Philosophical Review
A Reasonable Self-Predication Premise for the Third Man Argument
Author(s): Sandra Peterson
Reviewed work(s):
Source: The Philosophical Review, Vol. 82, No. 4 (Oct., 1973), pp. 451-470
Published by: Duke University Press on behalf of Philosophical Review
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A REASONABLE SELF-PREDICATION
PREMISE FOR THE THIRD MAN ARGUMENT
I
PROPOSE a way of understandingthe self-predication
premise of the third man argumentwhich Plato used
The way I proposefulfills
someofthedesiderata
againsthimself.
of Plato: it is not unreasonableby
for a good interpretation
consistent
withtheotherpremisesofthethird
itself;it is formally
man,singlyand jointly;'it couldhave seemedthattheargument
containingthepremisewas a seriousthreatto thetheoryofforms,
I 35A-B). I do not,however,
as Plato evidentlyfeared(Parmenides
intendto say thattherefore
myproposalgiveswhatPlato meant.
SectionVI explainswhat I do intend.
I.
THE THIRD
MAN ARGUMENT
The thirdman argumentof Parmenides
I32A-I32B strongly
appears to have as premisespart of Plato's theoryof forms;
the argument'sconclusionis thatthereare infinitely
manyforms
associated with each predicate. The conclusion contradicts
anotherthesisof the theoryofforms,the thesisthatthereis just
one formassociatedwitheach predicate.Obviously,theargument
presentsa difficulty
forthetheory.
The followingformulationis an instanceof the argument
for the predicate "large." There is, accordingto Plato, an
analogousargumentforeverypredicate.2
' The desideratumwhichthe featuredescribedin thisclause fulfillsis that
the premisesnot be obviouslyformallyinconsistent.
I omit here the demonstration
of the formalconsistencyof the premises.
There is room forargumentthat some of the premisesentail the denial of
others,or entail the denial of othersin conjunctionwith some otherbeliefs
Plato had or could or should have had. I am glad thereis room forsuch
an argumentPlato could not
argument.I do not wish to be constructing
have evaded. It seems clear to me that at least by the time of the Sophist
Plato thoughtthat the thirdman did not vitiatethe theoryof forms.
2 My formulation
of the argumentowes a great deal to the formulations
of C. Strang("Plato and theThird Man," Proceedings
oftheAristotelian
Society,
45I
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SANDRA PETERSON
i.
2.
There is a plurality of things that are large (fact).3
If a plurality of things are all of them large, there is
(at least) one formof large things in virtue of which all
of them are large (one-and-the-same form).4
XXXVII [i963], 147-i64) and P. T. Geach ("The Third Man
Supplement,
[New York, i965],
Again" in R. E. Allen [ed.], Studiesin Plato's Metaphysics
uses somethinglike my 2a, but does not
pp. 265-277). Strang'sformulation
enter it as a premise.My formulationis simplerthan Geach's. (Plato's is
simplerthan mine.)
3 Numeralswithno attachedletterlabel premiseswhich are foundin the
Numeralswith attachedlettersgo to premiseswhich
textof the Parmenides.
I have suppliedto fillin gaps in the argument.
PremiseI occursas part ofan adverbialclause: "Wheneverit seemsto you
there is a certain pluralityof large things" (I32A2), which amounts to
"sometimesit seems to you thereis a certainpluralityof large things,and
then...."
As G. Vlastos points out in his "Plato's Third Man Argument(Parm.
I32Ai-B2):
Text and Logic" in Philosophical Quarterly,i9(I969),
289-30I,
hereafter"TMA II," n. IO, P. 298, "it seemsto you" (his "you thinkthat")
is not intendedto cast doubt on what follows.It is safe to take what follows
"it seemsto you" as PremiseI of the argumentPlato intended.
4 (q) "Wheneverit seemsto you thereis a certainpluralityof large things,
as you view them,it perhapsseems thereis a certainsingleform,the same
over them all" (132A2-3).
The qualification"in virtueof which (by which) all of them are large"
does not appear until later in the text (132A7-8 and Bi). I have supposed
Plato intendsit in Premise2 also.
It is made clear that the certainsingleformspokenof in (q) is a formof
large thingsby the nextsentence:(r) "For whichreasonyou thinkthatthere
is a singlelargeness"("the large," literally)(132A3-4).
whether"a certainsingleform"means"at leastone form
It is controversial
(of large things)" as my Premise2 takes it to mean, or means "a unique
form(of large things)"-i.e., "the one and only one form(of large things)"
as Vlastos ("TMA II") takesit.
The crux of Vlastos' argumentfor "unique" is this: "single" or "one"
withinthethirdman argument
clearlymeans"unique" at variousoccurrences
which occurrencesmake clear that it means "unique" in
of the Parmenides,
(r); (q) is givenas a reasonfor(r); if "single" did not mean "unique" in (q)
"a transparent
from(q) to (r) wouldobviouslybe unsatisfactory,
thetransition
fallacy" (Vlastos,p. 293). Therefore,"single" must mean "unique" in (q).
I agreewithVlastos'viewsas I have summarizedthemup to the"therefore."
fallacy"seemsdeliberateto me. One lessonintendedby the
The "transparent
thirdman argumentis thatthe observationthatvariousthingshave one and
the same propertyis suspectas a reason forpositingthe unique form.One
mightcapturethe tone of Parmenides'argumentthus: "You give as a reason
fortherebeing a unique formof large things(a unique largeness)that there
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THIRD MAN ARGUMENT
2a. Anypluralityof largethingsand a formoflarge things
in virtueof which theyare all large is itselfa plurality
(conditionforpluralities).
3. Any formof large thingsis large (self-predication).5
.6
3a. Nothingis largein virtueofitself(non-self-explanation)
are severallarge thingssharingin one and the same characteror form.Well,
using that reason, you mightas well argue that thereare infinitely
many
formsof the large. Here is how."
H. Cherniss,Aristotle's
Criticism
ofPlato and theAcademy
(New York, 1962),
p. 294, describesthe "one over many" principlein a way thatbringsout the
transitionfrom"one and the same" to "unique" (without,however,commentingon its doubtfulness)."The principleby which an unique idea is
positedto explain the identicalattributeobservedin a multitudeof objects."
To set out the transitionthatI thinkis beingmade: (a) a numberof things
are large; (b) theysharein one and thesame formoflargethings;(c) theform
theysharein is a unique formof large things.To complicatemattersslightly,
one mighthave between(a) and (b) a step (as): theyshareone and thesame
character-being large. See Vlastos' note i6 ("TMA II," p. 298). See
I32D9-Ei fora generalstatementof the move from(a) eitherto (ai) or to
(b): "Is therenot a greatnecessitythata thingwhichis likesharein one and
the same thingwith what is like [it]?" (Maybe "share one and the same
eidos"[form?character?]if you read eidousin Ei.)
Vlastos givesa usefulreviewof manypassagesin whichPlato clearlyuses
"one" to mean "exactly one" or "the one and only" in the phrase rone
form(of F things).-'Citing these passages,however,does not establishthe
sense of "one" in this passage. It is importantto notice, I think,that in
I32A2-3 "one" (or "single") occurs in connectionwith "the same"; the
phraseis "a certainsingleform,thesame. .. ." I takeit thatthewholephrase
amountshere to "one and the same" and that"one" hereamountsto "one"
in "one and the same." (In thismuch I followStrang,op. cit.,p. i50.) It is
clear that roneand thesame Fl does not mean,amountto, or usuallysuggest
rtheone and onlyone F.l E.g., at Parmenides
I3iB3-4 we find"one and the
same day," which does not mean "the one and only one day."
I emphasizethatI do not claim that"one" in any ofitsoccurrencesin the
Parmenides
passage I32A-B is ambiguous.
6 "[T]he large itselfand the otherlarge things"(I32A6) certainlysuggests
that the formof large thingsgeneratedat the firststage of the argumentis
large. Since the argumentis supposedto go on analogouslyto the firststep
infinitely
manytimes,it seemsappropriateto summarizetheimaginedinfinity
of analogous cases by Premise3, whichis general,and makesa claim forany
formof large things.
By "self-predication"
I mean to indicateat least claims of the formrthe
F is F" (e.g., "The camel is a camel") as well as rF-nessis F' and others.
6 This fills the gap in the Parmenideq
argumentwhich Vlastos' "nonidentitypremiss"("TMA II," p. 291 ) fills."If anythinghas a givencharacter
by participatingin a form,it cannot be identicalwith that form."Vlastos'
453
3
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SANDRA PETERSON
many formsof large things(con4. There are infinitely
clusion).'
PremisesI, 2, 3, and the conclusion4, are stated in the
The premisesstated do not even begin the infinite
Parmenides.
regress.It is assumedthatPlato intendedthe readerto take for
grantedpremisesneeded to fillin any obviousgaps in the argument.
2a and 3a are verysimpleclaimswhoseadditionto the given
premises,I, 2, and 3, yields4, Plato's conclusion.8
note 37 says that it appears to have been "universallyaccepted"-that is,
everyoneagreesthatsomethinglikeit,roughlyspeaking,musthave been used
in the argument.
Agreementthatsomethinglikethepremisewas used shouldbe distinguished
fromagreementthat what was used is a compulsorytenetin the theoryof
forms.It is, at the least,not clear (but see Strang,op. cit., p. 158) thatnonis an appropriatepartofthetheory
(likeVlastos' non-identity)
self-explanation
of forms.(I will not here speculateon whetherthiswas the flawPlato came
to see in the argument.)
The reasons to suppose that non-self-explanation
is, nevertheless,being
used in the argumentare two. First,thereis a gap which it fillsnaturally.
Second, Plato clearlyheld thatnothingwhichis not a formis large in virtue
of itself;the latter mighthave been conflated,especiallywhen not stated
onlyin thequalification
fromwhichitdiffers
clearly,withnon-self-explanation,
"which is not a form."
This qualificationis important;one mighteven supposethatit could never
have been overlookedby Plato, and that accordinglyhe would never have
feltthreatenedby an argumentthatused unstatednon-self-explanation.
7 "And each of yourformswill no longerbe one, but theywill be infinite
in number" (I32Bi-2).
8 Remarkson pluralities.All together
the premisesimplythat thereis no
pluralityconsistingof exactlythe thingswhich are large.
The contentof 2a may be broughtout ifwe notice (as was pointedout to
me by John Wallace) how replacing 2a by the simpler 3b weakens the
premises:
a plurality.
3b. A singleitemby itselfconstitutes
If we are to use Premise2, as Plato does, to generateotherformsof large
by Premises
thingsbesidestheform(call it "largeness,")providedimmediately
I and 2, since Premise2 begins conditionally"if a pluralityof things...,"
it is naturalto expectin additionto i, 2, 3, and 3a, a premisewhichprovides,
as 2a did, some new pluralities(oflarge things).
3b so provides,but it carriesus only as far as a second formof large
things:by 3, largeness,is a large thing;by 3b, thereis a pluralityconsisting
just of largeness,so by 2, thereis a formof large things(call it "largeness2")
in virtueof whichlargeness,is large; by 3a largeness2F largeness1.
By similarreasoningfrom3, 31, and 2 we can establishthatthereis a form
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THIRD MAN ARGUMENT
The Parmenides
(I35A-B) gives evidencethat Plato held the
thirdman a seriousdifficulty
forthe theoryofforms;thereis no
announcedanswerto the argumentin Plato's writings;Plato
later-for example,in the Sophist-develops
thetheoryas though
he thoughtit had no cripplingdefects.There is the historical
question:what was Plato's answerto the argument?
II.
THE SELF-PREDICATION
PREMISE
The historicalquestionwould be answeredby thesupposition
that Plato took the thirdman argumentto reduceto absurdity
part,but not thewhole,ofthe theoryofforms.A versionof this
suppositionwhichhas someadvocatesis thatPlato was reducing
to absurdityself-predication.
The self-predication
premisefor "large" is: a formof large
thingsis large. Largeness,which Plato would say large things
shared,is a formof large things.So the self-predication
premise
contributes
to the consequencethatlargenessis large.9
(call it "largeness3")in virtueofwhichlargeness2
is large; by 3a largeness3
,#
largeness2.But we cannot prove that largeness3# largeness. That is, the
altered premisesare consistentwith therebeing exactlytwo formsof large
things,each large in virtueof the other.
See note 22 forevidencethatPlato did not hold thata singleformcounted
as a plurality.
9 A typicalresponseto "Largenessis large" is that it is neithertrue nor
falseunlessthereis an answerto the question"Largenessis a large what?"
This questiondoes not arise fora numberof self-predications-for
example,
"Man is a man," "White is white."
There is some chance thatPlato held thatfortheformlargenesstheanswer
was: "Not a large somethingor other,butjust large." For example,at Phaedo
74ag-I2, whichinvolves"equal," like "large" in need of completion,though
of a different
kind,Plato perhapsmeans to say of the formthe equal thatit
is not an equal pair ofsticks(equal in length)or an equal pair ofstones(equal
in weight) but is just equal. (The Phaedoremark,understoodas a hintof a
general view about predicatesthat are incompletein one way or another,
apparentlyconflictswith the remarkin the Sophistat 255 that the different
[which includesat least the formof the different]
is always spokenof with
referenceto a different
thing.)
I have notconsideredanyspecialdifficulties
whichmayariseforformulating
the argumentforattributiveadjectivesand otherssimilarlyin need of some
supplement,if the above paragraphdoes nqotrepresentPlato's view. If there
are insuperabledifficulties,
then my proposal gives only a way of understandingtheself-predications
whichdo notinvolvethetroublesome
expressions.
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SANDRA PETERSON
In the analogous argument for other predicates, the analogue
to the self-predicationpremise for "large" will help lead to selfpredications such as "Justice is just," "Holiness is holy," "Man
is a man," "The camel is a camel."
These sentences strike many people as patently false. Faced
with "Justice is just," they are disposed to say that it is people
and laws and institutionsthat are or can be just; to say that
justice is just is to make a category mistake.'0
For one who held that in giving the third man argument
Plato meant to show need to abandon an absurd, indeed insane,
self-predication assumption, there would be the additional
historical-medicalquestion: why was Plato temporarilyso mad
as to hold self-predication?
The self-predicationpremise seems to me not implausible.
If Plato was using the argument to get rid of some part of the
theory, I see no immediate reason why self-predicationshould
be what he wanted to discard.
The strongestevidence that Plato ever held something expressible by the general self-predicationpremise is Parmenides
I32A-B: for first,it claims that the third man argument will
go throughfor any form; second, it is likely that it contains the
self-predication premise for largeness in the remark "What
about the large itselfand the other large things?"
There are particular claims of the self-predicationalsyntax
in other dialogues.11 The premise is in Aristotle'sreport of the
argument in the fragmentsof his On Ideas.
10 "Such a view is, to say the least, peculiar. Proper universalsare not
of themselves,
instantiations
perfector otherwise.Oddness is not odd; Justice
is notjust; Equality is equal to nothingat all ... not even God can scratch
Doghood behind the Ears. The view is more than peculiar; it is absurd."
R. E. Allen, in R. E. Allen (ed.), Studiesin Plato's Metaphysics
(New York,
I965), p. 43.
11PhaedoiooC: "if anythingelse is beautifulbesides beauty. ... Hippias
Major 292 E: "Beauty is always beautiful.
..
." Protagoras330: "Justice is
such as to be just ... nothingelse could be holyif we will not allow holiness
to be so." Republic597, TimaeusSIA, mentionedin note 21 infra.Lysis 217D,
whereit looksas thoughwhiteis white.
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THIRD MAN ARGUMENT
III.
SOME GRAMMATICALPOINTS
In English and in Greek, sentenceswhich count as selfare
predicationsare of at least two kinds whose differences
relevanthere. Examples of the two are: (I) "Justiceis just";
(2) "The camel is a camel."
They differthus.The firsthas an adjectiveas predicate.The
secondhas a sortalpredicate,"camel."
I call (self-)predicationsof the firstkind "adjectival (self-)
predications"and (self-)predicationsof the secondkind "sortal
(self-)
predications."
The firsthas as subject an abstractsubstantiveexpression,
one kind of expressionwhich Plato used to name forms.The
secondsentencehas as subjecta phrasewhichit is mostnatural
to the species,the camel,if you
to take in isolationas referring
knowthatthephraseis not ellipticalfor"the camel overthere."
Plato also used such phrasesas namesforforms,whichare presumablynot the same as species.
Plato usedphrasessimilarto suchspeciesnamesas "the camel"
as names of formsassociated with adjectival predicates:the
of the neutersingular
Greekfor"the just," a phraseconsisting
definitearticleand appropriateadjective,is as good a name of
for"justice."
theformjusticeas is theGreekabstractsubstantive
IV.
PAULINE PREDICATION12
A customaryobjectionto many self-predications
is that the
or speciesname,forexample,
formofwords-abstractsubstantive
in subject positionand predicateappropriateonly to entities
whichthe subject-expression
does not name-is absurd. Or, to
direct the objection especiallyat Plato: self-predications
are
in
which,according
absurd attachingto somesubjectexpression
to Plato,namesa forma predicatewhichobviouslycould not be
true of the named form.
12 I am grateful
to GregoryVlastosforaskingmanyquestionswhichaffected
thissectionparticularlyand forencouragingme to workon thispaper.
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SANDRA PETERSON
There are sentences which are not self-predicationswhich
display the allegedly absurd formof words, but which, far from
seeming absurd, seem true-for example: "Charity suffereth
long and is kind ... rejoicethwith the truth,beareth all things"
fromSt. Paul's firstletterto the Corinthians.13
I call "Pauline predications" sentences which (a) attach to
some subject expressionwhich Plato would say named a forma
predicate which someone might reasonably allege as inappropriate to the named form as "just" is alleged inappropriate to
justice and which (b) we naturally take to be true.
If one can accept as true the Pauline predication "Charity
sufferethlong," despite its having the feature held a defect of
self-predications,one should not object immediately to the
self-predications"Charity is charitable" and "Justice is just."
Adjectival self-predicationshave at least no more objectionable
features than adjectival Pauline predications.
To turnto sortalpredications: the disparitybetween the degree
to which sortal self-predicationslike "The whale is a whale"
are toleratedand the degree to which closely related predications
like "The whale is an animal" are tolerated14is similar to the
disparitybetween the degrees of acceptance of "Charity is charitable" and "Charity suffereth
long." People who thinkthe sortal
self-predication"The whale is a whale" is obviouslyfalse,because
the species the whale could not be an individual whale, are
willingto say thatthe sortalpredication"The whale is an animal"
is true. Consistency does not, however, seem to require that
assent to "The whale is an animal" should compel assent to
"The whale is a whale" as assent to "Charity sufferethlong"
should compel assent to "Charity is charitable." One can rather
naturally claim a differencebetween the two sortal predications.
One may say that "is an animal" is true both of individual
animals and of species of animal, while "is a whale" can be true
13 CompareLactantius:"Plato and Aristotle
said muchaboutjustice(justitia)
bestowingthe highestpraise on it because it assignsto each man what is his
vol. XII of The
own and preservesequity in all things." SelectFragments,
intoEnglish,W. D. Ross (ed.), (Oxford, 1952),
Translated
Worksof Aristotle
p.
101.
14
Geach, op. cit.,has noticed thiskind of disparity,p. 270.
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THIRD MAN ARGUMENT
onlyofindividualsand ofvarietiesofwhale,so thewhalecannot
be a whale, althoughit can be an animal.
"The whale is an animal" countsas a Pauline predication,
however,on the groundthat someonemightreasonablyview
itspredicateas truesolelyofindividualanimals.Withthe predicate so viewed,the sentenceis a Pauline predication.
Given that people accept Pauline predications(and ought
not to rejectwithoutexplanationPlato's self-predications)
the
questionarises:how can theyaccept themwithoutabsurdity?
to treatthe latter
what can theymean by them? It is fruitful
questionas the question:what semanticalrolesmightthe parts
of the sentenceshave?
V.
THREE
RESPONSES TO PAULINE PREDICATIONS
Here are threeways one mightreact to Pauline predications
The last would be appropriate
and to Plato's self-predications.
forPlato. In summary,the threeare: to recoil,to reparse,and
to reinterpret.
(I) To recoil is to declare that locutionslike "Charitysufferethlong" are irredeemablyfalse,despitepopular assent to
them.
(2) To reparseis to redescribethe logical structureof the
on Plato have offeredtwo
sentencesin question.Commentators
kindsof redescription.
The firstkind is Aristotle's:he claims that certain sortal
self-predications-for
example,"Man is a man"-say no more
than or are paraphrasableintosentencesin which"man" is not
the subjectexpressionbut has assumedthe role of a predicate.
"Man is a man" becomes"Everything
whichis a man is a man."
Of the unparaphrasedsentenceAristotlecommentsthat the
word "man" in it does not referto an individual,as it appears
to do. His comment,
whichoccursin an analysisofwhythethird
man argumentarisesforPlato's theory,is meantas a criticism
ofPlato'streatment
ofthegrammatical
roleofcertainexpressions
like "man" and doubtless"justice."These appear to be names
or singular terms-that is, expressionswhich referto some
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SANDRA PETERSON
individual.Accordingto Aristotle,on reflection"man" turns
expression.Sentencesin
out to be only apparentlya referring
whichit is the subjectexpressiondo not attributeanythingto
The Aristotelian
an entitynamed by theirsubjectexpressions.'5
man."
a
"Man
is
is
like
just"
is
to
treat
"Justice
course
does away with apparent form
Aristotle'srecommendation
does away withdefinite
namesas Russell'stheoryofdescriptions
descriptions:sentencescontainingthem are just shortways of
not containingthem;formnames,like definite
sayingsomething
neednotbe assigneddenotatain givingthesemantics
descriptions,
of your language; the truthconditionsof sentencescontaining
will alreadybe determined
formnames (or definitedescriptions)
of otherexpressions.
by yourtreatment
by Allenand perhaps
is offered
A secondkindofredescription
by Cherniss.Allen takes "Justiceis just" as a veiled relational
claim, an identityclaim, "Justiceis justice.""'
our Pauline predications
(3) A thirdmeansof understanding
A
I
is what call "reinterpreting."
and Plato's self-predications
does not redescribethe logical structureof such
reinterpreter
but takestheirgrammaticalformas theirlogicalform.
sentences,
16 Soph.El. I78b36-I79a5: "Isolation does not produce the thirdman but
agreeingthatit [i.e., man] isjust whata certain'this' is does ... it is apparent
thatone mustgrantnot thatwhat is predicatedin commonof themall is a
certain'this' but that it signifieseitherwhat it is like or in relationto what
or how much or somethinglike that."
Maybe "isolation" means "the using expressionslike 'man' (and 'justice'
and otherabstractsubstantives)."If so, Aristotleis saying that it is not a
mistaketo employsuch expressions;the mistakeis to take theirapparent
grammaras theirlogical grammar.Compare Cat. 3aIo. To paraphrase: it
appearswhenone speaksofman or theanimal thatone is speakingofa certain
"this"; but one is not.
16 Cherniss,ACPA, p. 298; Allen, op. cit.,p. 44. Allen's view seems to me
of Plato as the one I proposeinfra.To
not as good a possibleinterpretation
sketchone disadvantage:one would expect the account one gives of Plato's
"Justiceis just"-to help one understandpredications
self-predications-e.g.,
like "Justiceis holy." If we suppose the latterto be a relationalclaim, as is
"Justiceis just" on Allen's view, "Justiceis holy" amounts to "Justiceis
330 has "Justiceis holiness"
holiness." Then the argumentin Protagoras
as a premiseto an argumentwhose conclusionis "Justiceis holiness." So
But the
Protagoras330's argumentturns out to be highly uninteresting.
fromstep to step
participantsin it sound as thoughtheyfindthe transitions
and not trivial.
in it difficult
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THIRD MAN ARGUMENT
That is, he agrees that the subject expression'justice" or
"charity"is a referring
nota deviceto helpsaysomeexpression,
thingwhich could equally well be said withoutit. "Justice"is
to be classifiedas a singulartermreferring
to justice when one
givesthe semanticsof the languagecontaining"justice."
A reinterpreter
aims at consistently
holdingthesebeliefs:the
apparent referring
expression"justice" is an actual referring
expression;the sentence"Justiceis just" says somethingabout
what "justice" refersto-namely, justice; the predicate'just"
is trueof what the subjectexpressionrefersto if the sentenceis
true; thesentenceis true.So thereinterpreter
mustsay thatthe
predicate"just" has justicein its extension.As a gestureof appeasementto the criticswho recoil fromPauline predication
I use "reinterpretation"
forwhatmightequallywell be thought
of as philosophicaldiscovery.
Here are two quite different
The
ways of reinterpreting.
first-whichI call "conservativereinterpretation"-is
to hold
In "Socratesis
that the predicate"just" has two extensions.17
just," if that is true,it has the extensionthat thosewho recoil
fromPauline predicationsclaim "just" always has; that is, it
is true of people, theircharacters,acts, institutions.
To mark
offthisrole of the predicate,I use justt1" In "Justiceis just"
or "Piety is just," "just" has the extensionof "is such that if
anythingx participatesin it, thenx is just." To markoffthis
role of the predicate,I use justt2" Lest the explanationof
'just2" look circular,let me spellit out in twoclauses:
x is just2ifand onlyif
either (i) x is a formand if anythingy participates
in x,y is just1
or (ii) x is a formand if anything
y participatesin x,
y is jUSt2
ory
is just1
For any predicateF, sortalor adjectival,with a recoiler'suse
17 This is not the same as sayingthat "just" has two uses whichhave differentextensions.The latterway of speakingis meantto indicatethat "just"
is true of widely different
kinds of thingsbut meant to be neutralon the
question whether"just" is thereforeambiguous.
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SANDRA PETERSON
an analogous distinctionbetween F1 and F2 can be made, with
analogous clauses given for F2.
This familiarkind of explication is not circular. It gives some
initial conditions, devoid of use of "just2" under which certain
items are just2. Given these items, you can go on to find others
which are just2.18
A second way of reinterpreting,which I call "expansive
reinterpretation,"is to hold that "just" is more widely applicable
than one might have thought before reflectionon "Justice is
just": that is, it is held that "just" has the same extension as
"just, or just2" where "just," and "just2" are as explained above.
In explaining the extension "just" has in the reinterpreters'
use I rely upon there being people who recoil from Pauline
predications and who assign to their use of "just" a very narrow
extension.
It should be noted that the "if... then.. ." within clauses
(i) and (ii) of the definitionof 'lust2 cannot be the material
conditional'9 For I am tryingto sketch a position which would
be open to Plato; if the "if.. then. . ." were material, then, on
the ground that nothing participates in non-self-identity
or the
unicorn, "Non-self-identityis just" and "The unicorn is just"
would turn out to be true, as Plato would probably not have
held.
18 Remarks:clause (i) and some otherinformation
let us know that legal
justice-suppose it a kind ofjustice whichhas no subspecies-is just2.Clause
(ii) and some otherinformation
let us knowthatjusticeitselfisjust2.
thetwoclauses
Evidently,onlyformswill be just2. Perhapsnot so evidently,
leave open the question whetherjustice participatesin itself.Clause (i) is
superfluous.
It may look as thoughit would be simplerto describethe extensionsof F1
and F2-in particular,"just,."and "just2"-by theseclauses: x is just, if and
only if x is just in the way appropriateto non-forms;x is just2 if and only
ifx is a formand everyparticipantin x is just in theway appropriateto nonforms.But suchclausesfor"virtuous"wouldnot guaranteethat"is virtuous2"
was trueof virtue,sincesome of virtue'sparticipantsare forms(e.g., charity,
justice). The two clausesforthe definition
ofF2 allow forthe latter.
"I I owe noticeof thisto a memberof an audience at Rochesterto which
I read thispaper.
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THIRD MAN ARGUMENT
VI.
PLATO AND REINTERPRETATION
I do not claim that Plato explicitlyadopts eitherway of
He does not.
reinterpreting.
I have describedtwo extensions-oneconservative,
one expansive-for the predicatesof Plato's self-predicative
claims.
Given these extensionsfor the predicates,the self-predicative
claimswould be true.
Supposein Plato's use thepredicateshad one ofthe described
extensions;it would not follow,nor do I claim, that "just, or
just2" gives what "just" meant to Plato, or that Plato would
have used the phraseto describethe extensionof "just." I am
beliefthat"just" has the
not attributing
to Plato an unexpressed
two rolesof, or is to be explainedvia, "just," and "just2."20
To indicatean extensionpossibleforPlato's predicate"just,"
I mightsimplyhave starteda listand put Socrates,justice,and
a generaldescription
holinesson it. The pointof offering
of the
extensionI have in mind insteadof merelystartinga list is to
forestallthe objectionto the listthatthereis no way of characterizinggenerallywithoutincoherencetheitemson the list.
The mostI assumeabout Plato is that he knewhow to use
"just" withoutimmediateabsurdity.Such an assumptionhas
no interesting
consequencesforwhat he mighthave meant by
"just" in the sense of how he might have explained "just."
The proposal I am makingis that Plato, consistently
withthe
premisesofthethirdman argument,
mighthave meantby 'just"
somethingwith the extensionof,for example,just1 or just2."
VII.
WHY CONSERVATIVE REINTERPRETATION
EVADE THE THIRD
DOES NOT
MAN
Will reinterpreting
avoid the thirdman argument?It may
look as though a conservativereinterpreted,
holding that a
could avoid the regresswhere
predicateF had twoextensions,
the associatedformthe P had no participants
whichwereforms
exceptperhapsforthe P itself.
20
For the observations in this paragraph I am grateful to Paul Benacerraf.
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SANDRA PETERSON
He wouldclaimthatsincethe predicateF had twoextensions,
eitherwhollyor largelydisjoint,thepredicateF was ambiguous.
Our notion of ambiguityis captured by Quine, who says of
certainambiguouswordsthat(at thesame time)"fromutterance
to utterancetheycan be clearlytrueor clearlyfalseof one and
the same thing.This trait,if not a necessaryconditionof ambiguityof a term,is at any rate the nearestwe have come to a
clear conditionof it.'"21 The conservativereinterpreter
I am
for ambiguity:the
imaginingtakes the conditionas sufficient
declarationthat "just" has two extensionshas the resultthat
"just" is ambiguous. Suspendingjudgment on the question
whetherPlato could usefullyhave declared an ambiguity,in
oursense,ofF, I willexploretheconsequencesofthedeclaration.
Clearly the one-and-the-same-form
premise would fail to
generatea commonformof the seal over the seals in the Los
AngelesZoo and the Great Seal of the United States: we may
describeitsfailureby sayingthatthepremiseis supposedto generate a commonformof P thingsonlyfora pluralityof things
whichare P in thesame sense.If the' and theplurality
ofthings
which are P do not, on groundof ambiguityof F, count as a
new pluralityof thingswhichare P in the same sense,theclaim
an applithatF is ambiguous,as "seal" is,willrenderillegitimate
cationoftheone-and-the-same-form
premiseon a mixedbatch of
in thisspecialsortof case.23
0 thingsand will avoid the regress22
But citingthe describedambiguityofF is not enoughto flaw
the argumentformostpredicates.For example,take "virtuous."
21 W.
V. Quine, Wordand Object(New York, 196I), p. 131.
I mean: will avoid a regressfromthe premisesI have set out. Another
regressforany formthe0 could be establishedusingPremises2, 2a, 3, and 3a,
if Plato did not deny that the 0 all by itselfcountedas a pluralityof things
22
which are 0.
There is some evidencethat Plato did not hold thata singleformcounted
as a plurality:at Republic597 and Timaeus31 A Plato givesargumentsclose
in formto the thirdman. These argumentshave a shortregress,though
nothingpreventsthe infiniteone. The argumentsgo: if therewere two forms
ofthebed (Timaeus:theanimal) therewouldhave to be a third.One presumes
that Plato did not thinkthe singleformthe bed (the animal) generatedthe
regress;that may be because the single formdid not count as a plurality.
23 Neil Lubow's insistenceon this special case provokedusefulreflection
on avoidance of the regressgenerally.
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THIRD MAN ARGUMENT
Virtue, charity,justice, and humilityare virtuous,all in the
preThe one-and-the-same-form
same way-namely, virtuous2.
mise,then,requiresa commonformof virtueoverthem.So the
argumentgeneratesa regressforvirtueand forany formof the
el when thereare kindsof the (. 24
VIII.
DEFINITION
AND THE
ONE-AND-THE-SAME-FORM
PREMISE
have claimed
Turnto thequestionwhetherPlato couldusefully
F
a recoiler's
with
ambiguityin our sense for any predicate
use. It is not crucialto knowif Plato would or would not have
used a word translatable"ambiguous" to characterize"just"
uses.25Our questionis whetherthe difwith its two different
forsomepredicatesare so generIt shouldbe notedthatself-predications
ally accepted that theycould not count as Pauline (theyfail the firstclause
is self-identical"
ofPauline predications);e.g., "Self-identity
in thedescription
reprintedin
(see Vlastos, "The Third Man Argumentin the Parmenides"
it seemsto contain
Allen,Op.Cit.,p. 241). On itsmostnaturalunderstanding,
"self-identical"with the same sense as "self-identical"in "Socrates is selfidentical." There seems to be no reason to say that "self-identical"is
Doubtless
ambiguous because it is true of both Socrates and self-identity.
is self-identicall
as well as being self-identical2.
self-identity
have used a phrase translatable"not ambiguous."
25 He would evidently
See G. E. L. Owen, "A Proofin the Peri Ideon," reprintedin R. E. Allen,
on Platonicdoctrine,
Op. Cit., pp. 293-312. Owen discussesAristotlereporting
and describesas "what mustbe intendedas an exhaustiveanalysisoftheways
in whicha predicatecan be used withoutambiguity"(p. 295) a listin which
item (c) below appears (pp. 293-294). "When the same predicateis asserted
but so as to indicatea singlecharacter,
of severalthingsnot homonymously
it is trueof themeither... or (c) because one of themis the model and the
restare likenesses,
e.g., if we were to call both Socratesand the likenessesof
Socrates'men.' "
The use of "just" forjust people and forjustice itselfwould clearlyfall
under (c). Plato wantsto distinguish(c) predication,whichhe mightnevergroundsfor
thelessagree was a case where therewere somewhatdifferent
as in
applicationof the same predicate,fromcases of enormousdifference,
the case of "seal."
Notice Owen's commenton type(c) predication(pp. 297-298): "The analitsPlatonicsourcesif(c) werenota typeofunequivocal
ysiswouldmisrepresent
predication.This is implied by the referencein Republic596-7 to a bed in
a picture,a wooden bed, and the Paradigm Bed as [threebeds] and more
generallyby such dicta as thatnothingcap be just or holyor beautifulif the
correspondingformis not so. These utteranceshave no sense unless the
of meaningto model and likenessalike."
predicateapplies withoutdifference
24
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S.<ANDRAPETERSON
ference between the two uses is so great that the one-and-thesame-formpremise would be as illegitimatelyapplied to a plurality of just thingsconsistingof, say, Socrates and justice as to
a pluralityof seals consistingof the seals in the Los Angeles Zoo
and the Great Seal.
I offera brief account, each point in which is controversial
and deservingof more detailed treatment,of some reasons which
weigh on the side of a negative answer to our question, although
they do not compel a negative answer.
"Just" used forjust, things differsfrom "just" used forjust2
things in applying to items that are widely, even categorially,
differentfrom what "just" used forjust2 things applies to. But
we are not entitled to use this differenceto establish that there
is not one and the same formofjustice over just1 thingsand just2
things, unless we can adequately distinguish (as I cannot) the
latter differencefrom the differencebetween "just" used for
just acts and "just" used forjust people; just people and just
acts are quite different(even categorially so): yet there is supposed to be one and the same formofjustice over them.
A differenceuseful to find would be a differencebetween the
definitionsthat Plato would have given "just" in its two uses.
I shall assume that failure to find such a differencewould be
strong reason to say that the employment of the one-and-thesame-formpremise on "just" in the recoiler's use and "just"
said ofjustice is legitimate.26
A Platonic definitionof "just" may be representedas an "if
and only if" claim: "x is just if and only if . . . ." Let us label
Plato's requirementthat the predicate D defininga predicate F
26 In effectthis is the assumptionthat difference
in Platonic definition
is likelyto be necessaryforillegitimacy.
Notice, incidentally,that it may not be sufficient.
Owen, op. cit.,p. 297,
paraphrases(Platonic definitions?)are approsuggestscases wheredifferent
uses of a predicate,but where Plato would nevertheless
priate to different
not hold the predicateambiguous(in his sense).
It is awkwardto speak of Plato defininga use of a predicate.What I ask
you to imagineis: Plato firstdefining"just" while supposingit true only of
and then defining"just" while supposingit true only of forms.
non-forms
There is of course somethingbizarre about imaginingPlato agreeingto
of a predicatewithonlya recoiler'suse.
attempta definition
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THIRD MAN ARGUMENT
must be true of exactly what F is true of by saying that Platonic
definitionsare to be adequate.
Suppose that there is an analysis of "just" which is adequate
to a recoiler's use of "just." Let the analysis be "is disposed to
allot to each man his due."27
The recoiler'sanalysis will also be adequate to Plato's presently
supposed reinterpretiveuse of 'just" forformssince the defining
phrase "is disposed to allot to each man his due" has a reinterpretive use. The reinterpretingPlato would hold not only
that justice is just. He would hold also thatjustice is disposed to
allot to each man his due.28 For, on the assumption that the
definingphrase in the recoiler's use is adequate as a definition
of the recoiler's use, justice is disposed-to-allot-to-each-man-hisdue2.
That the recoiler's phrase "is disposed to allot to each man
his due" is definitiveof the recoiler's "just" seems reason to
suppose that Plato's use of the phrase, which is adequate to
Plato's use of "just" for forms,will also be definitiveof that use.
It might be objected to this supposition that a Platonically
acceptable analysis of "just" with the extensionof 'just2" would
state that only formsare what are just in this use of "just" and
that a Platonically acceptable analysis of "just" with the extension of justt" would, in contrast, say that only non-forms
are what are just in this use of "just."
Mention of the categoryof their extensions,however, does not
turn up in Plato's definitionsof predicates which have a recoiler's
use. The absence of such mention is some indication that such
mention does not belong there. The differenceswhich Plato
certainly recognized between a just person and a just form are
not part of what it is for them to be just. If the only differences
27 If thisanalysiswere adequate, it would
hold, as it does not, for"just"
as said ofparticularacts,kindsofacts,people,institutions.
Perhapsan adequate
analysisof "just" would have to be disjunctiveto cover all of these.The argumenthere,however,would notbe affectedifthedefinition
weredisjunctive,
so long as it was an adequate definition.
"Is disposed to" is the usual gestureagainst the suggestionthat the just
man is in a continualfrenzyof activity.
28 Recall the citationfromLactantiusin note
13 supra.
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SANDRA PETERSON
mentionable between the two uses of "just" are those which
amount to a differencewhose mention does not belong in a
Platonic definitionof "just" (or any predicate with a recoiler's
use), the same phrase will be definitiveof "just" as used for the
extension of "just," and of "just" as used for the extension of
justt2"
That the same phrase will be definitiveof the recoiler's and
Plato's reinterpretiveuse of "just" is some reason to suppose
that the two uses get the same Platonic definition.
It is unsuitable to object here that the alleged sameness of
definitionis "merely verbal" and that the defining phrase "is
disposed to allot" must have two differentsenses because the
two uses of "just" which the phrase definesare said of categorially
differentitems. Unsuitable, because our present question is:
will the differencein category of what falls under the two uses
of "just" make for a differencein sense that would be revealed
by a differencein Platonic definition? In quest of an answer
for"just" we are not entitledto assume that for"disposed to allot"
the answer is yes.
I said at the beginning of this section that I would notice
considerationsthat weighed on the side of answering negatively
the question: if Plato were a conservative reinterpreted,would
he hold illegitimate the application of the one-and-the-sameform premise at the crucial stage of the argument? "Weigh on
the side of" was to indicate this: the position of a conservative
reinterpreteris consistent with those of Plato's views so far
mentioned, but for him to take the position-to declare "just"
ambiguous by Quine's condition-would not be for him thereby
to avoid the regress.For it looks as though he would affirm(i)
that there is neverthelessno differencein the Platonic definitions
of the two uses of "just"; and such an affirmationseems strong
reason to affirmas well (2) that an application of the one-andthe-same-formpremise to any group of items of which "just"
in the two uses was true would be legitimate. Reinterpretation
of the kind I have described offersa reasonable hypothesisabout
how Plato might have used self-predicativeclaims; but it does
not by itselfprovide a distinctionwhich would block the use
of the one-and-the-same-formpremise.
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THIRD MAN ARGUMENT
In fact, the distinctionamong uses of any predicate F which
is needed in order to fault the argument as relying on an illegitimate application of the one-and-the-same-form
premise is
a distinctionwhich puts F's self-predicativeuse on the one side
of the distinctionand puts all the non-self-predicativeuses on
the other side,29 as the discussion in Section VII and note 24
indicates.
To summarize and make general the above points about
"just": For any predicate F with a recoiler's use I have provided
other predicates F1 and F2 such that rthe F is F21 and rthe F
is F1 or F21 is true. It is consistentwith the premisesof the third
man argument to take such a predicate F to have the extension
of F2 when it occurs as a predicate in self-predications,
or to have
the extension of rFF or F2.1
For any such predicate F, if its analysis or definitionD forthe
recoiler's use is adequate, then rtheF is D1 will be true,when D
has the conservative reinterpreter'sextension, the extension of
D2. Moreover, D with the extension of D2 will be definitive,so
far as one can see, of F with the (conservative reinterpreter's)
extension of F2.30 The predicates which define any recoiler's
predicate are exactly as able to have the kind of extensions I
propose for predicates in Pauline predications and self-predications as "just" is.
29 The Cherniss-Allen
account of the uses of "just" is an example of a
distinctionwhich does so.
There is some evidence that Plato did make a distinctionbetweenselfpredicativeand non-self-predicative
uses of F as a responseto the thirdman
argument.I agreewithCherniss(ACPA,pp. 308 ff.)thatAristotle's
Metaphysics
1079a32-bI I is evidencethatPlato did make such a distinction;I do not agree
withhis accountof what the distinction
is (see n. i6).
30 Likewisewhen F and D are takento have the expansivereinterpreter's
extensions of -Fp or F21 and of FD1 or D2,1 respectively.
On the conservativereinterpreter's
position,notice,F withinthe subject
expressionof rtheF is F' is ambiguousalso by Quine's criterion.The four
ways of understandingFtheF is F1 have the same truthconditionsas (I)
FtheF1 is F21; (2) rtheF2 is F21; (3) rtheF2 is F11; and (4) rtheF1 is F1.'
The firstway of understandingFtheF is F' is the way whichis employedin
the thirdman. The firsttwo ways are true; the second two are false.
It is importantto noticethat if the discussionof sec. VIII is correct,the
subjectphrasesin all fourof thewaysofunderstandingFtheF is F1 designate
one and the same form.
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SANDRA PETERSON
If the Platonic analysis D of a predicate F as used in the recoiler's way is the same for F as for its associated form,there is
that much reason for Plato to affirmthat the one-and-the-sameform premise generates a common form over participants in
the P and the P itself.The differencebetween the way the P is
e and the way many of itsparticipantsare 1 is best brought out
by saying that the 1 is a form which is 1 perhaps3' solely by
bringing about that its participants are q. Marnyof its participantsmay be i withoutbeing able to have participants.Such
categorial differences,however,do not make a differenceto what
it is to be 1i and do not get mentioned in the account of what it
is to be A.
It is not only self-predicativeclaims or their consequences
by definitionwhich we can now understand to be true. For any
predicate G with an associated form the 0 such that all the
participantsin a formthe 0 thereby (as a matterof entailment)
are /-that is, therebyhave G true of them,the formthe d5will
have G2 true of it. That is, it will have G true of it, if G has the
extension of G2 or of rG, or G2j as the reinterpreterproposes.
SANDRA PETERSON
ofMinnesota
University
31
Recall note 24.
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