in calling Three "Odd" no lessthan "Three" we are not implying that Three and Odd areidentical. On this he is most emphatic. He makes the pointsix times over in the course of 21 lines of text. By the same tokenhe might have added that "Odd" and "Three" are not synonyms:the fact that both may "name" the same thing, does not imply thatthey are.

With this in mind let us return to the Protagoras. Havingestablished thatJustice isWisdom, Temperance, Courage, Piety, and Virtue,52

we may now avail ourselves of the descriptive use of "naming" toconvert this sentence intoJustice is named [descriptively] "Wisdom," "Temperance," "Courage,""Piety," and "Virtue."

Shifting to the other use of "naming," we may convertJustice is Justice,53

intoJustice is named [referringly] "Justice."

We can now see that Socrates is in a position to hold that all sixof these "names" apply to the same thing. To explain himself hewould have had to say that the first five of these "names" apply to

51 103E3; 104A2; 104A5-6.52 Pauline predications (like the one in "Three is odd": cf. n. 49above). 53 Pauline predication.


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 433Justice quite differently from the sixth: the first five as descriptivepredicates, the sixth as a proper name. This, of course, Socratesdoes not say. But the fact that aman does not explain what he isdoing in no way precludes his doing it. To use a rule of languagewithout the least awareness of the rule is an all too commonphenomenon of linguistic behavior.54 So we have no reason todeny that Socrates could be using the ambiguity in "name" in theabsence of any allusion to the ambiguity, exploiting it in speakingof both "Justice" and "Wisdom," "Temperance," etc. as "names"of Justice. Once we allow this, the question of Socrates' therebyidentifying Justice with Wisdom, Temperance, etc., or of taking"Justice" and "Wisdom," "Temperance," etc. to be synonyms,does not arise: we do not identify the thing we are talking about

with any of its attributes nor do we take the names of its convertible attributes to be synonyms.

Can we get textual confirmation for the proposed interpretation? At first sight, this looks like a hopeless undertaking,because Socrates

'debating tactics are so unsystematic that not oncein the course of the four arguments 55by which he vindicates hisdoctrine does he so much as even mention the formula of the

Unity Thesis. In none of those arguments does he allude to hisclaim that the names of all the virtues "are names of the samething" or "apply to one thing." We see neither hide nor hair ofthis phraseology in the demonstrands or the conclusions of thesearguments. However, we do get in the sequel several closelyrelated sentences. The most striking of these occurs at the conclusion of the dialogue, where Socrates says that he had tried toprove that

54 Cf. Chomsky [1965, 8] ". . . every speaker of a language hasmastered and internalized a generative grammar that expresses his knowledge of his language. This is not to say that he is aware of the rules of thegrammar or even that he can become aware of them. ..." (If "a generativegrammar" is obscure, "a set of rules of grammar" may be substituted forit.) I have italicized the most striking part of the statement. If it seemsincredible on first hearing, let one reflect on this: A normal four-year-oldknows how to use correctly the definite and indefinite article (ask him,"A dog and a edit are fighting. Who do you think is going to win?," andyou can count on his answering, "The dog" or ^The cat"); but it will beyears before he can be made aware of the rule of language which prescribesthe behavior he exhibits.55 Cf. n. 1 above.


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434 GREGORY LASTOSAU [the virtues] are Wisdom,

which he spells out as

Justice isWisdom,Temperance isWisdom,Courage isWisdom.56

These sentences are respectively no more than translations intothe material mode of

Justice is named [descriptively] "Wisdom,"Temperance is named [descriptively] "Wisdom,"Courage is named [descriptively] "Wisdom."

Similarly the grammatical converse of "Courage isWisdom,""Wisdom is Courage" (350C4-5)

is a material-mode equivalent of

Wisdom is named [descriptively] "Courage."

This being the case, it yields valuable, if indirect, confirmation ofthe present interpretation. On its terms we can explain perfectlythe otherwise puzzling fact that Socrates, after using the formulaeof the Unity Thesis so fulsomely and repetitiously in the course ofrestating the issue of the debate in 349B1-C5,57 should then becontent to formulate the proposition he thinks he has proved in theensuing argument as

Wisdom is Courage,

rather than, as he would have done had he stuck to the dictionof the Unity Thesis, as

Wisdom is named "Courage" and Courage is named "Wisdom,"

56 Cf. the citation from 361B1-2 in n.* 34 above. I am now substituting"Wisdom" for "Knowledge" which is clearly meant to express here preciselythe same thing as is expressed by "Wisdom" elsewhere in our passage.57 The formulae were quoted above, at the start of I, 1.


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 435or as

"Wisdom" and "Courage" are names of the same thing.

On the proposed interpretation the latter pair of sentences followsso directly from "Wisdom is Courage," that Socrates might wellfeel no need to spell out the consequence 58 in this tense, rapid,highly compressed argument.59 The interpretation also makesgood sense of the fact that he should say he has proved that"Wisdom is Courage," when what his argument has in fact provedis (at most) that Wisdom and Courage are biconditionally related,which Protagoras had denied (349D5-8). He is evidently taking"Wisdom is Courage" to be so transparent a consequence of theBiconditionality Thesis that he does not feel called upon to explainthe reason for the consequence.60Will my interpretation of the Unity Thesis square with theconclusion of the second argument,

Would not then Temperance and Wisdom be one? (333B).

It would not, all too obviously, if "Temperance and Wisdom areone" were meant to assert that Temperance and Wisdom areidentical virtues. But that this is not what is meant can beargued on two distinct grounds: first, on the highly generalground that Socrates could not have wished to prove these (or anyother) virtues identical, because, as has been already explained, he

58We cannot remind ourselves too often that our passage is not aleisurely investigation, like the Philebus, but a contest, whose tempo andtactics are determined by the exigencies of a live debate. Time and againSocrates skips over steps in his argument which he takes to be so obviouslycorrect that Protagoras would have no interest in challenging them.59We would get the same explanation for his failure to allude to theformula that the names of all the virtues are names of the same thing at theconclusion of the dialogue. If the proposed explanation of this formulais correct, Socrates would see no point in dragging things out by showingthat the sentences he uses at 361 Al-2 are fully translatable into the phraseology of that formula, as explained in my text above.60Having proved, as he thinks, a proposition about persons?that

brave men are wise and wise men brave?he translates it forthwith into aproposition about the corresponding virtues. He sees the two as so closelyconnected that he feels no need to argue that since brave persons are wise,Courage must be wise, and since wise persons are brave, Wisdom must bebrave. He would no doubt have done so in a more leisurely context.


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436 GREGORY LASTOScould not have accepted the same definiens for both; secondly,on the more specific ground, which I now wish to explain, thatthe logical structure of the argument by which this propositionis derived shows that what the argument proves is simply andsolely that Temperance and Wisdom are coextensive classes (as isrequired by the Biconditionality Thesis)?not that they areidentical virtues (which is required by nothing in our passagenor, for that matter, by a single statement in the whole of thePlatonic corpus). The italicized propositions follows from themeaning wblich the crucial term "opposite" carries in thepremises from which the conclusion is deduced:

1 Wisdom and Folly are opposites.612 Temperance and Folly are opposites.623 To one thing there is only one opposite.63What "opposite" means in this context is what is called "complement" in set theory: for set S, its complement, S, is such thatS and S are mutually exclusive and jointly exhaustive of theiruniverse of discourse.64 That this is precisely what "opposite"is being used to mean in this argument can be established byinspecting the derivation of 2?the only one of those three premises whose deduction gives us a context from which we can deter

mine the meaning of the term. 2 is presented as the consequence of

If. Those who act correctly act temperately,6561 "Is not Wisdom completely opposite to this thing [i.e., to Folly,

cuppoamm] ?" (332A4-5).62 "Hence Folly is the opposite of Temperance?" (332E4-5).63 "We have agreed that to one thing there is only one opposite, notmany?" (332C8-9).64Hence S is the contradictory of S?not just a contrary of it, C, such

that "ScC" is true, but "SqC" need not be true.65 I get t from 332A6-8,When men are acting correctly and usefully, do they then seem to

you to be acting temperately, or the opposite? (following Stallbaum'stext, now generally accepted and reproduced by Burnet in the OxfordText).

I contract "correctly and usefully" to "correctly," since "usefully" is onlyepexegetic: it is not an independent qualification for no use of it as aseparate premise is made in the sequel. I streamline the syntax to bringit into line with the next premise and get the uniformity of style one needsin a formal argument.


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438 GREGORY LASTOSWhat 7 and 8 tell us is that the class of the foolish and the classof the temperate exhaust the universe of discourse: those who doact foolishly do not act temperately (8) and those who do not actfoolishly do act temperately (7). This makes it crystal-clear thatall 2 can mean is that Temperance and Folly are each other'scomplements. And since "opposite" could only be used in 1with the same sense as in 2, these two premises assure us thatWisdom and Temperance are both complements of Folly.Premise 3 then spells out the notion implied in the definition of"complement" above, from which it follows that if S and S' havethe same complement, S, then S and S' are coextensive classes.

Hence Temperance and Wisdom are coextensive classes?a proposition which can be expressed in the formal mode by the conjunction

(Temperance is named [descriptively] "Wisdom") & (Wisdom isnamed [descriptively] "Temperance") ?

and the question of their constituting one and the same virtue doesnot arise. They may be said to be "one" in the perfectly innocuous sense of being one class, i.e. that the class of temperatepersons and the class of wise persons are one and the same class.70

2. Reinterpreting the Similarity ThesisInsisting that the virtues are very similar,71 Socrates does not

say how, in what respects, they are so very similar. What kind ofsimilarity could he have had in view which would have struck himas far-reaching enough to be analogizable to that of bits of gold,yet not so unqualified as to blot out the distinctive qualities of theseveral virtues, reducing them to the homogenized uniformity

incurring the tyrant's wrath, with disastrous consequences to his ownfortunes). Savan's argument (24-25) that Protagoras is really committedto Jf. and to 8 fails to reckon with this rather obvious line of objection.70 In this sense Temperance and Wisdom could even be said to be "thesame," i.e., the same class of persons, each of whom has both virtues?

which is a far cry from saying that Temperance and Wisdom are the samevirtues. 71 Cf. especially the language used in [1], [4], and [5] under 1.2above.


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THE UNITY OF THE VIRTUES INTHE PROTAGORAS 439which is the unhappy, and surely unwanted, suggestion of theanalogy? Guessing one's way to an answer would be a hopeless enterprise ifwe did not know how closely Socrates is associating the similarity of the virtues with the biconditionality of theclasses of their instances. He introduced the latter (329E2-4)immediately after he had thrown out the gold-bar analogy, evidently not to bring up a new doctrine, but to clarify further theone he has been expounding in the language of Unity andSimilarity. And we know that Protagoras, with Socrates' tacitconcurrence, thinks of the Biconditionality Thesis as implied bythe Similarity Thesis: we see this at 349D2-8, where we hearProtagoras say that the falsehood of the latter in the case ofCourage shows the falsehood of the former in the same case.72We may, therefore, make heuristic use of this logical relationbetween the two theses, asking ourselves: What sort of similaritywould imply biconditionality? To this a plausible answer suggests itself: the sort that follows directly from L above, which isnot only implied by the Biconditionality Thesis, as was explained,but also implies it, as should be obvious: if each virtue has thequalities of all the rest, then to have one virtue is to have all therest as well; thus to be just one will have to be also wise, temperate, etc., since Justice is wise, temperate, etc. In telling usthat each of the virtues is wise and temperate and brave and piousand just, L as good as tells us of a five-point similarity betweenthem: each is like the rest in all five of these respects.73 Thissimilarity could have struck Socrates as so pervasive as to prompthim to analogize it to the similarity of the parts of a gold bar: aseach of its parts has all of the qualities characteristic of gold

72 "And this is how you will know that I speak the truth [in sayingthat Courage 'is very different from all these' other virtues] : you will findmany men who are most unjust, most impious, most intemperate, andmost ignorant, but exceptionally brave." One who assumes that the falsehood of p implies the falsehood of q is implying (by modus tollens) that heassumes that q implies p.73 And, to recall the language of [3] under 1.2 above, P tells us also

that the corresponding similarity will hold between the dynameis of thevirtues. Thus the dynameis of Justice and Temperance?the active dispositions to behave justly and temperately?will both be dispositions to behave

wisely, bravely, and piously as well, since each of the two virtues is wiseand brave and pious.


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440 GREGORY LASTOS(each is yellow, ductile, malleable, and so forth), so each of thevirtues has all of the qualities characteristic of virtue (each iswise,

temperate, and so forth).74 And if this is the point of theanalogy, we purge it (and therewith the Similarity Thesis itself)of its most obnoxious feature: the suggestion that the virtues

would be as destitute of individuating qualitative characteristics asare bits of a gold bar. This suggestion now be totally irrelevantand unwanted. The virtues would be left in full possession oftheir distinctive dispositional physiognomies, though strikinglyand massively similar, since each would be virtuous in all of the

ways in which (on Socrates' theory) it is possible to be virtuous.So far, then, the proposed interpretation works well. How doesit fare when checked further against the text?In this case we have the good luck to find one of Socrates'

four arguments stating its demonstrand quite explicitly in termsof the Similarity Thesis: what Socrates has undertaken to provein argument (1) is

that Justice is such as [i.e. similar to] Piety and Piety and Piety suchas Justice (331B6).75

So here we can dispense with the indirect lines of reasoning thatwere required to show that the interpretation of the Unity Thesisagrees with the textual data. Here checking interpretation againstthe text will be easy. All we have to do is to see how Socratesgoes about proving the similarity of Justice and Piety. If theproposed interpretation is correct, his proof should consist inshowing that Justice and Piety are like each other in some or allof the respects which follow from the fact that the different

74 By contrast to the parts of a face, each of which has l?ictv (private,i.e. not common) ?uvapiv (an expression which Plato must find very apt:

he uses it in 330A4, and then again in 349C5, having repeated the adjectivein phrases like ??io? oua?a [349A4], ??icp 7rp?ypaxi [349C4]): the "power"of the eye is to see and only that?not to see and hear and smell, while the"power" of Wisdom is not only to act wisely but, given P, to act temperately and courageously and justly and piously.75At the conclusion of the argument Socrates says that this is whathe would himself say "most of all" (p?X,icrca) , i.e., that this would be theformulation he would find most satisfactory. The same thing was impliedat 330B3-7 and again at 330E3-331A4, where the refutand is expressed in amore general form by saying that no "part" of virtue is "such as" any other.


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 441virtues can be predicated of each other (proposition L). And so itdoes:

To prove his thesis Socrates invokes two premises:1 Justice is just (330C4-5) and Piety is pious (330D8-9).2 Justice is pious and Piety is just (331A7-B3).

How does he come by 1 and 2? Not by inferring them from theBiconditionality Thesis, from which I deduced L above: thatwould have been arguing in a circle, since Protagoras rejectsBiconditionality pari passu with Similarity. Socrates finds another way to the above premises?a very easy one, as he thinks.Premise 1 he gets by arguing in effect: If Justice were not just,it would be unjust;76 no one would want to say that Justice isunjust; so it has to be just.77 Ditto for Piety being pious. By thesame reasoning he justifies Premise 2: Justice must be pious, forotherwise it would have to be impious,78 and who would want tosay that? For the same reason Piety must be just. The fallacy inthis reasoning, the same one in both cases, need not detainus. It has long been recognized as a slide from "is not F"to "is the contradictory of F" 79?and we know from other pas

76 This is implied at 330C4-5, where the question is posed: Is Justice"just or unjust," thereby foisting on Protagoras the assumption that thedisjunction is exhaustive. J. Adam and A. M. Adam who catch the samefallacy in 331A8-B1, where it is more explicit, and also at 330D5-6 (see theircomments ad loc.) fail to notice that Socrates has slipped into it already hereat 330C4-5: without it his derivation of the first conjunct in Premise 1above would be arbitrary and out of line with his derivation of the secondconjunct in the same premise.77 I am blowing up the argument in this way, for the whole force of thededuction of "Justice is just" (which is not taken as self-evident, but isinferred: note the apa in 330C7) depends on some such course of reasoning, though only the first step (the initial posing of what looks like anexhaustive disjunction) and the third (opting for the first disjunct) areexplicit in the text; the elimination of the second disjunct is left implicit.78 331A8-9.79Moreau [1939, 43] contends that there is no substantial error:... si cette substitution du terme contraire [a?iKOV, ?voaiov] auterme n?gatif [utj ??Kaiov, prj ocriov] ne se justifie pas vi formae, ellen'en est pas moins justifi?e en ce qui concerne la mati?re de la discus

sion ; tout objet susceptible d'estimation morale et qui est non justeest n?cessairement injuste. . . .This is surely wrong. The general opinion both in antiquity and at presentwould deny that every moral act must be either just or unjust, pious or


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442 GREGORY LASTOSsages 80that Plato could easily have imputed this to Socrates, or

might even have fallen into it himself in this early phase of his careerwhen he might still have been wobbly on points of logic which hefirms up later on.81 In any case, the premises are the only thingthat concern us now, for they show?exactly what sort of similaritySocrates had in view, and give us textual authority for saying thatit is the sort I have hypothesized. By making the four propositionsthe premises of his demonstration Socrates tells us that Justiceand Piety are proved to be similar virtues when shown to besimilar in two crucial respects: each is both just and pious.82If he were interested in pursuing the matter further, he could

impious, brave or cowardly, temperate or intemperate. Consider an act ofspontaneous generosity to a friend, "an act susceptible of moral assessment." We would hardly call it "just" (the benefit is not conferred inconsideration of his right to it?he has no such right). Must we then call it"unjust"? It is not classifiable as a brave act (no confrontation of danger).Must we then say that it is cowardly? If the agent is an atheist it could notbe pious. Would it then be impious? To be sure, on Socrates' own moraltheory what Moreau says would be true. But it would be a flagrant petitioprincipii to use that theory (which Socrates is now engaged in defending)as a premise in its own defense.80 The same fallacy is palmed off by Euthydemus on his interlocutorin Euthd. 276B2 ("and if they are not wise, must they not be ignorant?")

without protest from anyone. But this is not good evidence of Socrates'unawareness of the fallacy, for he is not taking a hand in this exchange.Far more relevant are Prt. 360B2-3, "and if they [their fear and their confidence] are not noble (Ka?xx) must they not be base (a?axpa) (nothinghad been done to establish that "noble" and "base" constitute the exhaustivepossibilities for the fear and confidence which persons may feel); andSmp. 201E-202A: Diotima asks Socrates if he believes that "whatever is notbeautiful (icaX?v) must be ugly (a?axp?v) ," and he replies, "Certainly!"Thereupon Diotima proceeds to instruct Socrates that there are "inter

mediates" between KaX?v and a?axp?v, as e.g., "true opinion" is intermediate between "knowledge" and "ignorance." (Other Platonic passagesadduced as parallels in the Adams' note on 331A are probably not examplesof the fallacy; at any rate, they are not clear examples.)81 Such as the insight that contraries need not be contradictories,

which is communicated with such didactic emphasis by Diotima in thepreceding note, and is reasserted in Sph. 257B.82 Crucial in that, if the predications in "Justice and Piety are just andpious" are Pauline (as will be argued in Section III below), the biconditionality of Justice and Piety would follow from their similarity in thesetwo respects: If Justice is pious, then whoever is just would be pious; andif Piety is just, then whoever is pious would be just. There is no allusionto this point in the text. But biconditionality, closely connected withsimilarity by Socrates (325D-E), had been denied vehemently by Protagoras


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 443have proceeded to establish by iteration of the reasoning that eachis also wise, temperate, and courageous.83 In that case his resultwould have coincided with my hypothesis of what the similarity ofthe virtues means for him, i.e. that each has the five-pointresemblance with each which follows immediately from the factthat each is just and pious and wise and temperate andcourageous.84

(329E5-6). It would be reasonable to think that Socrates is conductingthe vindication of similarity along lines which would have a bearing onbiconditionality as well, offering him the materials with which he couldconstruct a corollary* proof of biconditionality under appropriate circumstances. 83 It is reasonable to assume that Socrates would have done so in a lesspolemical, more systematic, context.84Though there are many differences in detail between the aboveanalysis of the argument and Gallop's [1961], they are not nearly as great asthey may seem to be at first sight, and none are worth arguing over excepttwo:

(1) He sees the big fallacy of the Socratic argument in the assumption that Premises 1 and 2 jointly imply the demonstrandD Justice is such as (o?ov) Piety and Piety is such as Justice (I retain

my reference-marks, translations, etc. rather than his, to avoid burdeningthe discussion with complications which I consider inessential). Gallopthinks that Protagoras would have been entitled to concede Premises 1 and 2yet deny D:even if he [Protagoras] agrees that Justice and Holiness resembleeach other in certain respects (viz. in both being just and holy) he

need not agree that they are homogeneous (90).I cannot follow him because I do not know what criteria of "homogeneity"

he has in view. Socrates hasn't stated his, and we can agree in faultinghim for that failure. However, if we are also going to charge him with anon sequitur, we will have to assume the burden of explaining the sensein which "homogeneous" is being used in statements like the one I havequoted from Gallop. For there is a sense of "homogeneous" in which theinference from Premises 1 and 2 to D wrould follow with analytic certainty:if Justice and Piety are both just and pious, then they are certainly

homogeneous in those two respects. (If it be objected that this is astrained sense of "homogeneous," the answer would be that, after all, thisis not Socrates' term: he operates with the still vaguer language of"similarity," in which no one could find fault with the claim that if both Justice and Piety are just and pious then they are similar in those two respects.)

The reason why Gallop finds that inference so objectionable can only bethat he is invoking some strong sense of "homogeneity"?how strong hedoes not say. If Socrates is to be understood to mean complete homogeneity

?i.e., that every quality of Justice is shared by Piety and conversely?then,of course, the inference is grotesquely fallacious. But in that case whybother with the inference? If that is what D is supposed to mean, itbecomes virtually self-refuting.


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444 GREGORY LASTOSI have now done what I undertook to do in this Section.85

From the Biconditionality Thesis I have derived a proposition, L,which has shown the way to an interpretation of both the Unityand the Similarity Theses that rids each of their unacceptablefeatures. All three theses turn out to be complementary expressions of the same basic claim which may be put most clearly bysaying that having any virtue entails having every virtue, lessclearly but still understandably, by saying that what names eachnames all, and that they are all cogeners, all alike.

IllImay now tackle the task, deferred from the preceding sec

tion, of justifying the assumption that all substitution-instancesof the "B is A" formula in L occurring in our passage are meantto be read in a special way: their predicate-term is asserted not oftheir abstract subject, but of the concrete instances of thatabstract. As I explained above, the whole of the argument of thepreceding section was conditionalized on that assumption. It isnow time to ask if the assumption is warranted. In a sentencelike "Justice is pious" the predicate certainly seems to be assertedof Justice and of nothing else. Why should we not take thesentence at face- value ? Is there good reason to think thatSocrates is saying anything other than thatP There is, but it isnot as obvious as it has sometimes been thought to be:

We know, to begin with, that Socrates thinks of "Justice" asthe name of a universal and that he does not think of universals aspersons, nor yet as ontological dependencies of persons, such asthe actions, decisions, dispositions, practices or policies of this or

(2) Another point (a more minor one) on which I disagree withGallop's analysis is his claim (92) that the fallacy by which 1 and 2 arederived (a fallacy he acknowledges, insisting on it in the face ofA. E. Taylor's perverse denial that it exists) is unimportant because "Socratescould have amended his argument to avoid it": 1 and 2, thinks Gallop,could have been derived from "inoffensive" premises, such as thato?ov e?vai KaA-?v could be asserted of both Justice and of Piety. Surely this

will not do. The suggested substitute premise is inoffensive enough, butonly by fallacious reasoning could 1 or 2 be inferred from it. Thus from"Justice is KaX?v " and "Whatever is pious is Ka>,?v

" it would not follow,except by illicit conversion of the latter premise, that "Justice is pious."85 Cf. the terminal paragraph of Section I above.


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 445that person.86 This being the case, to say of any universal that itis just or unjust, pious or impious, brave or cowardly would besheer nonsense: these are moral predicates, and for that reasonthey are as impredicable of a logical entity, like a universal, as of amathematical entity, like a number or a geometrical figure: to saythat Justice is pious would be as absurd as to say that the numbereight or a hexagon is pious. Could this, then, be what Socratesis doing here? On what grounds could we convict him of sogross an error? We have his sentence, "Justice is pious." Butthis is not unambiguous evidence, for it is not an unambiguoussentence. It is the sort of sentence which could be used, absurdly,to predicate "is pious" of the universal, Justice. But it could alsobe used, impeccably, to predicate "is pious" of the instances ofthat universal. To be sure, to use it in the latter way one wouldhave to disregard its surface grammar which is the same as thatof "Abraham is pious." But is there any difficulty about that?That is what we do as amatter of course in reading the examplesI tossed out in Section II above?"Justice is impartial," "Ignoranceis bliss": our linguistic intuition assigns unhesitatingly "is impartial" to those who are just, not to the abstraction, Justice, and"is bliss" to those who are ignorant, not to the abstraction,Ignorance. Or consider the following sentence from a contemporary writer, Iris Murdoch, whom no one could charge withwriting stilted or artificial English:

The best kind of courage (that which would make a man act unselfishly in a concentration camp) is steadfast, calm, temperate,intelligent, loving . . ,87

What is the natural reading of that sentence?the only way thatwould have even occurred to any of us encountering it in its owncontext, with our mind on the author's thought, instead ofinspecting it out of context, as a specimen of philosophical

grammar? Clearly, the reading that ascribes the adjectives,"steadfast, calm," etc., not to the abstraction, "best kind of

86Note that if we were to think of Justice as the disposition of someperson, we would not be thinking of it as a universal, but as a temporalinstantiation of the universal in the life of that person.87 1970, 57.


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446 GREGORY LASTOScourage," but to those persons, if any, who have that kind ofcourage; that is clearly what we would understand Iris Murdochto be saying: that those who have the best kind of courage, theyare "steadfast, calm, temperate, intelligent, loving" in theircourage. Or, finally, take St. Paul's, "Charity suffereth long andis kind." We may be certain that everyone who has ever read orheard that sentence before philosophical grammarians got hold ofit has taken it, as a matter of course, to be predicating longsuffering and kindness of those who have the virtue of charity.It would have taken satanic perversity to construe the apostle tobe imputing those moral properties to an abstract entity.Now it would not be difficult to find sentences of the sameform whose sense does conform to their surface grammar:

Justice is a universalJustice is definableJustice is a moral property.

In all of them the obviously correct construction is the one thatassigns the predicate to the term in the subject position in exactlythe same way as does "Abraham is pious": "is a universal" is notbeing predicated of the instances of Justice (we would not wantto say that if Socrates is just, he is a universal), but of Justiceitself. Let us call this reading of the sentence-form "B is A"(where "B" names a property) "Ordinary Predication." Thealternative reading, required by sentences like

Justice is impartialCourage is steadfastCharity is kind,

we may call, after the Pauline paradigm, "Pauline predication." 88So when we look at the Socratic sentence, "Justice is pious,"what we have to decide is whether it is Ordinary, or Pauline,

88 1 owe the term and much else (cf. n. 96 below) to a paper on selfpredication in Plato, presented to my seminar (fall of 1965) by ProfessorSandra Peterson Wallace, who was then a graduate student at Princeton.

However, my use of "Pauline predication" differs substantially from hers.It does so for reasons whose explanation had best await the publication of

her paper (which I have been urging on her for years).


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THE UNITY OF THE VIRTUES INTHE PROTAGORAS 447predication.89 When the question is put that way I doubt if anyone would hesitate in opting for the latter. But how would wejustify that choice? Would it be by arguing that to read it theother way, as an Ordinary predication, would produce absurdity?That would be too easy. That Socrates would not want to affirman absurdity we may all agree. But can we be sure that he wouldsee that reading of it as an absurdity? I would find it absurdto predicate moral properties of numbers or geometrical figures.But would a Pythagorean? Probably not.90 Why then shouldSocrates' standards of what makes sense, and what does not, becloser to mine than to a Pythagorean's? That sort of questioncan only be decided by empirical evidence?that is to say, if it isbeing raised and answered by historians of philosophy. And bythat I do not mean people who write books on the history ofphilosophy. To do this in the way Bertrand Russell wrote muchof his?half of it out of his own head, the other half out ofother histories of philosophy?is not to qualify as a historianof philosophy. Russell, who was a clear-headed and honest man,would undoubtedly have conceded that he did not qualify, exceptbriefly, in his youth, when he wrote The Philosophy of Leibniz.The crux of the matter is this: If history is an empirical discipline, so is the history of philosophy. And no one can practice theempirical method unless he is willing to submit even the mostdeeply entrenched presumptions?his own or those of others?tothe arbitrament of factual data.

Do we have such data here? Certainly. We have the context. "Justice is pious" does not come to us as an isolated text,like a Heraclitean fragment. I comes in a longish, argumentative,passage, where it is joined by inferential links to dozens of othersentences. So if our question is if "Justice is pious" is being used

89The analysis of argument (1) in II.2 above had been conditionalizedon the hypothesis that this sentence (and the other three in Premises /and 2 of this argument) are Pauline predications (cf. the opening sentence in n. 82 above). I have now reached the point where I can argue forthat hypothesis.90 See e.g. the passages cited by Guthrie [1962, 302-303], I say"probably" because the evidence is second-hand and it is hard to knowexactly what they meant if, as Alexander reports (Met. 38, 10 ff.), they madereciprocity "the defining property of justice and found this to exist innumbers."


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448 GREGORY LASTOSabsurdly, as an Ordinary predication, or non-absurdly, as a

Pauline one, we may look for the answer not to our intuition?which would only inform us how we would have used it, whilewhat we want to know is how?Socrates used it?but to its own

inferential context. How does that sentence behave there? Whatwork is it made to do?

The foregoing discussion presents us with a clear pictureof what Socrates does with "Justice is pious" in our passage: heteams it up with the three other sentences that make up Premises 1and 2 of Argument (1)?all of them substitution-instances ofour "B is A" sentence-form?to establish the Similarity of Justiceand Piety, this, I argued, being the sort of similarity, whichfollows directly from the fact that, given those premises, it followsthat Justice is just and pious and Piety is just and pious, andhence that the two virtues resemble each other in these tworespects. Now I noted at one point 91 that the Similarity Thesisis supposed to imply Biconditionality. So here we have a condition which must be satisfied by our reading of the statements thatJustice is just and pious and that Piety is just and pious. Call it"Conditions C." Let us try out both readings on those state

ments, and see what happens. Read as Pauline predications theymeet Condition C to perfection. For so read, "Justice is just andpious" implies directly that anyone who instantiates Justice willbe just and pious; and exactly the same is true for the Paulinereading of "Piety is pious and just." Suppose, alternatively, thatwe read those statements as Ordinary predications. Then all wecan get out of "Justice is just and pious" is that the universal,Justice, has those two properties. And from the fact that a universal has certain properties nothing follows to the effect that itsinstances have those properties. Thus from the fact that theJustice, is an abstract entity, is invariant, is incorporeal, it doesnot follow that each of those human beings who instantiate it isan abstract entity, is invariant, is incorporeal. So if "Justiceis pious" and the other three substitution-instances of our "B is A"sentence form which make the premises of Argument (1) areread as Pauline predications,

Condition C is satisfied: thelogicalconnection of the Similarity Thesis with the Biconditionality

P. 439 above.


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THE UNITY OF THEVIRTUES INTHE PROTAGORAS 449Thesis, on which Socrates is counting, works like a dream, Ifthey are read as Ordinary predications it does not work at all.This is good empirical evidence for the claim that the Paulinereading of "Justice is pious" is the right reading?the one inwhich Socrates meant his sentence to be understood.

Additional evidence of the same sort for the Pauline readingof substitution-instances of the "B is A" sentence-form can begot out of our passage. Thus consider the conclusion of Argu

ment (4): "Wisdom is Courage." I trust it is obvious by thistime that the "is" here cannot mean identity. So it has to bepredicative. And if the predication is convertible, as it is probablymeant to be,92 what Socrates thinks he has proved is that Wisdomand Courage are inter-predicable?that Wisdom is courageous andCourage iswise. What kind of predication would that be? Thatit has to be Pauline follows from the fact that it ismeant to implythe biconditionality of Wisdom and Courage, that is to say, thatCondition C has to be satisfied here as before. There can be nodoubt about the fact that Socrates does expect that condition to besatisfied: He takes it for granted that his conclusion "Wisdom isCourage" has proved the contradictory of Protagoras' claim 93thatCourage and Wisdom are not biconditionally related: So hereagain we can argue as before, appealing exactly to the samereasoning, which need not be repeated: If the sentences "Courageis predicated ofWisdom" and "Wisdom is predicated of Courage"are Ordinary Predications, they do nothing to sustain Socrates'confidence that his conclusion implies the biconditionality ofCourage and Wisdom. If, on the other hand, they are Pauline,they sustain that conclusion fully, and so immediately that we canunderstand why Socrates does not trouble to spell out the fact thatthey do.94

92 N. 34 above.93 See Protagoras' statement quoted in n. 72 above. He denies biconditionality between Courage and any of the other four virtues. Socratesresponds by undertaking to establish the biconditionality of Courage andWisdom. 94

Supplementary (and logically independent)reason for

reading"Courage is predicated of Wisdom and Wisdom of Courage" as PaulinePredications may be derived by considering the premises from which Socrates purports to have proved that "Wisdom is Courage." The immediateantecedent of this conclusion is


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450 GREGORY VLASTOSI could proceed to show that all of the other substitution

instances of the "B is A" sentence-form in our passage are meantto be read as Pauline Predications.95 But this would not be to mypurpose. There is one pair of sentences that interests meparticularly, as I stated at the start of this essay: "Justice isjust," and "Piety is pious." These came into my argument inthe paragraph before the last. But I did not single them outthere for special attention. I wanted to bring them up in thesame way in which they are brought up in the text: as two offour sentences, all four of which must mesh in to implement theinference that Justice and Piety are similar because Justiceis just and pious and Piety is just and pious. By observingthem in their own linguistic environment we have the best chanceto see two complementary things about them, neither of which hasever been noticed in print: We can see, first, how similar in formare the sentences in Premise 1, whose syntax has been thoughtso scandalous with those in Premise 2, whose syntax, so farfrom scandalizing anybody, does not even seem to have caughtthe eye of anyone who has ever published on this topic.96 If we

the wisest are also most confident, and being most confident are bravest(350C2-4Vwhich should probably be understood to mean that the wisest are most confident and bravest (cf. Vlastos, 1956, xxxii-xxxiii and notes), implying thatthose who are wise are brave, which is precisely what we would get outof "Courage is predicated of Wisdom" if we read it as a Pauline predication.If, however, we read it as an Ordinary predication, to mean "Justice scourageous," we would produce a non sequitur: from the premise "All whohave property

F have propertyG" it does not follow that "the property Fhas itself the property G"; thus if "All who are just are persons" it would not

follow that "Justice is a person."95 Thus "Virtue is noble" and "Courage is noble" have to be Paulinepredications; to mesh in with the other premises in the argument (all of

which are in extensional form) they have to be translated into "All thevirtuous are noble" and "All the brave are noble." I did the latter withoutexplanation (without so much as noticing that I was making a syntacticaltransformation of importance) in 1956, xxxii. Again, if one reflects onwhat has been said on the conclusion of Argument (2) in Section II,1 above?that "Wisdom and Temperance are one" could only mean that

Wisdom and Temperance are coextensive classes?one will see that if it wererestated in the canonical form of the Unity Theory, sc. that "Wisdom is'named' [predicatively] 'Temperance' " and "Temperance is 'named'[predicatively] 'Wisdom'," the predications could only be Pauline.96 It was first called to my attention in Sandra Wallace's paper (n. 88

above).


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THE UNITY OF THE VIRTUES IN THE PROTAGORAS 451were going by surface grammar we would have to say that in allfour sentences a property is being predicated of a property, andwe would then be bound to say that the absurdity perpetrated by"Justice is just" is perpetrated no less by "Justice is pious." Noone has ever turned a hair over "Justice is pious"?obviouslybecause everyone has been reading it as a Pauline predication.

Why then read "Justice is just" differently? Secondly, when wesee the four sentences working together, we observe that theircooperation demands that their true syntax should be the same?that all four have to be Pauline predications, if they are toproduce a conclusion which satisfies conditions C, that is to say,if they are to empower us to infer from the premise-set the sort ofsimilarity between Justice and Piety which implies their biconditionality. We have, therefore, the best of evidence?empiricalevidence?that when Socrates asserts with such vehemence in ourtext that Justice is just and that Piety is pious he did not meanto assert the absurdity that Justice is a just eidos and Piety apious one, but the analytic truth that the eidos, Justice, is such thatall of its instances are just, and the eidos, Piety, is such that allof its instances are pious. It follows that neither sentence impliesthat Justice or Piety are self-predicative: 97 there is no reason tothink that they were meant to have that implication, and there is

97 The term "self-pr?dication" seems to have entered Platonic exegesisvia my 1954 paper. There "O is self-predicable" is used to mean "O s F,"where "O" is the name of a Form, "F" the character corresponding to thatForm (as e.g. "just" to "Justice"), and "e" is the Peano symbol for classmembership). This use of "self-predication had been inherited byA. E. Taylor (who had illustrated "predicated of itself" inter alia by"Whiteness is white" and explained it as turning on a confusion between apredication and the assertion of an identity" [1937, 355]) from BertrandRussell (where the meaning of "predicable" in the expression "predicateswhich are predicable of themselves" was explicitly elucidated in terms ofthe Peano e [1903, 78 ff.]. Every scholar who used "self-predication" inprint in discussions of the Third Man Argument and allied topics in Platoadher

vlastos -unity of virtues in protagora

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