Miles Burnyeat Self Refutation

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Protagoras and Self-Refutation in Plato's TheaetetusAuthor(s): M. F. BurnyeatSource: The Philosophical Review, Vol. 85, No. 2 (Apr., 1976), pp. 172-195Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2183729 .

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The Philosophical eview,LXXXV,

2

(April

1976).

PROTAGORAS

AND

SELF-REFUTATION

IN

PLATO'S THEAETETUS

M.

F. B

URNYEAT

T

IS paper

is a sequel

to an

earlier

one in

which

discussed

an

argument

n Sextus

Empiricus

M 7.389-390)

directed

against

the

sophistProtagoras

and

his doctrine

that man

is the

measure of

all

things.1

extus

nterprets

rotagoras'

famous

proclamation

Man

is

the

measureof

all

things" s

the subjectivist

hesis hat very ppear-

ance

whatsoever

s

true,

and

his argument

s that

the thesis s

self-

refuting ecause

one of the

things

hat

ppears

(is

udged)

to

be the

case

is that

not

every

ppearance

is

true:

f,

s

the

subjectivist

olds,

every

appearance

is

true,

but at

the same

time

t

appears

that

not

every

ppearance

is

true,

hen

t

follows

hatnot

every

ppearance

is

true. The

problem

was to

discover how

this

argument

could

be

classified s aperitroper self-refutation. ysuggestionwas

that

n a

context

where

it

can

be

presupposed

that

subjectivism

meets

with

disagreement,

he

second

premise

s guaranteed

to hold

and

we can

argue

straightforwardly

hat

f

subjectivism

s true,

t

s false. Such

a

context,

proposed,

would

be established

by

the dialectical

debates

toward

whichGreek

ogicalreflections

ere

typically

irected,

nd

it

is

thisdialectical

etting

which

provides

the

key to

Protagoras'

self-

refutation.

But therealProtagorasdid nothold thesubjectivisthesis.As the

earlier

paper

explained,

the more

authentic nterpretation

f

Pro-

tagoras

s that

given

n

Plato's

Theaetetus,

ccording

towhich

he

was

a

relativist

homaintained

hat very

udgment

s truefor

in

relation

to)

the

person

whose

udgment

it is; that

s

what

the doctrine

that

man

is the

measure

of all

things

riginally

tood

for,not

the crude

subjectivism

hat

Sextus

refutes.

o it s

natural

o

ask how

the

charge

of self-refutationares

against

the subtler

relativism

f

the

sophist

himself.

The question

has

both

a philosophical

and a

historical

spect.

From

Plato

to

Husserland

John

Anderson,

philosophers

of

various

persuasions

have found

it

mportant o

show

that Protagoras'

doc-

I

"Protagoras

nd

Self-refutation

n Later

Greek

Philosophy,"

hilosophical

eview,

(1975),

p.

44.

172









M.

F.

BURNYEAT

does not hold that every udgment is true (period)

but-very

differently-that every udgment

is

true for the person

whose

judgment t s.The differences crucial.Starting rom n adequately

formulatedrelativism,

(M) Every udgment is trueforthe person whose udgment

it

is,

and given

(N)

It is

udged

that

M)

is

false,

all that can be inferred s that

(0) (M) is false-or "(M) is false"

s

true-for

the

person

who

judges it to be so.

This establishesthat the Measure doctrine s false for

Protagoras'

opponents

but

notyetthat

t

is falsefor Protagorashimself;con-

sequently,his relativism

s

not so far shown to be self-refuting.

is

thesis hatevery udgment is true forthe person whose udgment

it

is does not commithim to endorsingwhatever nyone thinks

s true

for

himself s well as forthe

person

who

thinks

t;

hence

it

does not

require

him

to concede the truth f his opponents' opinion

thathe is

mistaken.Or so it is generally hought.

The position,then, s this: the argument as

it

stands

in

the

text

appears

to be

an

ignoratio lenchi, tarting

ut from

a

subjectivist

position, A),

which

Protagoras

did not

hold,

and

recasting

n

the

relativisticmould of M) yieldsonly the seeminglyharmless onclu-

sion that the Measure doctrine s false for

Protagoras' opponents.

An

impasse so obviously nsatisfactoryhould give us pause. Critics

from George Grote to GregoryVlastos have protested

at the way

Socrates at the climacticmoment drops the relativizing ualifiers

with

which Protagoras specifies or whom a judgment

is

true,

but

few

have

thought

t

necessary

to wonder

why

Plato

should

make

Socratesproceed

in

thisfashion nd none, to mymind,

has convinc-

ingly explained his foisting upon Protagoras

the unrelativized

premise A).

Vlastos

writes:

Protagoras s veryfussy bout adding "for. .." after "true"or "is" or

"real."

..

. Even Plato himself

s

not as careful

as

he should

be

on

this

4 George Grote,

Plato and the ther

ompanions fSokrates3

London, 1875), II, 347

ff.; Gregory

Vlastos, Introduction

to the

Library

of Liberal Arts Plato's Protagoras

(Indianapolis and

New York, 1956),

p. xiv,n. 29; also

W. G. Runciman,Plato'sLater

EpistemologyCambridge,

1962), p. 16, Kenneth M. Sayre,

Plato's AnalyticMethod

(Chicago

and

London, 1969), pp.

87-88.

174







PROTAGORAS

AND

SELF-REFUTATION

point.While e puts n the for. ." almostnvariablyhile eportingr

describingrotagoras' octrine

notonly

t

170a,

but

at

152b,c, 58a,

and allthrough

66c-167c,

here he

repetitionets lmost iresome,

and then gain at 171e-172a; lsoatCrat. 85e-386d), e sometimes

drops t nthe ourse f

rguinggainst rotagorase.g., n the exquis-

ite" rgumentt 17 a),therebynadvertentlyitiatingis wnpolemic.

On

reading

this

I

want to ask: can we be satisfiedwith a

simple

diagnosis of inadvertence

f

Plato is so conscientious

n

reporting

Protagoras'doctrine?How

could he be blind to the omissionof the

qualifiers rom key

rgument gainst positionhe has so carefully

described?Runciman, n the otherhand, suggests hatPlato maybe

consciouslyoverstating

his case. But

what would be

the

point

of

deliberately verstating ne's case

to

the

extent

of

making

t

a

case

against a position quite other than

its

official arget?

The task of explanation

becomes harder still

f

we attend to the

context

n

which the self-refutation

rgument

occurs.

This is

at a

stage

in

the dialogue after

he

youthful

heaetetus

has

conceded

a

series

of

objections

(161c-164b) against

the

Protagorean

doctrine

(more precisely, hey are objectionsto Theaetetus' definition f

knowledge s perception,

ut

the

dialogue

takes

thisdefinition

o

be

equivalent

to the

Protagoreandoctrine,

o

that

objections

to either

tell

against both; compare

164d with

15

e-

152a, 160de).

These criti-

cisms

having

been discounted as verbal and

superficial 164c),

and

Protagoras thoroughly

defended against them (166a-168c),

Theodorus is prevailed

upon to replace Theaetetus as Socrates'

interlocutor-in order that the distinguished mathematician's

maturity nd professional ense of rigor shall ensure more serious

and

responsible reatment orthe deas of his friendProtagoras cf.

162e, 168b-169d).

n

effect,

hen,

Socrates

begins

the section

which

concerns us

with promise

to deal

fairly

nd

ustly

with

Protagoras

5Runciman,

loc.

cit.,relying

n remarksmade at the conclusion of the

argument

(17 lcd)

in

which Socratesentertains he dea that Protagoras mightpop

up

with

n

answer. The passage

in

question will be discussed

in

due course.

It

has

helped to

trigger thirdview, hat heomission f the qualifiers s deliberatebut

ronic, ecently

put forwardby Edward N.

Lee,

"

'Hoist with His Own Petard': Ironic and Comic

Elements

in

Plato's Critique of

Protagoras Tht. 161-171)" in E. N. Lee,

A. P. D.

Mourelatos, R. M. Rorty eds.), Exegesis nd Argument,tudies n Greek

Philosophy

presented

o

Gregory

lastos

Phronesis,upp.vol.

I

[1973] ); I

discussLee's

interpretation

in nn. 6 and 23 below.

175







M.

F.

BURNYEAT

(cf. 167e).6

Not

only that,

but since

for chronological

reasons Pro-

tagoras cannot be present to defend

his thesis n person,7Socrates

offers he

further

afeguard

thathe willuse Protagoras'own work o

authorize the admission he intends to elicit,rather than rely,as

before,on the udgment of himself

nd his interlocutor s to what

Protagoraswould or should be willing

o admit 169de). The refuta-

tion of

Protagoras

is

to be derived directly

rom

Protagoras'

own

statements, ogether

with

the empirical

fact,whichProtagorascan-

not credibly eny, hatother people

think hatwhat Protagoras ays

is false. The whole section is peppered

with references to Pro-

tagoras'book Truth nd

its

hesis hat

man

s the measure of

all

things

(170c2, dl-2, d5, 170e9-171a 1, 17lb7,c6);

twice ocrates

even makes

a

direct address

to

its defunct

author, Protagoras

himself

170a6,

c2).

And in

embarking n

this

project

of

refuting rotagoras

out of

his own book Socrates opens witha perfectly air and responsible

statement f the main thesis of that work:

He says, oeshe not, hat

what

eems

oeachperson s so for heperson

to whom

t

seems?

To which Theodorus replies, "Yes,

he does say that" 170a).

6

Lee, op. cit., pp. 226-239,

has done valuable service to the dialogue by calling

attention o the deep irony

hatpervades the peeches

n

which

ocrates

mpersonates

Protagoras demanding serious

and responsible dialecticaltreatment or his theory

(162de, 168b), not long after

ocrates has pointed out that, f Protagoras' account of

truthstaken seriously, ialectic r thetesting y rgument nd discussion f people's

viewsand theoriesbecomes

a farce 16 le-162a). But thisdoes

not annul the promise

to deal fairlywith rotagoras

r make ronic he refutationwhich

arries tout. On the

contrary, he irony s

in

thefact hat one such as Protagoras

demands, is promised,

and finally as we shallsee) is given a refutation f unexceptionable

eriousness.

The

joke

is

rather spoiled when

Lee finds lements of irony n the refutation

tself.He

claims

that,byomitting

he

qualifiers

n whichProtagoras

nsists, ocratesteaches

an

ironic lesson about the conditions

for assertinganything hat

can significantly e

discussed or denied. This

suggestionwill concern us

in

due course

n. 23 below)

-I

think t

overdoes the rony

nd fails o mend Socrates' ogic

-but it

should

be said at

once that Lee

is

open

to

the

same damaging objection as Runciman:

it

ought

to

be

Protagoraswho

is

attacked whether

eriously r ironically), nd

this

ought to mean

beginning from M) ratherthan

A). In fact, here s not a word in Lee's discussion

about the omission of the qualifier

n

premise (A) and how

that

tallies

with

the

(admittedly ronic) palaver about

securing ustice forProtagoras.Yet preciselywhat

justice involveshere is a man's

right o

bejudged

by the views

he reallyholds (168bc

with

167e).

7The dramaticdate ofthe

dialogue is 399 B.C., well after he

death of Protagoras.

176







PROTAGORAS

AND

SELF-REFUTATION

After such

a

beginning twould be

nothing

ess than perverse

dishonesty

were

Plato without

eason to make

Socrates

argue

in

the

sequel

in

a

way

that

depended for ts

damaging

effect

n omission

of

therelativizing ualifiers. need hardly aythatperversedishonesty

is not a

charge to be

leveled

lightlygainst a

philosopher

of Plato's

stature nd

integrity.

ut the

onlyway

to forestall

t

sto

workover

the

text

n

thehope

that a

more detailed

understanding

of what s

going

on will

presentSocrates'

reasoning

in

a

new aspect.

We can make a

start

y

ooking

nto the

more immediate

ontext

of the

self-refutation

rgument,

which

s

merely he ast

n

a

closely

knit

sequence of

three linked

arguments

againstProtagoras. The

sequence goes as follows.Either (1) Protagoras himself did not

believe

the

Truth

e

wrote,

n

which

case, since no

one else does, it s

not (sc. the

truth)for

anybodyat all

(170e7-170a1).8 Or

(2) he did

believe it,but

the

majority f people

do not

share his

opinion,

in

whichcase

twothings ollow.

First, a) the more the adherents

of

his

Truth re

outnumberedby

people who

do notbelieve

t,

he

more

t s

not (sc. the

truth)

than it is.

"Necessarily,"

replies

Theodorus, "at

least

f

t s to

be and

not to be (sc.the

truth)

ccordingas each person

believes

or

does not believe

t"

17 a

1-5).

Secondly, b)

Protagoras

s

caught bythe

peritrope

rgument

s

quoted

earlier

17

lab),

and this

leads eventually o

the same

conclusionas argument

1)-namely,

that his

doctrine is not true

for

anybody

at

all, not

even

for

the

sophist

himself

17

1c5-7).

It is

(2) (b)

thathas

pre-empted

he atten-

tion;

it

is,

of

course,highlighted

y

Socrates as the

really

exquisite

one.

But

the

neglect

of its

companion arguments

has meant that

criticshave overlooked the evidencetheseprovidethatPlato thinks

Protagoras

vulnerable to

objections

which do notdepend

on omis-

sion of the

relativizing ualifiers.

For the first

rgument

of the trio

certainly

ses

the

appropriate

qualifier,

nd the

second is not unam-

biguously

at fault in

this

respect. But

before

discussing the sig-

nificance f this

evidence, we

need a

more formal tatement

f the

positionagainst which the

three

arguments re directed.

I

quoted

earlier the

formulation

What seems

to each

person s so

fortheperson to whom tseems" (170a). This lays tdown that for

all

persons

x

and

all

propositions

)

8

F.

M.

Cornford,

lato's

Theory f

Knowledge

London, 1935), p.

78, translates s

if

the

conditional

et

Uiv

KTX. were

contrary o

fact:

"Supposing

that

not even he

believed .. then

this

Truth

.. would not

be

true for

nyone."

The Greekdoes

not

present t as

such there

s no

'dv),but as

one limb

of a

dilemma:

whetherhe believed

it or

did not

believe it,

n either

case it s

not

true for

anybody.

177







M. F.

BURNYEAT

P

1.

If

it seems to x thatp,

9

then it is true forx thatp.

P

1

is indeed Protagoras'

major contribution o the extreme mpiri-

cist

epistemology

which thedialogue elaborates out of Theaetetus'

definition f knowledge s perception. t guaranteesthat,no matter

how "wild" and variable from the common-sensepoint of view) a

person's experience may be,

the udgments he is led to will be true

for

him,giving

him

certain

knowledge

of how

things

re forhim.

f,

as Protagoras holds, all thingsare for each person exactly s they

appear to him, no one can be

mistaken bout the reality hat con-

fronts

im,

ofwhichhe is the sole

authoritativejudge

measure).

But

it s clear thatPlato also

understandsProtagoras o make the further

claim thatnothing s true for person unless t eems tohimto be so,

unless he believes t.

In

other

words,the converse rule also holds:

P2.

If

it is true forx that

p, then

it

seems to

x

thatp;

which s

equivalent to

P3.

If

it does not seem tox thatp, then itis not true

forx that

p.

That is to say,Protagorashas to defend the equivalence of"It seems

to

x

that

p"

and

"It

is true

for

x that

p,"

not merely

n

implication

fromthe former o the latter.

Protagoras ommits imself

o the full quivalence when he claims

that man

(sc. each man)

is

the measure not only of what

is

(sc. for

him), but also of what s not

(sc. for him). At least, when Plato first

quotes theoriginaldictum

n

full, Man

is the

measure of all things,

of thosethat

re,

that

hey re,

and of those

that re

not,

hat

hey

re

not,"

he

explains it

in

terms

of the example of two people

in

the

wind,one of whom feelscold while the other does not; in which

situation

Protagoraswould have us believe that the

wind s

cold for

one of them and

is

not so for the

other

152b). Here,

to

derive the

Protagorean reading of the

example we need

P

1

to

tell us that the

wind

scold fortheone who

feels old and P3 to tell

us that t s

not

cold for he second

person. For

it

was not said

that he

secondperson

feels warm

in

the

wind,

or even that he feels the wind is not

cold;

given either f these as

premise, o conclude that he wind s not cold

forhimwe would need no more than

P

IN

If it seems to x

that

not-p,

hen it is true forx

that

not-p.

which s a

simple substitutionnstance of

P1.

What was said of

the

second

person

was

simply

hathe

does

not

feel

cold. On

Protagoras'

9

Alternatively,f x

believes/judges hat

p; cf.

my earlier

article, op. cit.,

n.

2.

178







PROTAGORAS

AND

SELF-REFUTATION

view,then,if

the wind

does not

appear cold

to

someone, that is

sufficient roundsto

assert hat

t s not

cold forhim,

nd this

means

that we must

include P3 (or its

equivalent

P2)

in

any complete

formulation f the doctrine thatman is themeasure of all things.

The

doctrinemaintains

hat It

seems to

x thatp"both

mplies

nd is

impliedby "It

is true

forx that

p."

That

being

so, weneed not be

surprised hat 3

should come

into

play

n

the

arguments hat

urrently

oncernus. Consider

the

first f

the

triple

equence,

the

argument hat

f

the

Measure doctrine

does

not seem

true

either to

Protagoras or

to anyone else,

then t is

not

true foranyone

at all.

Clearly,to argue

thus s

to assert

P3 forthe

special casewherepisthe Measure doctrine tself:f tdoes notseem

to

anyone that

theMeasure

doctrine s

true,then it is

not true

for

anyone. And

if

P3 is part

of

Protagoras'theory,

he argument s that

the

theory ands

Protagoras

n

trouble

when it is

applied to itself.

We

may

ask

why

the

theory

hould have

to

apply

to

itself,

s

it

s

made to do

in

all

three

arguments

of the sequence.

Plato

does

not

consider

the

possibility

hat

Protagoras

might

laim

for

his doctrine

a special status xempting tfrombeingcounted as one among the

propositions

with which

it

deals. Elsewhere,

in

fact, Plato insists

strongly

hat

philosophical

heory

mustbe

statablewithout

nfring-

ing itself; hus n

the

Sophist e holds it

against

monism that everal

terms enter

nto the

formulation f it

(244bd), and he finds hat

a

certain

ate-learners' iew

of

predication

has

only

to be statedfor

t

to

refute

itself

252c). But even

waiving

twentieth-centuryualms

about

self-applicability,

here s a

question

that

urgently

eeds to

be

asked. (It is perhaps a measure of thepull exertedbytheexquisite

argument

that

no

commentator,

o

myknowledge,

has

asked

it.)

Why

s t n

objection

o

Protagoras hat,

n his

own

showing,

f

no one

believes his

theory

t

s

not true for

anybody?Protago-ras

might

for

various

reasons

be embarrassed

to admit

this,

but

would he be

refuted? s it

so

surprising hat

theory

ccordingto which

ll

truth

isrelative o

belief hould

itself

e nomore than

a relative

ruth, rue

only

for

someone who believes it?

More

important,

how does this

show that there s somethingwrongwith the theory?

There

can be no

doubt that

Socrates presents the

point as

an

objection;

so much is

guaranteed

by

the

position

of the

argument

n

the

sequence

of

three.Our task s

to understand

why.The

solution

want

to

propose

is that

Plato takes

t

that,

f

relativism s

not true

for

someone,

it

does

not hold

of that

person's

udgments

and

beliefs.

Suppose

the

person

in

question s

Socrates.

Applyinghis

doctrine

179







M. F. BURNYEAT

to Socrates, Protagorasmaintainsthat for all propositions

)

PI

s

If

it seems to

Socrates thatp, then it is true for

Socrates thatp.

and

P3s

If

it does not seem to Socrates thatp, then it is

not true for

Socrates thatp.

Socrates replies

that he

profoundlydisagrees.

For a

start,

S1 It

does not

seem

to Socrates

that, PIs )if

it

seems

to Socrates that

p, then it is true for

Socrates thatp.

This is a plain matter f fact

whichProtagoras annot credibly

eny.

And

having asserted the

conjunction

of

P

Is

and

P3s,

Protagoras

s

committed o agreeing

that S

1

is

equivalent to

S2

It

is not

true

for Socratesthat, P1)

if it

seems

to Socrates thatp, then it is true for Socrates

that

p.

All

this s simply o say thaton Protagoras' theory, ince Socrates

does not believe

P

1,

t

s

nottrue forhim,

nd

a fortiori

t s

not

true

forhim nits pplication o hisown udgmentsand beliefs P Is). But

simple

as

the deduction s,

tsconclusionS2 requires nterpretation.

For it nvolves hat urious

ocution trueforSocrates," nd it s

time

to inquiremore closely nto

the meaning of the relativized dioms

that

Protagoras

uses

to

formulatehis views.

One

thing

we know s that

"It

is

true

for

Socrates

that

p"

is

to

be

equivalent to

"It

seems to

Socrates thatp";

if

one of these s true the

other s

the

same, and so too

f

either s falsetheyboth are. But

it

s,

think, mistake o suppose on thataccount thatthe two statements

have the same meaning,

that the novel locution "true for Socrates"

simply

means the same

as the more familiar seems

true

to Socrates"

or

"is believed

by Socrates."

This is a mistake hathas

been made

in

both ancient and modern

discussions f Protagoras nd

his self-refutation.ohnPassmore,for

example,

wonde

rs

(rhetorically)

what

it

can

mean

to

say

that

a

proposition

s true

for someone other

than

that

he thinks

t

true.10

Again, there s an argument nSextuswith he form thoughnot n

this

case the

name) of a peritropergument against Protagoras' op-

ponents,according to which,

f

someone

asserts hatman

is

not

the

l0

Philosophical

easoning London,

1961), p. 67, quoted below. The conflation

s

prominent lso in Lee, op. cit., p.

246-248, 253., nd important orhis account of the

self-refutationrgument; see n. 23

below.

180







PROTAGORA4SAND

SELF-REFUTATION

criterion f all

things,

he willconfirm hatman is the criterion

f

all

things, ince

he

is a

man, assertingwhat

ppears

to

him,

nd

thereby

conceding

that

the

very thing

he

says

is

one

of the

things

that

appears to him(M 7.61). This ratherfeebleargumentreceived an

approvingendorsementfromGrote,

who

in

similar

vein writes

s

if

Protagoras

were sayingno more than

that n discussing nyproposi-

tion, he

Measure doctrine ncluded,all

anyone can do is

express his

own

conviction,

elief

or

disbelief,

nd the reasons which

seem

to

him tojustifyt.1IBut Socrates says s

much himself t 17

d,12

n

an

ironical

comment on the triple

refutationhe has just concluded.

Specifically,

is comment s that

Protagoras mightpop up

with n

answer,

but n

his

absence we have to make the best

use

we can

of our

own

powers

of

reasoning

and

continueto

say

what

seems

to

us

tobe

the case.

Protagoras

must

mean more. Otherwise why should he

press us to

adopt his relativized diom

and trumpet heequivalence

of

"It is true

for

x that

p"

and "It seems

to

x

that

p"

as a substantive

and

important

iscovery

bout

our beliefs?

f

the

equivalence

were

mere

synonymy,

1

and

P2 would both

reduce

to

thebare

tautology

P0 If itseems to x thatp, then it seems tox thatp.

And

to borrow

a

timely emarkthat

Socrates

makes

early

on

in

the

dialogue (152b),

t s

not ikely

hat clever man

like

Protagoras

was

merely

waffling.

Protagoras'

theory s, after ll, a theoryoftruth nd a

theory f

truth must

link

judgments to something else-the

world,

as

philosophersoftenput it,though for

a relativist he world has

to be

relativized to

each individual. To

speak of how thingsappear to

someone istodescribehisstateofmind,buttosaythat hings refor

him

as they

ppear is to point beyondhis stateof mind to the

way

things

ctually re, not ndeed

in

the

world

out ourt

forProtagoras

there

s

no such

thing),

ut

n

the world as

it

s

forhim,

n

his

world.

What

this

relativistic

orld

willbe

like

f

Protagoras'theory

f

truth

is

taken

seriously, he dialogue

explains in terms f the

Heraclitean

doctrine

of

flux.13

Plato uses the notion of flux to describe an

ontological

setting

which satisfies

Protagoras'

contention

that

I

Op. cit.,pp. 349-350.

The endorsement

f

the

argument

n

Sextus

s

n

a

note

on

p.

352.

Equally misguided

are those

who,

embarrassed

by

Sextus'

argument,would

make it betterby textualemendation; cf.

Werner Heintz, Studien

u

Sextus mpiricus

(Halle, 1932), pp. 88-94,

for proposals by

Jaeger and himself.

12

As

Grote points out

in

a note, op. cit.,p.

350

13

I must here simply

tatewhat take to be the outcome of

Theaetetus 52a-160d,

without

dwelling on the

many exegetical

questions that arise along

the way.

181







M.

F. BURNYEAT

genuine disagreement

s

impossible

and no

one's

udgment

can

be

corrected itherbyanotherpersonor

by the udgment-makerhim-

self t anothertime.The outcome of this

Heraclitean nterpretation

of Protagoras

s that ach of us lives n a

private

world

constituted y

a successionof momentary

ppearances,

all

of which re true

n

that

worldquite ndependently f

what

happens next

n

a

givenworld.

n

a given world-say, that of Socrates-whatever appears to

him

is

then and there the case (P

is)

and nothing s the case unless

it

then

and there appears to

him

(P3s).

Such

is

the

kind

of world presup-

posed by Protagoras'

doctrine that each man

is

the measure of

all

things.

Accordingly,

2

is not to

be disarmed on the grounds that t is

merely novel way of

expressing 1. On Protagoras'philosophy

I

has immediate nd drastic

consequences forhow things re in Soc-

rates' world, and theseconsequences are what

S2

seeks to express.

We mightparaphrase S2,

therefore, y

S3

It

is not true

in

Socrates'

world

that,

f

it

seems

to Socrates that

p,

then

it is

true

in

Socrates'

world thatp.

S3 seems

to

say that

n

Socrates' world

t s not a sufficientondition

for

the

truth

f

a

proposition

hat t

eem trueto Socrates.

A

parallel

argument from Socrates' disbelief

n

P3s

willyieldthe conclusion

that t

s

not

a

necessary ondition

ither.

And if

the same

reasoning

applies to everyone who does not

believe the

Measure

doctrine,

which

n

argument 1)

is

everyone, heconclusion hat he doctrine

s

not true for nyone s both

validlydeduced and highly amaging to

Protagoras. No one livesin a world in which his mere beliefin a

proposition

s

either sufficient

r

a

necessary ondition

for

ts

ruth

(in that world). But that

everyone ives n such a world s precisely

what

the Measure doctrine sserts.

Given, herefore,

he

assumption

on

which

argument 1)

is

based,

that

not even

Protagoras

himself

believes his philosophy,

Protagoras' position

becomes

utterly

elf-

contradictory: e claims that

everyone

ives

in

his

own relativistic

world,yetat the same time he

is

forced

by

that

very

laim to admit

that no one does.

But

we can now

see

that

Protagoras' position

would be

equally

inconsistent f, asserting s he does that everyone ives

in

his own

relativistic orld, he could be

forcedto admit that some people do

not. That,

in

fact, seems to

be the essential point of the second

argument

n

the

sequence, (2) (a),

which

aysthat ven

if

Protagoras

did

believe his

doctrine,

t is

that much less

true

than

it

is false

in

182







PROTAGORAS

AND

SELF-REFUTATION

proportion s

thenumber of

people who do not

believe

t s

greater

than

the numberof

those

whodo.

Admittedly,

he

conclusion

of

this

argument s

ambiguous:

it is

not clear

whether Socrates

wants

to

infer imply hatthedoctrine sfalseformorepeople than t strue

for,

which

on the

understanding

we

have

ust reached

would mean

that t

holds of fewer

people's

beliefs han t

fails

for,

r

whether

he

tries o

gobeyond this

othe

conclusion

that t s

more

false

than

true

in

some

absolute

sense.

If

the

latter, hen

he

has

already

begun

to

relax his

grip

on the

relativizing

ualifiers

beforehe

gets to

the

peritropergument

2) (b).14

Supposing,

however,

that

he is to be

censured

on

this

score,

his

argument can

still be

regarded

as an

extension, lbeita questionableone, of the correct

point

that

Pro-

tagorascan

be

forced

nto

nconsistency

f

there

s

anyone

who

does

not believe his

doctrine-indeed

if

there

are

people

who

do not

believe tfor

the

simple

reason

that

theyhave

never

heard of t.

For

on

Protagoras'own

showing

such

persons

do

not,

as

Protagoras

alleges

we

all

do, live

in

a

world

in

which

their

mere

belief

in a

proposition s a

sufficient

nd

necessary

condition for ts

truth

in

thatworld).

All

this

omewhat

lters

heposition

with

regard

to

argument 2)

(b) of

the

sequence.

The

position was

that

the

argument Plato

ap-

pears to

give

starts

out

from an

unrelativized

premise

A)

which

Protagoras

does

not

hold, while

the

argument

to

whichPlato is

entitled,

the

argument under

(M)

which

respects

the

role of the

qualifiers,eads

only to the

seemingly

harmless

conclusion

0)

that

the

Measure doctrine s

false

for

Protagoras'

opponents.

But

we now

have reasonto askwhether0) really s as harmless s it sgenerally

thought to

be.15

The

evidence of the

earlier

argumentsof

the se-

quence, as

I

have

interpreted

hem, s

that

Plato for

one

would not

think

t

harmless.

f

the Measure

doctrine's

being false for

a

whole

lot

of

people

means

that

Protagoras'Truth

oes

not, s

it

purported

14

Either

way,

Plato

evidently

njoys

the irony

of

measuringthe

extent

of truth

Protagoras

can claim

for his

theoryby

counting

heads. Such

a

procedureshould

be

anathemato Protagoras, inceone greatargumentformakingtruth elative o each

man is

that

therwise ruth

willbe

decided by

he

arbitrary eight

f

numbers,

what s

called

truth

bsolute

being

nothing

but what

seems

to

the

majority

o be

the case

(for

this

line of

reasoning in

association

with

Protagorean ideas,

cf.

Aristotle,Met.

1009bl-7 and

the analogous

argument at

Theaet.

158de).

15

E.g., Sayre,

p.cit.,

p. 88,

describes

he

result hat

he

Measure

doctrine s

true

for

Protagoras

nd

false

for omeone

else

as "neither

here

nor

there s far

s the

original

thesis s

concerned."

183







M.

F.

BURNYEAT

to do, give a valid theory f truthfor their udgments and

beliefs,

and

this

unhappy consequence (0) follows rom

he assertion

f the

Measure doctrine M) togetherwith he

undeniable

fact

N)

that

M)

isjudged falseby ll thosepeople, then M) is ndeed self-refuting;t

least, it is self-refuting

n

the same sense and

in the same sort of

dialectical ontext s

I

sketched

n

my arlier

paper when discussing

Sextus' versionof the

argumentunder A).

That

being so,

we should

at least consider the possibility hat theargumentunder (M) is the

argument Plato intends all along. A hypothesiswhich creditsPlato

with n argument hat s both validand relevant s

at least as deserv-

ing of notice as hypotheseswhich accuse him ofinadvertence, on-

scious overstatement, r perverse dishonesty.

Let us

be clear

what this

new hypothesis sks

us to suppose. First,

we are to understand true"

n

"Everyjudgment

s true"

A)

to mean:

true

for he person whose udgment

it s.

Just

his,

f

course,

s

what

we expect

to

find

fter he nitial eference o

Protagoras'

own view

(17 la7),

which

A)

is

meant to formulate.

urthermore,

f

A)

is not

so

understood,

what

the opponents disagree

with

when

they udge

that A) is falsewill not be the view of Protagoras;that s,notonly

Socrates'

argument

but

Protagoras'opponents

too

willbe

guilty

f a

striking rrelevance.Second, having once

adopted

the

appropriate

reading of "true," we must stick to it

throughout the argument.

Thus the conclusion (C) which follows from

A), so understood,

together with the empirical premise B), is that it is true forthe

person

whose

judgment

it

is-in

this

case, Protagoras'

opponents-that

the Measure

doctrine

is

false;

and the

further

conclusion D) whichfollows rom hat sthat hedoctrine s falsefor

these same

people.

In

a

sense, therefore,

we

need

only

to

give Plato

the benefit

f

the doubt once, the first ime he omits the

qualifier,

where

charity

s

easiest,

and

the

requirements

of consistency

will

carry

s

through he restof the rgument. would

claim,

t

any rate,

that

this,the most charitablehypothesis, sks rather ess of one's

credulity

han

the

rival

suggestions

f

nadvertence,

onscious over-

statement,

nd

perverse dishonesty,

ll

of which

compound

the

errortheyattribute o Plato by makinghis argumentcommitthe

philosophical sin of irrelevance s well.

It should be emphasized thatthe hypothesis s

meant to deal only

with

Protagoras' predications

of "true" and

"false,"

not with

his

opponents'

use of

those

terms.

Theiropinion

is

correctlyepresented

bythe unrelativized ccurrenceof the predicate"false"

n

B) or N).

The

opponents are people who hold the

doctrineof

Man the Mea-

184







PROTAGORAS AND SELF-REFUTATION

sure to be false withoutqualification,not

merely false for them-

selves, for

n

rejectingProtagoras' philosophy

they o ipso reject at

the same timehis dea that he ordinaryman's

predications f "true"

and "false"stand nneed of relativizing ompletion. n this nstance

omission of the qualifier

s

a

virtue,not a defect

n

Plato's exposi-

tion.

6

Having

thus

delimitedthe nature

and scope of my hypothesis,

should like now to plead that t has one

major advantage over its

rivals, hat

t

explains, or explains better,

why the peritropeif with

Sextus we

may

continue

to

call it

that)yields

onlyan interim onclu-

sion. I haveinsisted hat heperitropergument s not meantto stand

on

its

own

but

is

part

of

a more

complex

structure f

reasoning

formed

by

the

sequence

of

three linked refutations.

Within

that

16

Cp. 170b8-9where

the ordinaryman's concept

of expertise sophia) s (partially)

explained

n

terms f

the ordinary bsoluteconceptof truth: heordinary

man thinks

that expertise

s

true

udgment and ignorance

is false udgment, where

this means

true and false simpliciter.

Others who have

appreciated the point are

Steven S. Tigner, "The 'Exquisite'

Argument at Tht. 17 a" (Mnemosyne, 971), and John McDowell, Plato Theaetetus

(Oxford, 1973), p.

171, but they further uppose there

is

a difficulty

n it for

Protagoras-the difficulty,amely, hat fhe must

llow his opponents to

say that he

Measure doctrine s false

without ualification, his commitshim to recognizing

or

making ense of the ordinary,

bsolute conceptof truth nd falsity. ut what

xactly s

the difficulty?rotagoras'

theory s a theory bout

the unrelativizedpredicationsof

the

form

x

sF,"

"x

s

G,"

withwhichpeople ordinarilyxpress their iews,

nd as such

it can cover unrelativizedpredicationsof "true" and "false" no less than

ordinary

predicationsof "hot"

and "cold," "large" and

"small," etc. What the theory annot

countenance sthat uchpredications hould be true s they tand,without comple-

tion specifying or

whom they re true-but that

hey re so true as they tand could

hardly e established

t this tage of the rgumentfrom he mere fact hat

Protagoras'

opponents express

their opposition

in

ordinary

nonrelativisticanguage (Tigner's

contrary iew

is

based

on faulty easoning, exposed

by Lee, op. cit.,pp. 244-245).

On the other hand, the presence

of one

(justifiably)

nrelativized

premise

might

suggest, ywayof explanationof theotherunjustified

ne, thatPlato was confused

by

the need to

handle qualified

nd

unqualifiedpredications

f "true"

and "false" at the

same time; cf. esp. 17

b

1-2 where he moves from"The opponents think

hat Pro-

tagoras'

view s

mistaken" o "Protagoras

oncedes that

his

own view s

false." would

prefer hishypothesis o those of nadvertence, verstatement,nd perversedishon-

esty,

ut t

seems

unlikely

ll the same.

The move at

17

b

1-2,

for

xample,

s

explicitly

licensed by Protagoras'

greement thathis opponents'

opinion is true,

which t once

takes us back to the question of how

we are to understand A).

It

is

perhaps

sig-

nificant hat Plato reserves

the verb ei68ecrOat,o be mistaken,

or the

opponents'

unqualified views:

Protagoras,theythink, s

mistaken 171a8,b2),

while

they

them-

selves are not (171b4).

Protagoras' udgments,

by contrast, se

the

adjectives

"true"

and

"false" throughout17 a8-b

1.

185







M.

F.

BURNYEAT

structure

t serves

to

complete

the dilemma

posed

at

170e-171a.

Either

Protagoras

did

notbelieve

theMeasure

doctrine

r he

did.

If

he did

not,

then,

since

no

one

else

does

either,

he doctrine

s

not

true foranybody.That was argument 1). The otherlimb of the

dilemma

s complicated

by

the

subdivision

nto 2) (a)

and

(2)

(b),

but

itseventual

outcome

s meant to

be

the

same:

supposing

Protagoras

did

believe

his

doctrine,

tstill

ollows

hat

he

doctrine

snot

true

for

anyone.

This

outcome

is reached-and

the

argument

s

not

com-

plete

until

then-when

Socrates

is

in a

position

to

conclude

that

since

Protagoras'

Truth

s disputed

by everyone,

Protagoras

in-

cluded, it

is

not

true

for

anyone

at

all

(171c5-7).

(Notice

that

the

conclusion

s

expressed

nproperly

elativistic

erms,

o lessthanon

its

firstppearance

as

the

conclusion

of

argument

1].)

To

get

to

the

point

where

he

can deliver

this rowning

blow,

Socrates

has

to

show

that

Protagoras

oins

with

everyone

else

in

disputing

his

theory

of

truth.

That

is

the

function

of

the

peritrope,

o

demonstrate

that

Protagoras'

own

belief

in

his

doctrine

counts

for naught:

he

is

committed,

espite

himself,

o

agreeing

with

other people

that

t

s

false.False simpliciterrfalsefor hem? f(D) is takenat facevalue,as

saying

hat

Protagoras'

iew

s false impliciter,

ocrates

would

seem

to

have completed

his

refutation

y 171b2,

where

myoriginal

quota-

tion

of

the peritrope

assage

ended.

He

would

have

established

that

the

theory

in

(A)

-never

mind

that

it

is not

Protagoras'

real

theory-is

false,

that

Protagoras

must accept

it as false,

and

con-

sequently

lso

(though

by

now

it hardly

matters)

hat

t

is false

for

Protagoras.

n

the

text,

however,

ocrates

has

quite

a lot

more

to

say.

In the firstplace, myquotation lefta dangling "for his part"

(171a6:

1.v)

introducing

Protagoras'

udgment

on

his

opponents'

opinion

that

his

theory

s

false.

This

is

picked

up at 17 1b4

8Uy')

and

a contrast

s

drawn

with the

opponents'

own

judgment

on

this

opinion

of

theirs,

which s,

of

course,

that

t s not mistaken

but

the

correct

opinion

to

hold:

Whereas

they,

or their

part,

do not concede

that

they

re

mis-

taken.... And he, once more,fromwhathe has written grees that

this

udgment

lso

is true 17

b].

This

udgment

also

Protagoras

will

have

toadmit

s true

f

he

is to

be

consistent

with

whathe

wrote;

the

further

eference

o

Protagoras'

written

octrine, ight

n

the

middle

of

therefutation,

harpens

the

difficulty

f

the

nadvertence

nd

overstatement

ypotheses.

On

my

186







PROTAGORAS

AND

SELF-REFUTATION

reading,

by

contrast, all we

have

here

is a small

but

perfectly

correct

point

which can be

unraveled as

follows:

Protagoras must

concede

that his

opponents'

judgment that their

opinion

that his

theory

is

false (simpliciter)s not false

but true

(simpliciter)

s

itselftrue

-for the

opponents

whose

judgment

it is.

More

important,

however,

than

this

extra turn of

the

screw is that

Socrates next

proceeds

to

argue

that

since

Protagoras joins with

everyone

else

in

disputing his

theory, it is

not

true for

anyone,

neither for him

nor

for

anyone else.

It is

disputed,

then, by

everyone,

beginningwith

Protagoras-or

rather,t sagreedbyhim,when he concedes tothepersonwho says he

opposite

that

he judges

truly-when he

does

that, even

Protagoras

himself

oncedes

thatneither

dog

nor anyman

you

chance

to meet sa

measure

concerning

anything

t all he

has

not

learnt.17 s that

not

so? ...

Accordingly, ince

t s

disputed by

everyone, rotagoras'

Truth

cannot

be

true for

anyone: not for

anyoneelse

and

not for

Protagoras

himself

171bc].

My hypothesis makes intelligible the need for this last stage of the

argument.

If

(D)

is

understood

as

stating

no more than

that the

Measure

doctrine is

false for

Protagoras'

opponents-that

is.

(D)

=

(0)

-Socrates at

17

1b2

still has

work to do

to

get

from

Protagoras'

17 After

heurbane irony

of the

"exquisite"

paragraph,

this

trikinglynacoluthic

sentencewith

ts

erky yntax omes

ike a

suddencrescendo of

quite

savage

triumph.

If

thatdoes catch the

tone, t

would

help toexplain

Theodorus' shocked

comment t

theend oftheargument, We are runningdown myold friend oo hard,Socrates"

and

Socrates'

unrelenting

eply,

But, myfriend,

t

s

unclear

f

we

are also overrun-

ning what is

correct"

(171c8-10). I

would

like to

think

that while

Theodorus

is

prepared for

Protagoras to be

refuted-he has, after all,

undertaken to

see the

discussion

through

to the point

where

it

can

be

decided whether t

is his

friend's

philosophyor his

own

claims to expertise

that must

give

way (169a)-he is

taken

abackby the

spectacularform

n

which he

refutation

inallyomes,

with

Protagoras

himselfoining the

ranks

of the

many who

dispute the

doctrine

that man is the

measure of all

things.

Certainly ocrates n

his

speech of

171c9-171d7 s as

cuttingly

sarcastic s anywherenthedialogue. Later,whenTheodorus has had timetoreflect,

his

considered view

of the substance

of the

argument

s that t s

conclusive

against

Protagoras (179b).

This

verdict is not to

be

discounted

on the grounds that

Theodorus

is an old man who

prefers

igressions o

philosophic

rgument Sayre, p.

cit.,p. 90, n.

29,

alluding to

177c). Theodorus is

old and a bit stiff

or

rgumentative

combat

(162b),

but

we have seen

enough of

the great

mathematician's

dramatic

stature

n

this

part of

thedialogue to

know

thathis

opinion sto be

taken

seriously.

n

anycase, the

context at

179b

precludes

doing

otherwise.

187







M. F. BURNYEAT

acceptance

of

this

o

his final onclusion

that he doctrine

s

falsefor

Protagoras

as well

as for

his

opponent.

How

does he manage

thefurther

tep?

Protagoras'

undoing,

he

says,

s his admission

that n opponentwho contradicts im udges

truly 17 1b9-

1).

To

admitthat s to

admitthat dog

or

any

man

you

like to

pick

is not the

measure

of

anything

t all,

unless

he has

acquired

knowledge

sc. objective

knowledge

n the

ordinary

ense)

of

the

thing

n

question

17 Ic 1-3).

This

I

take

to

be a

reference

othe

claim of

the Measure

doctrineto

give

a theory of

truth

for

the

judgments

of

any

and every

man, and

of

his dog too

if t

s insisted

thatdogs are capable of udgment.18And we can understand

the

reference,

ven

while

construing

rotagoras

to

mean

that

the udg-

mentopposed

to

his assertion

f the

Measuredoctrine

s truefor

he

opponent

whose udgment

it

is,

if

we recall

what was said

earlier

about the connection

between

S2

and S3.

I

suggest,

n

fact,

that

Socrates

is

drawing

that connection

here. He

is

pointing

out

that

what

it means

for

the

Measure

doctrine

to be

false

for someone

is

that

he

is not a Protagorean

measure:

which s

to

say that

his

mere

belief n a proposition sneither sufficient or a necessary ondi-

tion

forthat

proposition

o be true

n

some

relativistic

ense. Thus

it

is

fromProtagoras'

dmission

hat he

Measure

doctrine

ails

ogive

a

generally

validtheory f

truth hatSocrates

finally

nfers

hat

he

doctrine

s not truefor

Protagoras

or

for anyone

else

(171c5-7).

This

yieldsthe

following-account

f argument

2) (b) as

a whole.

The peritrope

ets

Protagoras

to accept

the

interim

onclusion

that

his theory

s false

for thers.But

to

admit his, t

s argued,

s to admit

thatnoteveryone s a Protagoreanmeasure.Hence itfollowsfrom

Protagoras'

dmission

that

his

theorys false

for

others

hat t

s

false

for

himself s well. There

is a

passage

from p

s falseforProtagoras'

opponents"

to

"p

is false

for

Protagoras"-in

the one

special

case

wherep

is

the Measure doctrine

tself

M).

And

it

s

this

passage

that

has still

o be

made after

he

nterim

onclusion

has

been reached

at

17 b.

Such is

the

reading

that

my hypothesis

uggests

for

thistrouble-

somesectionofthe dialogue.As a hypothesis oexplainwhatPlato s

up

to here

it s, submit,

uperior

tothe rival

hypotheses

withwhich

18

A

dig at

Protagoras-one

of several-for

putting

theranimals

on

a level

with

man as

regards

cognitive

apacities

cf.161c,

171e with

154a,

162e, 167b).

As becomes

clear at

186bc,

the skirmishingn

this topic

dramatizes

fundamentalphilosophical

disagreement

over

the nature and

interrelations

f

perception,

udgment,

and

knowledge.

188







PROTAGORAS AND

SELF-REFUTATION

I

have contrasted

t,

but

a fulltreatmentwould

require an

equally

close

examination

of an

earlier

paragraph where

the

qualifiers

re

omitted,170c,

and

of the

section 170de between

that nd

the

triple

sequence which s a model ofclarityn the matter fputtingn the

qualifierswhen

Protagoras

s

speaking and

leaving them out

when

other

people's

udgments

are

reported.

All

this

s

to be

weighed

in

the balance and compared with

other places in

the dialogue

where

Plato omits the

qualifiers there are, in fact, a

number of

places

where

this

happens, though none

is

so

problematic s the one

under

discussion). But

I

do not wishto

undertakethese further

xegetical

inquiries here.19

have

recommended my hypothesis, nd

with

more

in

view

than

that t

should carry

conviction

s an

account

of

Plato's procedure. It

embodies

a philosophical

claim which

I

am

anxious

should stand

in

its

own

right-namely, the

claim

that

the

argumentunder

(M)

is

not

the harmless

thing

that

defenders

of

Protagorashavealways aken t

to be. About this

have a littlemore

to

say.

19

Dogmatically, owever, yway of orientation: he argument t 170c s a dilemma

forced

on

Protagoras by the fact that people believe, contrary

o

the Measure

doc-

trine,

hat

mistakes

nd

false udgments

occur.

If

they re right

o think hat here s

false udgment, there

s. But

equally,

f

they re wrong n thisor any otherjudgment

of theirs, hen there

s

false udgment (forhere

is an

instanceof t). So, whether ight

or wrong, heir pinion spells troublefor Protagoras

n

the form f

a

conclusion, he

existenceof false udgment,whichhe must deny. Accordingly, ocrates goes on to

claim

that

to

dodge

the dilemma a

Protagorean

will

have no

recourse but to

deny,

quite implausibly, hat people do think each other ignorant and guilty of false

judgment

(170cd).

Now it s possible,but not obligatory, o understand the text s stating r implying

for

the first

imb

of the dilemma not the straightforwardnferenceust given but the

following

ariant

of

the

peritropergument:

If

A) everyudgments true,

and B)' it s udged that ome udgments false,

then

C)'

it s

true

hat ome

udgment

s

false

and,

consequently,D)

(A)

is

false.

(It is not possible, because it simplydoes not square withthe text, o read back the

exquisite peritrope

ith

B) or (N)

in

place of (B)', as does McDowell, op.

cit.,

pp.

169-170.) Eitherway, he refutations so cryptic

hat

Theodorus naturally sks for

n

explanation 1 70d3).

Socrates

responds by prefacing

his

triple

efutation

with lucid

and

entirely ccurate account 1 70de),

first

f the key dea that ne may

think

nother

person's udgment is false, and second of what Protagoras' theory ommits

him to

saying bout the situation.The effect f this ntervening aragraph

is

to give

a model

treatment

f the qualifiers o be applied both tothe subsequent refutation-it is,

n

fact, he model followedby my reading of those arguments-and, so far as may

be

needed, to the preceding refutation t 170c also.

189







M. F. BURNYEAT

My

argument has assumed,

as

I

thinkPlato's arguments all as-

sume,thatProtagorasputs

forwardhis doctrine s a

valid theory f

truth

for veryone's

udgments and beliefs. t is

meant to be true of

those udgments and beliefs;what it assertsof them t asserts, m-

plicitly

t least,to be true

period). Now it s often aid that o assert

somethings to assert tto be

true. What s meant s,

roughly, hat n

assertion

one manifests n

intention f presenting

truth, ot that

everyonewho makes an

assertion xplicitly redicates

ruth

f some

proposition or describeshimself s propounding

something rue;

thesewould

themselves e

assertions ike any other.)

The point s no

doubt

correct.But we mustbe

carefulnot to use it gainstProtagoras

in a question-beggingway.Passmore, for example,writes:

[E]ven

f

we can make ome ense f

thedescription

fp

as

being

true

forx"-and what an

we take

t

to mean

except

hat x thinks

is

true"

which t

onceraises he

uestion

whether

t

s

true?

Protagoras

is still ssertinghat pis trueforx" and

"p

is not truefor

y";

these

propositions e

is

taking

o be true. t has to be

truenot

only

forx

but for

everybody

hat

p

is

true

forx" sincethis

s

exactly

what

s

involvednassertinghat man sthemeasure fall things."

The fundamentalriticism

f

Protagoras

an now

be put thus:to

engage

n

discourse t

all

he hasto

assert

hat

omething

s

the ase.20

No doubt

Protagorasmust ssert omething o be the

case. There

is

certainly

o lack of

assurance

n

the way he begins

his

book:

"Man is

the

measure

of all

things, f

thosethat re, that hey

re,

and ofthose

that

are not, that they are not." No

qualifier

s

attached

to this

assertionof his. Nor to his assertion of itsconsequences, that the

wind is

cold for

x,

that it is

not cold for

y,

and

so on.

But will

Protagoras, when cornered,

admit that he asserts

these thingsas

truth

absolute? We should at

least consider

whether

t is

open

to

Protagoras to reply that he

asserts the Measure

doctrine and its

consequences

to

be true

only

for himself.For

if

he can make

this

defense,we

will

have tomount the

self-refutation

ot from

M)

as it

stands but

from

(Me) It is trueforProtagorasthatevery udgment is

true for the person

whose udgment it is.

20

Op.

cit.,

p.

67.

Passmore's

criticismsa more

developed

version f the one

byJohn

Anderson

mentioned

earlier, n. 2 above.

190







PROTAGORAS

AND SELF-REFUTATION

And fromthis

t is

not so clear how'the

argument

s to proceed.

Here

I

would like

to bring

n

the

curious mage

Socrates

presents

at 17

d

of

Protagoras ticking

is

head

up above the groundto

rebut

Socrates'arguments, nd then disappearingto runaway.Platodoes

not

tell us

what objection

he envisages

bringing

Protagoras

back

from he

underworld,

but

I

doubt

he would

have

written hisway

f

he thought

t a good

one.2'

In fact, t could

not

be a good reply

because,

if

t

were,

n showing ocrates

and

Theodorus

to be mistak-

en

it

would at the same

time prove

Protagoras

wrong as well,

since

on

his

theory

no one

ismistaken

f

hey ay

what

eems

tothem o

be

the

case (cf.

170cand Euthydemus

87e-288a).

Socrates'

rony

t

this

point

is

far fromgentle.

And that

may

be all there is to it:

no

objection

is

specified

because

none

is possible.

Even

if

Protagoras

cannot attack

Socrates,

however,

he might

ry

to

defend

himself.

tseemsa significant

lement

n

the mage

that

he

runsaway after

delivering

his rejoinder;

he is not

preparedto stay

and defend

it in

discussion.22

The

implication

s at least that

the

reply,whatever

t s, will not

stand up to

discussion. fancy

hatthe

irony s morepointedstill, nd thatwhattheonlyreply eft mounts

to

is a

refusal

to

submit

to dialectical

discussion.

For is this

not whatProtagoras

would be doing

if he insisted

hat

he asserted

the Measure doctrine

as true

forhimself nd

himself

alone?

That would mean

dropping

the thesis

hat

M)

is

true

of and

in

Socrates'

world and replacing

tby

the completely

olipsistic

laim

that

t s

only

n

Protagoras'

world that

M)

is true of and in

Socrates'

world,

where Socrates'

world

is

now incorporated

nto that of

Pro-

tagoras. fthis ounds incoherent, hat snot tobe wonderedat,for

what sense

can we make of the

dea thatSocrates

and

his world exist

only

for

Protagoras?

Socrates

cannot be

expected

to

find t

ntelligi-

ble;

he cannot dentify

withthe counterpart

hat

bears

his name

in

Protagoras'

world.

f

Protagoras

does

not speakto

the

human condi-

tion,

does

not

put

forwardhis claim

that ach of

us lives

n

our own

relativistic

orld

as

something

we can

all discuss

and, possibly,

ome

to

accept,

but

simply

sserts

olipsistically

hat

he,

for

his

part,

ives

n

a world nwhichthis s so, then indeed there s no discussingwith

him. His world

and his

theory

o

to

the grave

with

him,

nd Socrates

21

As Runciman's

hypothesis equires;

cf. n.

5 above.

22

So

H.

Schmidt,

KritischerCommentar

zu

Platos

Theatet"

Jahrbicherfir las-

sische hilologie,

Supp.-Bd. 1877-1878), pp. 492-493.

191







M. F. BURNYEAT

is fully ntitledto leave

them there and get

on withhis inquiry.23

But

really ven this s too

generous to

Protagoras, o allow thathe

can

buy safety or his

theory t the price of solipsism.The truth s

thathe isstill sserting omething-namely,

(Mp)

tself and assert-

ing it

withoutqualification. This is no

accident. In settingup

a

relativist heory ike thatof

Protagorasone begins with distinction

between, n the one hand,

the unrelativized

redicationswithwhich

people, Protagorasamong

them,ordinarily xpress

how

things

p-

pear to them to be,

whether

t s

that the

wind is cold or that some

proposition s true, nd, ontheotherhand, the

relativist'sccount

of

these statements,which s that they are true, and theirpredicates

hold ofthe things hey re

ascribed to, for

and only for the

person

whose

udgment the

statement xpresses. Now consider the state-

23

I can now pickup a thread fromnn. 5-6 above and comment n Lee's interpreta-

tion of the self-refutation assage, an interpretationwhich revolves around the

confessedly izarre suggestion hat he mage of Protagoras'return

t 17

d presents

the sophist as a plant rooted in the ground (Lee, op. cit., pp. 249 ff., omparing

Aristotle,Met. 1006a13-15).

It

seems an overwhelming bjection

to

this

dea

that,

f

reduced to a plant, Protagorascould hardlyrun away afterdeliveringhisrejoinder

(171d3:

olXioto

eoffrop0eXv,

hich Lee, op. cit., p. 251, has to place outside the

image), and the question of the meaning of the image, though well raised, s not as

novel as Lee repeatedly vers. In fact, n behalf of the nineteenth-centurycholars

who

did

discuss the matter, t should be said that they came up with at least two

answers quite as persuasive as Lee's.

One

interpretation akes note

of

the

fact that

the image

uses

a

pair

of

verbs,

'fVaKfnKVTElvnd

KaTat8VVal,

which oftendescribe the actionsof, respectively,ifting

the head out of and plungingdown ntowater cf., .g., Phaedo

109de)

and connects

t

withthe rather well-attested iographical detail that Protagoras died by drowning

(according to the oldest source, the fourth-century.C. historian

Philochorus

pud

Diogenes Laertius,

Lives

f

he

hilosophers,X, 55,

his

ship went

down when he was on

his way to Sicily).The explanation of the mage then s that o bringProtagorasback

from he dead Plato quite naturallyhas him raise his head out of the waves and sink

back

again;

thus

August

Bernhard

Krische, Forschungenuf

dem

Gebiete er

allen

Philosophie, (Gottingen,1840), 141; Anne Johan Vitringa,Disquisitio

e

Protagorae

vita t

philosophiaGroningen, 1852), p. 54; Hermann Muller-Strubing,Protagorea.

Zu

den Vogeln des Aristophanes"

NeueJahrbicherfiirPhilologie

ndP&dagogik1880],

Erste Abteilung),pp. 96-97. Protagoras'running way

s

a difficultyor

his

nterpre-

tation

too,

and a

further bjection

s that

the reappearance

is

located "right

here"

(17

Id 1:'EvTeOev)

-i.e.,

in

the

palaestra

or

wrestling

chool

where

the

dialogue

is

set

(cf.

144c

and

the

wrestlingmetaphor

f

162b,169ac). So one mayprefer

n

alternative

interpretation ccording to whichProtagoras merges from he ground ust as far s

the neck

because

that s

the way ghostsappeared

in

the Greek theater, oming up

through

an

opening

in

the stage; thus Karl Steinhart

n

Steinhart-Mfiller,latons

sdmmtliche

erke,

II

(Leipzig, 1852), 206, n. 32; F. A. Paley, The TheaetetusfPlato

(London

and

Cambridge, 1875), p. 59, n. 1; Schmidt,

oc.

cit.

192







PROTAGORAS

AND

SELF-REFUTATION

ments which formulatethe results of relativization, ropositions

such

as

"The

wind s cold for

me"

and

"The Measure doctrine

s

true

forProtagoras."More generally, uppose that, nstead ofspeaking

with

he vulgar,

we tailorour

speech

to the facts s the theorist

ees

them, explicitly elativizing

ur

statements.

hen, surely,

o avoid

applying he doctrine wice ver,wemustput their ruth onditions

in absolute terms. That is, a proposition of the form

"x

is

F"

is

true (relatively)

for

person a,

if

and

only

if

"x is

F

for

a" is

true

(absolutely).Call

this

he principle f translation. uch a principle s

needed,

I

submit,

f

we are to be able to give sense to the notion of

relativetruth nd operate with t in reasoning.

There would seem, then, o be a whole series of absolute truths o

which Protagoras commits himself by propounding a relativist

But

perhapssimpler nd

better

hanany of

thesewould be the

following,

uggested

by the

interpretation

have offered

of the

philosophical point

at issue.

It is not

Protagoras'

carriage or demeanor

that

matters, or the

mechanics of his

reappear-

ance,

but

the fact

that,

oming fromand

retreating o

another

world

than

ours, he

does notreally eave

the

underworldwhen,

upposedly,he

pops

up

to refute

ocrates

and

Theodorus for

talking

nonsense (cf. 17

1d2-3).

His

"refutation" r

defense,

n

other

wordsjustis a

refusal o enter

fully nto

common worldwith

his

opponents

for

discussion.

And

that, haveargued, s a fair

haracterization f the

move from

M)

to

(Me), the

only nd the obvious

move

left o

Protagorasnowthat

he

has

been refuted

on the basis

of the

Truth s

he

actually

wrote

t.

So much

for the

image

itself.Lee's

interpretation f

it

is

designed to supportan

account

of the

peritrope

rgument (op. cit., pp.

242 ff.)

which, as

I

understand

it,

involves

wo chiefclaims:

a) that the

effect f the

qualifiers s to

make

Protagoras'

statements

mere record of his and his

opponents'

subjectiveattitude,

so

that

Protagoras must omit them if he is to present a thesis that can significantlye

discussed

or denied

-although then, f course,

he

becomes iableto Socrates'

refuta-

tion; b) that

nce

Protagoras tarts

utting

n

the

qualifiers

o avoid the

refutation, e

must n

consistency o allthe way to

Me), so

thathe

ends up sayingnothing

hat an

seriouslybe

discussed. On this

basis, Lee

suggests

that

Socrates' omission of the

qualifiers s a

deliberateirony.

t

shows

Protagoras what

is

required

if

he is

to be

"takenseriously,"

n

accordance

withhis

own

demand, as

one who has

something o

say,

nd

what

onsequences

then

follow,

nd

leaveshim

the

uncomforting

lternative

of

withdrawing o

the reduced

and,

as

Lee thinks,

plantlikeposture of

(Me).

Myquarrel withthistheory s in part thatcertain of itssupportingprops do not

stand

firm

nder

examination: ee

n.

10

aboveon the

understanding f thequalifiers

premised in

(a), n. 6 on the

role of

irony n the passage

and the

importanceof the

missing

ualifier n A),

while as for

b),Protagoras s

onlybound

to go all

the wayto

(Me)

if

Socrates

successfully

hows,

n

all

seriousness,

hat

he cannot stop at

(M).

I

think,

nd

have

argued, thatSocrates

does show

this,

ut

by

hard

ogicnot

by

ronical

insinuation,which

s all

that Lee offers.Thus

while I

agree withLee about

where

Protagoras

nds up, our

interpretations iverge

fundamentally n

what

t

takesto get

him

there.

193







M. F. BURNYEAT

theory

f truth:

he

wind s

cold forme, the

wind s not cold foryou,

and so on.

Equivalently,when a person a

statesthatsome proposi-

tion

p is

true,

and

the Measure doctrinedeclares that p is true

(relatively) or , this n turn means, by theprincipleof translation,

that"p is truefor " is

true absolutely).

n

particular,

f

Protagoras

puts forward

his relativism nd agrees that

this doctrine, n con-

sequence

of

itself

nd

his belief

n

it, s true

for him, he must still

acknowledge t tobe an absolute truth hatthe

Measure doctrine s

true

for

Protagoras Me).

It may be

objected here thatthe predicate"true" s a special case.

In

its absoluteuse it allows ndefinite eiteration f the prefix It is

true that

9.,"

since

any proposition is true

f

and only

f

"It is true

thatp"

s

true,which

t

s

f

nd only

f

Itis true

that

t s

truethatp" s

true,

and so

on

indefinitely.

hat

being so,

why should not Pro-

tagoras adopt

a

relativisticnalogue of theprefix It is true that .. ."

and

say of the

alleged absolute truths hat

theyare not what they

appear to be -it is

not absolutely rue,but only

true forProtagoras,

that the wind is cold

for me? This is not

likely

to

be

true

for

Protagoras'opponents who, iftheyknowwhat they re about, will

say that he

wind

mayappear

cold to

me but

whether

t s

cold or not

is another

matter.And if, n the face of

Protagoras' ttempt o empty

the

dispute

of

content, he opponents go

further

nd

deny

that

t s

even true

for

Protagoras

that

the

wind

is cold

for

me,24

cannot

Protagoras come back again with It is true for

Protagorasthat t s

true for

Protagoras that the wind is cold for

me"? And so on

in-

definitely?

No, Protagorascannotevade the principleof translation ythis

maneuver.

His

position

s

supposed

to

be

that

x is

F

orp

is true for

just

in

case it appears to a or a judges that x

is

F

or

p

is

true;

and this s not

an

arbitrary

onnection

r one that an

be abandoned

without ur

losing grip

on the notion

of

relative

ruth.

Protagoras,

as Socrates

keepssaying,

s a

clever

fellow,

ut he

is not so clever

hat

there

s no limit

o

the

complexity

f

the

propositions

he can

under-

stand and

so

udge

to

be true.

Therefore,

the

relativistic

refix

It

is

true forProtagorasthat

...,"

unlike the absoluteprefix, dmitsof

only

imitedreiteration.

At

some

point,though

we

may

not

be able

to

say ust

where, Protagoras

must

top

and

take

a

stand.

And

once

committed,

f

only

in

principle,

to

an

absolute

truth,

he

can no

24

They ould ay

his

nthegroundshat othings

true or rotagoras:nce

his

theory

s

rejected,

ts

oncept

f relative

ruth

will ack

pplication.

194







PROTAGORAS

AND

SELF-REFUTATION

longer

maintain

hat all

truth

s

relative

nd

any

udgment

whatso-

ever

true

only

for

the

person(s)

whose

udgment

it

is.

In

the

end,

therefore,

assmore's

criticism

s

essentially

orrect.

No amountofmaneuveringwithhisrelativizing ualifierswill xtri-

cate

Protagoras from

the

commitment

o truth

absolute which

is

bound

up

with

the

very ct of

assertion.

To

assert

s

to

assert

that

p -as

Passmore

puts

t, hat

omething

s

the case -and

ifp, ndeed

if

and

only

if

p,

then

p

is

true

(period).

This

principle,

which

rel-

ativism

attempts

to

circumvent,

must

be

acknowledged

by

any

speaker. How

clearlyPlato saw

that,

hesitateto

say.

But

at some

level

it is

surely

what

he is

reacting

to.25

University

ollege

London

25

This

paper was

completed

during

my

tenure

of

a

Radcliffe

Fellowship.

I am

grateful otheRadcliffe rustforthe eisurethisgave me and toUniversity ollege

London

for

llowingme

totake

up

the

Fellowship.

The

inspiration

or he

paper

and

the

conviction hat ts

final

onclusion s

the

right

ne toaim

for

goes back

to a

lecture

I

heard

Bernard

Williams

giveas

long

ago as

1964.

I

owe thanks

o

himand

to

David

Wiggins,

Christopher

Kirwan,

and

Richard

Sorabji for

pointingout at

meetings

n

London and

Cambridge

fallacies

committed

n,

uccessive

ttempts o

vindicateor

make

sense

ofPlato's

argument. f, as I

hope,

I

have

got

tright

now,

hat s n

no

small

measure

due to

other

people's

encouraging

corrections.

195

Miles Burnyeat Self Refutation

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