burnyeat, m. f._protagoras and self-refutation in later greek philosophy_phr, 85, 1_1976!44!69

8/9/2019 Burnyeat, M. F._protagoras and Self-Refutation in Later Greek Philosophy_PhR, 85, 1_1976!44!69

1/27

hilosophical Review

Protagoras and Self-Refutation in Later Greek PhilosophyAuthor(s): M. F. BurnyeatSource: The Philosophical Review, Vol. 85, No. 1 (Jan., 1976), pp. 44-69Published by: Duke University Press on behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2184254 .

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2/27

The Philosophical eview,

LXXXV, 1, (January 1976)

PROTAGORAS

AND SELF-REFUTATION

IN

LATER GREEK PHILOSOPHY

M. F.

BURNYEAT

If

a

philosophical argument s worth attention, o is its history.

Traces it has left n the

thoughtof philosopherswho have con-

cerned themselveswith t have

the historical mport heydo in part

because they reveal aspects,

often unexpected ones, of the argu-

ment's philosophical nterest

nd significance. uch is the case, at

any rate, with the argument want to investigatehere.

This is an argumentdirected

gainstProtagoras, he mostfamous

of the

Greek sophists of the

fifth

enturyB.C., claiming

that his

doctrine hatman s the measure

of

all

things

s

self-refuting.

t

s an

argument

which had a

long

history.

The most familiar version

occurs

n

Plato'sTheaetetus

17 lab),

where

t has an

important art

to

play

in

refutingthe extreme empiricist pistemologywhich the

dialogue elaborates out of a

definition f knowledge as perception.

But already before PlatoDemocritushad used the argument,' and

in

his hands

it

no doubt

played some part

in

securing

the

epis-

temologicalfoundations f

atomism.AfterPlato the argument p-

pears

in

Book Gamma of Aristotle's

Metaphysics1008a28-30,

1012b13-18; cp.

K.1063b30-35)

in

connection with Aristotle's

de-

fense of the law of

contradiction.

t

then

turns

up again

in

the

writings

f Sextus

Empiricus

as

part

of the

Skeptic philosophy's

elaborately ystematic

efutation f

all

dogmatisms.

his lastcontext

is the one I shall be consideringhere.

Sextus

was the

leading Skeptic

philosopher

of

his time

circa

200

A.D.) and his survivingworks, utlines

f yrrhonismabbreviated

H

from he Greek title) nd Against heMathematicians

abbreviatedM),

are

full

of information bout the

controversies

hat

tookplace be-

tween and within he

philosophical movementswhich

grew up

in

1

The evidence is the

passage of Sextus Empiricus

which s to be quoted shortly.

Admittedly, extus s thesole testimony o the fact,

ut there ppears to be no

reason

to distrust him and there is independent evidence

that Democritus wrote, in

Plutarch'swords (Against

olotes1 109a, in Hermann Diels and Walther

Kranz, Die

FragmenteerVorsokratiker10

Berlin, 1960-1961; henceforth K] 68 B 156),

persua-

sively nd at ength gainst

Protagoras.The natural

nference s thatDemocrituswas

in

some sense the inventor

of the argument. t hardlycounts that Plato

does not

acknowledge his predecessor's

use of it, since the name of Dermocritus

s never

allowed to

appear

in

any Platonic work.

44


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3/27

PROTAGORAS

AND

SELF-REFUTATION

the period after he death of Aristotle.

he Greek Skepticswere en-

gaged on all-sides

n

attempting o show up the worthlessness

f

other philosophers'dogmatisms,

meaning any definite

iews

about

externalrealitynd matters ot mmediately vident nappearance.

The goal of theirargumentswas

to induce epoche, complete sus-

pension of judgment and the

cessation of all definite assertion

beyond the acknowledgment of

immediate appearances (cf. PH

1. 13-15). Naturally, hese argumentsdid not go unchallenged. The

Stoics

n

particular, he great logicians

of the period,

had much to

say

n

defense of theirown

brand

of dogmatism.What hope

to

do

byplacing the self-refutationf

Protagoras

n

the context f some

of

these controversiess,on the one hand, to illuminate heargument

itself nd, on the other, o call attention o some interesting eatures

of

the

controversies

nd the methods

by

which

hey

were conducted.

A

subsidiary im is to contribute

o dispelling he impressiongiven

by o manyhistory

ooks that he period was one of rigid

chools

and

systems,

without he discussion nd debate which

nlivens he work

of

Aristotle, lato,

and

their

predecessors.

But

first, preliminaryword

about Protagoras himself nd the

doctrine whichthe self-refutationrgument proposes to subvert.

Protagoras wrote a book entitled

Truth,which began

Man s themeasure f ll things,

fthose hat re, hat hey re,

nd of

those hat re not, hat hey re

not.2

According to Plato, whose account

in

the Theaetetus as by far the

best claim to

authenticity,

his

pronouncement

ntroduces form f

relativism. he doctrine hatmanisthe measureof all things sserts

that

each

man is the measure or authoritative

udge

of how

things

are for

him,

in

this

sense,

that

things

are for

him

exactly

as

they

appear to

him

to

be. Perceptualappearances

are the

paradigm

case:

here we can understand It

appears

to a that

p

as

recording

a

perceptual experience

which he doctrine

laims s

nvariably

eridi-

cal

(for

the

perceiver).

But

Protagoras pplied

the samn-e

rinciple

o

nonperceptual ases, where,

ne

might hink,

It

appears

to

a

thatp

hardly amountsto more than that judges or believes thatp. The

extension

may

have little

but bluff

o

support t,

but that

difficulty

2

The

title nd the positionof the fragment

re vouched

forbyPlato,Theaet.

16 c.

Sextus

Empiricus,

M

7.60,

confirms he positionof the quoted fragment

ut

gives

a

different

nd probably

ater title, ownthrowers,

hich no doubt

reflects he type

of

argument

to

be found

in

the book.

45




4/27

M. F. BURNYEAT

need not concern us here. It suffices hat Protagoras' position, c-

cording

to

Plato,

s

that, uite

generally, he way a man takesthings

to be is the waythey re for

him, o that very udgment whatsoever

is true for the person whose udgment it is.

AfterPlato, however,

n

Aristotle, extus Empiricus, nd the ater

sources generally,Protagoras

s understood ratherdifferently: ot

as

a relativist ut

as a subjectivist hose view s that

every udgment

is true simplicitertrue

absolutely,not merelytrue for the person

whose

udgment

it S.3

To illustrate

he difference: he subjectivist

version of the Measure

doctrine s in clear violation of the law of

contradiction, ince

t

allowsone person's udgmentthat omething

is so and another person's udgment that t s not so both to be true

together; whereas the relativist

ersion can plead that

there is

no

contradiction

n

something

being so for one person

and not so for

another.

The differencewill also show itself

n

connection

with he

self-refutationrgument.

t is

certainly

urious thatwhat

ppears

to

be one and the same argument hould be found

in

both Plato

and

the

later writers,despite their

different nterpretations

f Pro-

tagoras and despite the fact

that

it is

not at all obvious

that the

argumenthas equal validity gainst both the relativist nd thesub-

jectivist

versions

of

his

philosophy.

But

this

problem

is

part

of the

wider historical

puzzle

set

by

the transformation

n the ancient

traditionwhich eft Protagoraswith an

arid

subjectivist iewpoint

that

no one

is

likely

to defend

in

place

of an

intriguing

orm of

relativismwhich some think s stillunrefuted.We are to consider

here the argument

n

Sextus

Empiricus,

and that

means tackling

Protagoras

n

the subjectivist uise which prevailed fromAristotle

onward; in a companion paper I shalltakeup thequestionof how

3This is the over-all picture and accurate in the main, but certain qualifications

should be entered. Aristotle anvasses and rebuts relativist efense of the Protago-

rean position at Met. 101 al7-101lb12. In Sextus traces of relativism oexist with

reports to the effect hat Protagoras held that every appearance is true simpliciter

(chiefly

M

7.60-64;

cf. also

PH

1.

216).

The same bland

uxtapositionof relativist nd

subjectivist ormulationsmay

be

observed

n

Alexander's commentary n Aristotle's

Metaphysics,90-291 Hayduck; cp. 316, 12-15; 371, 31-33). Otherwise, the only

exception

to

a

uniformly ubjectivist

ecord

seems to

be

Cicero,

Academica I

142,

which

means that the Academic

Skeptic

whom

Cicero

is

reproducing (probably

Clitomachus

or

Philo

of

Larissa)

took

the trouble to

state

Protagoras'

view

correctly.

The subservience f other writers o Aristotle's ubjectivist enderingof Protagoras

may be udged from he not quite complete) collection

f

doxographical

references

to

the Measure

doctrine

in

Antonio

Capizzi, Protagora Florence, 1955);

cf. also

GregoryVlastos, ntroductionto the Libraryof Liberal

Arts

Plato'sProtagoras In-

dianapolis and New York, 1956), pp. xiii-xiv, . 26a.

46




5/27

PROTAGORAS AND

SELF-REFUTATION

thecharge of self-refutationares gainst herelativist rotagorasof

Plato's Theaetetus.

All this has been introduction nd backgroundto the following

passage:

One cannot ay

that

every ppearance

s

true,

because of its

self-

refutationperitrope],s Democritus nd Plato

urgedagainstProta-

goras;for

f

every ppearance s true, t willbe true lso,being

n

ac-

cordancewith n

appearance, hatnotevery ppearance

s

true,

nd

thus

t

willbecome falsehood hat very ppearance s true

Sextus

Empiricus,

7.389-90].5

This is the argument s it s preserved n Sextus

Empiricus, tsbare

bones laid out in proper order and marked with

logician's abel:

peritrope,elf-refutation

r reversal.

Both

name

and

presentation

bespeak a more sophisticated onsciousnessof ogical form han we

may uppose was to be found severalcenturies arlier nthe polemic

of Democritus

against Protagoras,

which

Sextus

here

suggests

was

the argument'soriginal home.

But

what does thename mean, and

whatview does itimplyof the form nd validity f the argument?

That is the

question

I

shall

try o answer.

I

have said, following ury, hat eritrope eans

self-refutationr

reversal.6

ornford,

n

a footnote o his translation fPlato's version

4 Protagoras

and

Self-refutation

n Plato's Theaetetus,

o appear in the

April

issue of

The Philosophical eview.

6r&o-aa

Av

oiV ?>avrao-aa

OVK e'irot TLS

&X75i

5ta

77V

reptTpOTr',

MOW

S O

re

A7Ao6KpLrOS

Ka

0

Xd

Wv

&vTAef'yovre7

TCf

HpWrcxWap~

eo55aC0KOV.

et

yap

7r&Oa

/cavrcaxIa

EaTZV &Xr7t9

S,

KayX

TO

A/7 7r&oav

a/vxotcaxv etvat

&X7,

KaTa

'

xvrTaoaiav

VU

7TaievOV,

e/TaXL

aXr7te'S,

Ka' OVTw

7O

r&oav a/vTXoLacv eivat aX'7Oi

'yevaeTa

fevo50s-

Two comments

n Greek terms:

(1)

Oavrao-iax

appearance) is usually,

and more

properly,

ranslated

presentation

r impression, ut the

technicalities

f this ater

Greek onceptmay

afely e disregardedere.

2)

VI0TVa'evoV

(being)

is either a

mere variant

for ov

or is a trace of Stoic terminology.

ither way it should be

translatednoncommittally,

he point

being simply hatthere

s an appearance

with

the proposition

that

not every ppearance

is true as its content.

On Sextus'

stylistic

variations

for

dyat,

cf.Karel Jandcek,

rolegomena

to SextusEmpiricus

Acta

Uni-

versitatis alackianae Olomucensis,1948), ch. IX; forthe Stoic terminology,f.M.

8.70

(KaTa

XO7yLK'V

q5aVT#a-t'aV

v9racevaV)

and

A.

A.

Long,

Language

and

Thought

in

Stoicism,

n

A. A. Long (ed.),

Problems

n

StoicismLondon,

1971), pp.

80-90.

6

R. G.

Bury n the

Loeb SextusEmpiricus London

and

Cambridge,

Mass., 1933-

1949):

his translation lternates

self-refutation,

s in thepresentcontext

nd PH

2.185,

and

reversal ; .g.,PH 2.128,

133

(but

see n. 9

below). Cf.

his

glossary

n III,

529.

47




6/27

M. F. BURNYEAT

of the argument, enders t more vividly, turning he tables, and

he implies hat he word served s a (proper) name for hisparticular

argument or variants

of

it.7

That the term is not, however, the

special property f the argument against Protagoras s clear from

the verynext sentence

n

Sextus,which aysthatProtagoras' ubjec-

tivism is plainly

false

quite apart

from self-refutationf

this

kind

[Kai

XwptS

SE'

Ty~

OMaVTr/

rEptTpOwry-p].

Here

peritrope

s used

to

denominate a

kind

or typeof argument, f which Protagoras'

self-

refutation s ust one specimen.

In

fact, he noun peritropend the

verbperitrepeinrom which t derives are common termsof art in

Sextus and

if

they ver sounded a metaphor s lively s turning he

tables, all trace of ithas vanished in his writing.

The verbperitrepein eans basically o turn round or over, hence

to refute a claim or idea-whether because this s thought of as

turning

t

around into its contradictory pposite or because the

notion of overturning s dominant PH 2.193, 206, 222, 3.28, 103,

109, 130, 161, 197, 259;

M

7.11, 8.361,

9.342).8

Any refutation, f

course,establishes hecontradictoryf what trefutes, utperitrepein

tends particularly

o

be used

of

the special case wherethe thesis

o be

refuted itself serves as a premise for its own refutation,where

starting ut with

p

we deduce not-p and so conclude that the

original premise was false (PH 2.64, 78, 88, 91, 185-186, 3.19;

M

7.440, 8.55,

9.204).

In

such

a case a thesis

is turned around

or

reversed nto tscontradictory ithin he confines f a single nfer-

ence,

and this

seems to be the notion the verb then expresses,

as

comes out in

a more

explicit

construction

o the effect

hat sonme-

I

F. M. Cornford, Plato's Theory f Knowledge London 1935), p. 79 n.1: Sex-

tus ... saysthat n argument

f

this

orm, nown

s

turning

he

tables' 7TEpLrpor1i),

was used against Protagoras byDemocritus, s well

as

by

Plato here. Strictly,

he

remark s ambiguous as to whether

he argument r its form

s

known s

1TEptrpoMr,

but I have little oubt that the former

s intended;

so,

clearly,ChristopherKirwan,

Aristotle's etaphysicsooks

,

A and

E (Oxford, 1971), p. 104: The argument

ofMet.

1008a28-30] came to be known speritroper turning f the tables. Another

cholar

who seems to have been misledbyCornford

n thismatter

s

Kenneth

M.

Sayre,

Plato's

Analytic ethod Chicago and London,

1969), p. 87. Cornford

n

turnmay

have been

followingJohn

urnet,

Greek

hilosophy,

art : Thales oPlato

(London,

1914),

p.

244,

n. 1.

8

The listing for

7repurpour?'1

7repLTpe7rW,

CuV/7repLTpe7rW,

a7repLTpe7rTWS

in K.

Janacek's

ndex

(vols.

II

or IV of the

Teubner Sextus Empiricus Leipzig, 1954 and

1962])

is

complete.

shall

pass over

twooccurrences:PH 1.81, which

snontechnical,

and M.

1.196,

which

I

do

not

understand. My classification f the remainder

s

at

some pointsroughand ready,beingdevised for he purposes of thispaper,

not togive

a

thorough analysis

of

the terms.

48




7/27

PROTAGORAS

AND SELF-REFUTTATION

one

saying)

p

is reversed

nto

7rEpt-pErErat

Etd]

saying)

not-p

PH

2.76;

M

8.295-296;

another

verb

sused

to

thesame

effect

t

7.399).

The

noun

too

has a preference

for

arguments

taking

the special

formof refutation yreversal PH 2.128, 133, 185, 187).9Add to

this

evidence

the

frequency

of

phrases

like peritrepein

eauton,

o

refute

neself

PH

1.122,2.188;

M 8.33

la,

360, 463,

10.18),

and the

interpretation

f peritrope

s self-refutation

ecomes

compelling.

For

precisely

whatself-refutation

onsists

n is a

reversal

whereby

advancing

a proposal

commits

one

to

its contradictory

pposite.

But

caution

is needed.

If in a peritrope proposition

s

turned

round

into

its contradictory,

oes

this

mean

that to classify

n

argument as a reversal is to claim for it the form (p

--

not-p)

->

not-p -in

other

words,

that

p is

the

sole

premise

used on

the way

to

not-p ?

f

so, our

argument

eems

wrongly

lassified,

or

t

uses

twopremises

to derive

itsanti-Protagorean

onclusion.

Let

us lay

this

out,with

he relevant

propositions

abeled

for

future eference,

as follows:

If

(A)

everyappearance

is

true,

and (B)

it ppears

that

not

every ppearance

is

true,

then (C) not everyappearance is true.

(If the

nference

holds,

then,

given

that

one

can assert

B)

as a truth

offact,

ne

can

proceed

to

detach

C)

as conclusion

nd

refutation

f

Protagoras'

subjectivism.)

The problem,

then,

is

this:what

is

the

justification

or

calling

theabove

a reversal,

r for

saying

hat A)

is

self-refuting,

hen

C)is

arrived

at

only

with

the

aid of

(B)?

Sextus

does

give

examples

of

single-premise

eversals.

n

uphold-

ingSkepticism

gainst

lldogmatizers,

heSkeptic

purports

o evade

the countercharge fdogmatizinghimselfbyallowingthatthefor-

9PH

1.200

is an

exception

where

the

reference may

be

a more

general

one,

although

the narrower

eading

would

make

sense

in the context.

PH

2.128

and

133

call

for a

word

on the

phrase

KOT&

T'IV

7rEpLTpO7r?7v

TOr

XOyov:

the

nominalization

involved

is clearly

of

repvrp

6Xreroct

oyoS

(PH

2.64,

76, 78, 88, 91),

where

XMyos

means

statement,

ot argument,

nd

the

phrase

should

be translated

ccording-

ly.

Bury's

reversal

f theargument

s

wrong,

f not

unmeaning:

what

gets

reversed

is

not

an argument

but a proposition.

Again,

t shouldbe

a

statement

maintaining

he

nonexistence

of

proof,

not an argument,

as

Bury's

translation

has

it,

that

Sextus

adduces

at M. 8.463

(Xoayos

ecudfldull)

n connectionwith the Stoic charge that it

is self-refuting

cf.

PH 2.179).

There

is argument

bout it,

which Sextus

in

the

im-

mediate

sequel

terms

Xoyos,

nd

later

he considers

whether

to admit

that

this

argument

does

away

with tself

M

8.479-80;

cp.

PH 2.188),

butfor

that

he

does

not

use

the

vocabulary

of reversal.

Oddly

enough,

Burygives

the correct

ranslation

t

PH 2.64

and

76. On

statement

vs. argument,

see

further

n.

17 below.

For

a

distinct

ense

n

which

ne can

speak

of reversing

n

argument,

ee

Appendix

below.

49




8/27

M.

F.

BURNYEAT

mulae

which

express

hisunwillingness

o

take

sidesone

wayor the

other

on

the ssues

that

divide

everybody

lse

-formulae

such

as

I

determine

nothing

nd

No more

this

han that

apply

to

them-

selvesand cancelthemselves, yreversal, longwith ll otherasser-

tions.

Just

s

the tenet

of

certain

dogmatists

All

things

re

false

or

Nothing

is true

says

that

Nothing

is true

is

not true,

so

the

Skeptic's

No more

this

han that

ounts

tself

s no more

true

than

false

(PH

1.13-15;

cp.

Diogenes

Laertius,

Livesof

the

Philosophers

[henceforth

DL],

IX,

76).

Alternatively,

without

the reliance

on

self-applicability,

extus

argues

that

There

are no

truths

mplies

t

is

truethat

there

re

no truths,

which

n turn

means

that

omething

is true (namely,thisverypropositionthatthereare no truths), o

that

the principle

There are

no

truths entails

its

contradictory

opposite

and

is,

n thestrictest

ense, self-refuting

M 7.399).10

He

does

not extend

the reasoning

to

showthat

No

morethis

han

that

also

carries

the self-refuting

mplication

hat something

s true,

n

this ase

that

nothing

s

more

true

than false,

but

he would

not

resist

the parallel,

which

at least

one

critic

f the

Skeptics

urged

against

them (Aristocles,

Peripatetic

writer

f

the

second

century

A.D.,

apud Eusebius,Praeparatio vangelicaXIV, 18, 5). The medicineof

Skepticism

s avowedly

designed

to eliminate

tself

long

with the

-noxious

humors

t

purges

(PH 1.206,

2.188;

M 8.480;

Aristocles

p.

cit.,

XIV,

18,

21).

But although,

that is to say,

Sextus

holds

the

proposition

All

things

re false

to

be

itself ne

among

all

the

things

t

claims

to

be

false (M

8.55;

cp.

7.397),

he shows

no sign

of

thinking

hat the

appearance

described

in

(B)

is already

given

as one

among

the

appearances (A) claims to be true.On thecontrary, is formulation

of

our

argument

uggests

hat

B)

is forhim n independent

premise

(cf.

also

PH

2.88).

And

rightly.

t is

quite

contingent

hat

subjec-

tivism

hould

appear

false

to

anyone

-just

as

it

s utterly

ontingent

that there

should

have

been

a

man

called

Gorgias

whose

intellect

pronounced

thatone should

heed

neither

ense

nor

ntellect

nd

so,

according

o

Sextus,

aused

a

reversal

f

thethesis

hat

hings

hould

be

udged

by

all the senses

and all men's

ntellects PH

2.64).

In fact,

this Gorgias-inspired eversal s a more typical pecimenthanthe

single-premise

xamples.

While

these

are

peculiarly

elf-refuting,

n

that heir ontent

s directly

esponsible

for

heir

alsity,

ther

rever-

10

St.

Thomas

Aquinas,

Summa

Theologiae

a2,

1,

adapted

this rgument

to prove

that

God's

existence

s

self-evident,

od

being

truth

tself.

50




9/27

PROTAGORAS AND SELF-REFUTATION

sals

retailed by Sextus involve a more complex mode of

self-

refutation.

The most interesting

nd the most tightly onstructedof these

reversalscome-and this s part of their nterest-from disputes

between Stoics and

Skeptics. Take the followingpieces of

Stoic

reasoning:

(i)

If

the Skeptic

uses a criterion to assert that there is no

criterion,11

he

will

refute

himself/be

eversed

nd

in

assert-

ing thatthere s no

criterionhe will acknowledge that

he is

using a criterion

n

proof of

this

assertion M 7.440).

(ii) If the Skeptic

argues for the nonexistence of signs,12

he

produces a sign for henonexistence f signs nd insodoing

acknowledges

that

there

s a

sign (M 8.282).

Thus

he who

states

that

there s no

sign

will

be reversed nto

saying

that

there s

a

sign

(ibid.,295).

(iii) If the Skeptic purportsto prove there

s no proof, by

this

veryfacthe

acknowledgesthat here s proof; the

rgument

which

provesthere

s

no

proof

s a

proof

that

there

s.

Thus

the thesis13

of

the nonexistence of proof is

rebutted/

reversed by itself, he very means it uses to abolish proof

establishing he

reality

f

proof by self-refutation/reversal

[&K

7Ept-powS3]

(M 8.463

ff.;

PH

2.185).

(iv) If the Skeptic cites

a reason whythere s no such thing s a

reason

[or

cause:

altTov],

he refutes

imself/is eversed,

nd

inthe act of saying

here s no such thing s a reason he

lays t

down that

there

s

(PH 3.19;

M

9.204).14

The pattern

f

reversal

n

these

examples

is no

longer

that

of

views

directlyfalsifiedby their own content. nstead, it is the Skeptic's

undertaking

o establish

his thesis

by

reason

that

falsifies

t,

for

his

thesis

s thatthere s no such

enterprise

o

undertake.

The

view

he

advances conflicts ot

with

tself

but with the

way

he

advances it.

It may be feltthat

an

anti-dogmatist

as

no

business

advocating

11

By criterion

n this ontext

smeanta criterion

ordecidingthe

truth

f

beliefs

or impressions-something the Skepticswere anxious to denycould be found (PH

2.14 ff.,M.

7.27 ff.).

12

Sign

is

a

technical

term of the

period

meaning, roughly,

vidence

for some-

thing;cf. Charlotte

L. Stough,Greek

cepticismBerkeley

nd Los Angeles, 1969),

pp.

97-99, 125

ff.

13Cf.

n. 9 above

on

the

translation

of

X6'yos.

14

The Stoic

originof these

arguments

s attested t

M 7.445,

8.298,

470.

51




10/27

M.

F. BURNYEAT

any

view.

The

answer,

as

Sextus

explains

(M

7.443-444,

8.298,

476-477),

is

that

within he dispute

the

Skeptic

attempts

straight-

forward

refutation

f notions

like

criterion

nd

proof

which

are

ordinarily ccepted, and itis thisrefutation hat theStoicshave to

meet.

The

twist

omes

whenthe

Skepticsays

that

he is not

actually

committed

o

his conclusion:

t s enough

for

himto

have shown

t

to

be

aswell

supported

as

his

opponents'

view,

o

that he

right

ttitude

is

to

suspend

udgment

between

the two

sides.

In

more

ways

than

one,

the

Skeptic's

arguments

re

like

a ladder

which

he

overturns

after

climbing

up

(M

8.481).

But to

return

othe

conflict

etween

the

way

the Skeptic

dvances

his view nd theview tself. here are twopossibilities ere,whichJ.

L.

Mackie

has used

to distinguish

wo

types

of

self-refutation.15

Pragmatic

elf-refutation

ccurs

if

a proposition

s falsified

y

the

particular

way

t

happens

to be

presented,

s when

write

hat

am

notwriting,

s opposed,

say,

to

whispering

t:

if

whisper

hat

am

notwriting,

what

say

may

well

be

true,

but

if

write

t, t must

be

false.

Operational

elf-refutation,

n

the other

hand,occurs

f

here

s

no way

of

presenting

proposition

hatdoes

notfalsify

t,

s when

say,whether nspeech,writing, r silent oliloquy, I am notsaying

anything.

Of

these

the

weaker,

pragmatic

type

of

self-refutation

would

seem

to

be the

one

at work

in

the Stoic polemic

against

Skepticism.

For typically

he charge

of

self-refutation

s embedded

in

an

argument

to the

following

ffect:

ither

the

Skeptic

contents

himself

with

bare

assertion

f

his

thesis,

n which

ase

he

is no

more

to

be

believed

than one

who

asserts

he opposite,

or he

argues

for

t

and

in

so

doing

refutes

himself

M 7.440,

8.281-282,464,

9.204).16

Bare assertion may be self-defeating n the loose sense that it

achieves

nothing,

ut ts

vailability

s

an

alternativeway

of

advanc-

ing

a Skeptic

thesis

eaves

pragmatic

rather

than operational

self-

refutation

he

more

appropriate

interpretation

or

peritrope.

Not

that the

alternative

of

bare

assertion

s of any

use to

the

Skeptics.

The

argument

hat

f

this

option

s

taken

by

the

Skeptic,

he

is

no

more

tobe

believed

than

an opponent

who

asserts

he opposite,

turns against

the Skeptics

an important

principle

of

their

own

15J.

L.

Mackie,

Self-Refutation-a

Formal

Analysis,

Philosophical

uarterly,

XIV

(1964),

pp.

193-203.

16

At

PH 3.19

itmay

ook

as

itboth

lternatives

ome

underthe

heading

of

reversal,

but

t

s more

ikely

ither

hatSextus

has

been

careless

n

arranging

he

components

of

his

argument

r

that

he

verb

eritrepein

arries

ts

broader

meaning

to

refute

so

Bury).

52




11/27

PROTAGORAS AND

SELF-REFUTATION

philosophy,

the

principle of

equipollence or

equal strength isos-

theneia),which says

thatto

everydogmatic

assertion

nother can be

opposed

of

equal

plausibility r

implausibility,

ith

the result that

one is unable to decide between themand is forced to suspend

judgment.17The

Skeptic's

choice is

betweenundergoing a

reversal

and

swallowing dose of his own

medicine-but

the factthat this

thankless hoice

exists

onfirms

hat

pragmatic

elf-refutations the

one to look for

n

these

controversies.

Even so the

equivalence is not

exact.Mackie would

hardly ounte-

nance the

presenting

f a proposition

with

upporting

reasons as a

wayof

presenting

t

on

a

par

with

sserting

t

on its

own. Nor would

wego alongwith heusage accordingto whichtheSkeptic salleged

tolay

t

down that

here s such a

thing s a

reason

n the

ctof aying

[9v

Tr X'yEtv,

M

9.204]

that there

s

not (argument

iv]

above). Simi-

lar

phrasing

n the other

arguments,

oo, shows that in

the Stoic

polemic

against

Skepticism, he

notion of

peritroper

self-refutation

is

the notion

thatwhat the

Skeptic says

s falsified

y his saying t,

where

his

saying

t

s

inclusive

of,

not-as

it

would be

in

a

present-

day

discussion of

self-refutation-exclusiveof,

thereasoningwith

which he supports his position.

It is no

doubt

confusing,

f

not

confused, o be

so lax with he verb

to say, but

there

is

some merit

n

the broadened

conceptionof

self-refutation hich

results.

A

man

who

says

that

nothing

can be

proved and

purports

to prove

it s not like a man

who says

I

can't

move a

muscle, moving one,

or even

like a man who

says,

I'm

sorry,

never

say sorry,'

merely

falsifying

hat he

says

as well

s

saying

it.

Reason-giving

s not

ust

another

independent

activity

alongside theadvancingofviews, ince a relation nd reference o

each

other

s

part

of our

understanding

oth

of

what

reason

is and

of

what t

s

to hold

a

view.

Even when

reasons

and views re

given

n

temporally

istinct

tterances

we understand them as meant to

go

together

n

propositions f the

form p because

q.

In

effect, hen,

what

the

Skeptic

s

saying

s: There are

no true

propositions

f the

form

p

because

q'

because

....

And

howeverwe

express

the

point,

this s

something

hat

deserves

to be called

self-refuting.

man

who

17

For an elucidationof the principle, ee PH 1.202-205, another

passage spoiltby

Bury's translation

f

XOyos

s 'argument': Sextus begins by saying xplicitly

hat n

the formula

To

every

Xo'os

an

equal

XOyos

s

opposed',

he refers o

any

XOyos

that

tries o establish omething bout what s not evident n appearance,

whetherrnot t s

based on premises nd a conclusion, .e. whether r not thas an argument o support

it.

53




12/27

M. F. BURNYEAT

cites

reason why

no reasoncan be

givenfor

nything

eemsbothto

do

and

to

acknowledgethat

he is

doing the

very hinghe is

claiming

to be

impossible.

Confusiondeepens, however-this timewithout xcuse-when

certain

Stoics

go

on to sum

up

and

justify heir

position

n

formal

terms.

f

proof a

sign,

nd

so forth) xists,

hese Stoics

argue,

then

proofexists;

f

proof does

not exist, hen

proof

exists; either

proof

existsor

proofdoes not

exist;

therefore, roof exists

PH

2.186;

M

8.281,

466,

9.205).

This formof

inference

was thesubject of some

controversy mong the Stoics

themselves,but rather

because of

problems bout

apparent

redundancy n thepremises

han

because

of doubts about the truthof the second premise.18This-that if

there s no such

thing

s

proof a

sign,

nd

so

forth),

henthere s-is

supposed

to be

alreadyestablished

by

the

self-refutationrguments

(M

8.281, 466-467,

9.206).

But, of

course, even

operational self-

refutationwould

not

establish ny

suchconditional s

If I

am

not

saying

nything, hen am

saying

omething.

Only

from

my

aying

I

am not

saying nything

would it

follow

that am saying

some-

thing;onlyfrom

my

rguing gainst he

reality f argumentwould t

follow thatargumentexists.

Furthermore,

f

my

rguingfor

thesis sactually o

falsifyt,

what

I

produce

in

its

support has

got to be real,

not ust

intended

argu-

mentsorreasons.

If I

merelypurportto

prove there s

no proof

but

do not

actuallydo

so, myprocedure does

not

definitely

stablish he

reality f

proof; tonly

oncedes to

be truethe very

hing am at the

same

time

denying.

There

is

some

unclarity

n

this

point

n

Sextus'

formulations,

ut in

the

couple of passages

(PH

2.185;

M

8.465)

wherethedistinctionsacknowledgedthis s done insuch a way s to

indicate

that hecharge of

reversal

ssumesreal,

notjust

purported,

arguing

for

the thesisthat

reverses

tself;

ny supposed

reasoning

that

does not amount

to

proof

can,

it is

said,

be

disregarded

as

proving

nothing.

And

certainly ny

Stoicwho thinks

imself ntitled

to the conditional

If

there s no

proof

thenthere s

proof will

have

in

mind

an

opponent

who,

rather han

merely onceding

the

falsity

of his

thesis,

ctually

falsifies t

by

the manner

in

which

he

puts

it

forward.

It may

be that all

this s

confirmation f

Mrs. Kneale's

suspicion

that the

Stoics

did

not

distinguish

properly

between the act

of

18

Cf.

M

8.292-294

and

William

and

Martha

Kneale,

The

Developmentf Logic

(Oxford,

1962), pp.

172-174.

54




13/27

PROTAGORAS

AND SELF-REFUTATION

asserting proposition nd

the proposition sserted.Their concept

of

axioma,usually translated

proposition

withmodern

analogues

in

mind, does not abstract o

much fromthe total

speech act as do

some modern concepts of a proposition. t does not abstract,for

example,

from

ense

or

token-reflexives

nd, being

co-ordinate

with

question, command,

and

other

types

of

speech act,

seems not to

abstract

from illocutionaryforce

either. Defined

as assertoric

n

itself,

he Stoic axiomawould thusappear to be the

propositionas

asserted rather than the

proposition

in

itself,even

though

this

makes

nonsense of their dea

that a conditional or other complex

axioma onsists f a number

of

simple ones;

forwhile a conditional

mayhave assertoricforce as a whole, itsconstituentsmay not.19

But

these re troubled

waters,

oth for he

philosophy f ogic

and

for ts

history,

nd

better

not aunched into

now. Ratherthanwhat s

abstracted from the total

speech act, the point germane to the

presentinquiry

s

what gets

included

in

and

with

t-namely,

as

already explained, the

adducing

of

argument

and reasons.

On

a

comprehensive,

ot to

say

hazy,view ike this f what t s to advance

a

thesis,we cannot look for

any very precise identification f the

factor esponsiblefor reversal.The Stoics might e expectedto be

more

scrupulous than most which s why have

dealt with hem at

some

length)but,

as

we have

seen, they re prepared to dismiss he

bare assertion

option

as not

requiring to be reckoned with

and

to

claim that thesis

s self-refuting

f

tcannot be

seriously dvocated

without

omething bout one's

advocacy havingthe

effect

f

falsify-

ing or

denying t.

To put

this nto

perspectivewe need,

I

suggest,to remind our-

selves that ogic at thisperiod had not yet ost its connection with

dialectic and

disputation in

Stoic parlance the studyof argument

was

in

fact

part

of

dialektike;

L VII,

43).

Think of a discussion

n

which a

Skeptic puts forwardfor

acceptance

his

thesis

thatthere

s

no such thing s reason,

evidence, or proof. There

are indeed only

the two

possibilities: ither he

declines to debate the question and

cannot

claim

the

edge over an

opponent who rejects he thesis, r he

does not

but

is

willing

o

argue

his

case-that is, givereason, evi-

dence,orprooffor t and promptly inds imself oingover to the

otherman's

view.Either

way

he loses.

His

thesis s

necessarily

loser.

And

having

established

this,people whose logical reflections

re

directed

argely

oward

dialectic

might

well think

t

unnecessary

o

19

References

and

discussion

n

Kneale, op. cit.,

pp. 144-145,

153-158.

55




14/27

M. F. BURNYEAT

look closer to find the precise factorresponsible for the Skeptic's

reversal.

That this s not too fanciful way of approaching the disputes

we

meet with in the pages of Sextus Empiricus s evidenced. think,

by

the

case

of

Hesiod (M 10. 8). Hesiod said that Chaos was

the first hing to come into being. He refuteshimself

~e

aiVTov

7rEptTpE7rETat]

because,

in

Sextus'

words,

if

someone

asks

him what

Chaos come into

being from,

he

will have no answer.

A

curiously

contorted way, surely, to make

the

simple (though no

doubt

question-begging) oint that oming ntobeing mpliescoming

nto

being

from

omething,

o

that

Chaos

cannot,

fter

ll,

have been the

first hing around-unless it be that the writer akesa dialectical

background

for

granted

nd

feelshe

need say

no more.

Thinking

of

Hesiod advancing his thesis for dialectical discussion and being

asked whatChaos came intobeing from, t

s

obvious to

him

that he

poet

loses

if

he does not answer the

question

that his thesis so

evidently nvites

and

loses

if

he does,

since

any

answer will be

inconsistentwith the position he has to defend.

Nowjudging

from extus'

further

ontext

ibid., 8-19),

thewriter

in this ase was originally n Epicurean, telling he story f Epicurus'

first dolescentstep

n

philosophy:on hearinghis schoolmaster ead

out that ine

of Hesiod, Epicurus asked what Chaos came intobeing

fromand the schoolmasterreplied that t was not his ob to teach

such

things, which were the business of philosophers.20

And

whether

t

was the

Epicurean writerwhom

Sextus is

following

r

Sextus

himselfwho conceived

the idea of

turning

he

story

nto

a

peritropergument, ertainly

he

Stoics

have no

monopoly

on the use

of the term and the method it stands for. The Epicurean

Philodemus replies to

the

Stoic

denial of the

validity

f inductive

inferencethat their denial is self-refuting,

n

fact confirmatory

f

induction,because

it

s based on grounds

which

are

in

effect hem-

selves

nductive,

uch as that

unobserved

cases

may

well differ rom

observed ones or

be as

unique

as certain

unique phenomena

within

our

experience (On Signs XXIX, 24-XXX, 15).21

Here

again

an

opponent

is said

to

refute/reverse

imself

because

his

arguments

20

In DL X, 2 the

story s recounted

froma source of

the second

centuryB.C.,

Apollodorus

the Epicurean'sLife

ofEpicurus.

21

Philodemuswrote

nthe middleof the first

entury .C.,

but he is

here reporting

an argument

from ome predecessor,

very

ikelyDemetriusLacon (second

century

B.C.);

cf.PhillipHowardDe Lacy

and Estelle

Allen De Lacy,Philodemus:

n Methodsf

Inference

Philadelphia, 1941), p.

91, n. 77.

56




15/27


run counter to his thesis.

Epicurus

himself, n a fragment f his

treatiseOn Nature,

[3

1] [28] Arrighetti)

ppears to argue that the

thesis of determinism

overthrows itself

ITEptKaTOJ...

TpEITETat]

on the grounds that to enter into a dispute on itsbehalfinvolves

treating one's opponent as responsible

for his own stupidity

n

denying t; the idea seems to be that the possibility f discussion

presupposes thatdeterminisms

false, t least with egard to beliefs,

so

that

t s

self-refutingo advocate

determinism

n

a discussion.22

And

a dialectical context s no

less strongly uggested by an argu-

ment of Sextus'

own

in

which a reversal s grounded on failure to

prove something: n what is almost

a parody of the Stoic polemic

against Skepticismhe insists n theone hand that,while t s notyet

conceded

that

any sign exists,none can be

used

in

proof

of

the

existence f

signs,yet

on

the otherthat

f

the Stoic cannot prove by

sign

that

signexists

he will

be reversed

nto

acknowledging

hat

no

sign

does exist

M 8.296).

Finally,

onsider how Sextus

appropriates

the patternof argumentwith

which

certain Stoics tried

to

trap

the

Skeptic

n

a formal

dilemma:

if

there

s no such

thing

s a

sign,

he

argues,

there

s

no

sign;

f

sign

s

what

Stoic

theory ays

t

s,

there

s

no sign (this having been alreadyshown); either there s a sign or

there s

not; therefore,

here

s

no sign PH 2.132-133;

forthe Stoic

original,

f.

bid.,131).

How does what follows rom he

Stoic

theory

of

signs get equated

with

what followsfromthe existence of signs

tout ourt,

f

t s

not thatwithin

discussion igns tand or fallbythe

account

their

defendant gives

of

them?

Evidently, eritrope

s a

commonplace

of later

Greek controversy,

available to

disputants

f

any persuasion

to confute he

other ide of

the debate. Since, moreover, uchevidenceas there s to be gleaned

about

peritrope

romother

philosophical

writings

dds

little

apart

from

ome

useful

confirmation)

o the essential

raitswe can

discern

22

The number

reference

s to Graziano

Arrighetti's

ollection,Epicuro

Opere

(Turin,

1960).The verb

occurs again

in activeform

7reptK&TW

rpe7rovreS TOp

Xo0yo]

in anotherpassage

([32]

[11] Arrighetti) oo

fragmentary

o

interpret ut from

ts

context

imilarly

oncerned withdeterminism

nd

mental

events. owe these

refer-

ences

and

help

with

Epicurus'

peculiar

Greek

to David

Sedley,

whose

improved

text

of the first ne

(see his Epicurus,

On Nature Book XXVIII [Cronache rcolanesi,

1973],

p. 27)

makes the argument

much clearer-but

he

is

not

responsible

for heuse

to which

I

have

put

them.

Note

that

Epicurus'

variant verb reptKaTW

Tpe7reLP

combines

n

one image

the ideas

of reversing ound

and

turningupside down;

this

could

well be the

nspiration

f a

picture

whichhas puzzled editors

t

Lucretius V,

472,

wherethe

skeptic

who

propounds

the thesis hatnothing

s

known,

which pplies

to

itself, s said to stand

himself pside

down

withhis head

in his own

foot tracks.

57




16/27

M. F.

BURNYEAT

in Sextus,23

et

us return

o the

self-refutation

f

Protagoras

nd

try

fitting

t

nto the

dialectical

perspective

which

has resulted

from

ur

inquiry.24

23

A

few dditional

examples

will

round

off hepicture.

From

thepseudo-Platonic

Axiochus 70a

comes

the Epicurean

thought

hatyou reverse/refute

ourself

f

you

fear (being

aware of)

not

being

aware of anything

when you are

dead.

DL

III,

35

recounts

reversal tory

not

tself

o be takenhistorically)

nwhich

Plato

showsup as

self-refuting

Antisthenes'

thesis

that

contradiction

s

impossible.

Sextus'

near-

contemporary

Galen records

in his De

libris ropriis

4 that

he

wrote a book

On

Self-Refuting

tatements

7reps

TWP

eCVaToUS

7reptTpeLroPrTwV

XO'ywv)-a

most regret-

table

loss to our investigation.

More

interestingly,

he dea of

reversal

gained currency

withNeoplatonist

writers

of thefifthnd sixth enturiesA.D. TheperitropefProtagorasreappearsinSyrianus'

commentary

n

Aristotle'sMetaphysics,

1, 23-27

Kroll,while

in

Damascius'

work

Dubitationest

Solutiones

e

Primis rincipiis

entral

Neoplatonist

ssertions

ike

The

One

is

ineffable,

nconceivable,

tc. are

found to incur

reversal

n the

manner

of

Plato's

If

the

One is,

t s not

even one (ch.

4,

p.

10

Kopp, ch.

5, p.

11, etal.).

Lastly,

illustratingnce

more

how therole

of a second

premisemay

be passed

over n silence,

here is a

reversalwhich

occurs

nSimplicius'

ommentary

n

Aristotle's

hysics,

205,

2-5

Diels

(the argument

is

quoted

from

Alexander,

but it is

Simplicius

n

propria

persona

who

calls it a

peritrope-Alexander,

o far as can

be

judged

fromthe

two

indexed occurrences fperitrepeinn hiscommentaries inTop.,556, 15Wallies;564,

12],

did

not

use the term

n

the technical

dialectical

sense

we

are

investigating):

If

nothing

moves and

there

is

no

motion,

but something

ppears

to move,

there

is

appearance;

but

if

there

is

appearance,

there is motion

and something

moves;

therefore,

f

nothing

moves

and there

s no

motion,

here

s motion.

As for Sextus

himself,

have for

the most part

confined

my investigation

o

passages

containing

the actual terms

peritrope

r peritrepein.

here

is a number

of

other

passages

where

the terms hemselves

o notoccur but

the same

idea

ormethod

of

argument

s

present.

This is

a

matter

f Sextus' stylisticariations,

n

which f.

the

chapter

on

the twoterms

n

Karel

JanAck,

Sextus

mpiricus'

ceptical

Methods

Prague,

1972), whereexamples are given.

24

On

the connection

betweenlogic

and dialectic

n

the later

periods

of ancient

philosophy,

t

maybe

worth iting

he following

xample of the

kind

of corroborating

evidence

that

might

be

gathered

from other

controversies.

t

comes

fromthe

Perl

Hermeneias

scribed

to

Apuleius

ofMadaura

(2nd

centuryA.D.).

Apuleiusis objecting

to

the Stoic schemata

exemplified

bythe following

rguments:

Either

t is

day

or

it is

night.

It is day.

Therefore,

t is notnight.

and

If

it is day, then

it is

day.

It is

day.

Therefore,

t is

day.

He rejects

these

as

unnecessary

supervacanei),

n

the

grounds

that

they

nfer

uselessly

what

s

granted

on the other

ide without

ispute frustra

nim

olligunt,

uod

sine ontroversia

ltro

onceditur;

ern ermeneias

II, p.

184,

23-31. Thomas,

trans.

by

Mark

W. Sullivan,Apuleian

ogic

Amsterdam,

1967],

p. 159).

The criticismmay

be

58




17/27


We are to

imagine Protagorasputting orward subjectivist oc-

trine ccordingto whichwhatever

ppears to anyone to be so is so in

fact, A). He

is

opposed by omeone

saying hat o him t appears, on

the contrary,hatnot everything hat ppears to someone to be so is

so

in

fact, B). But Protagorashas onlyto

be opposed like this nd he

will

be forced to deny

his

own thesis

and admit defeat, C). His

subjectivisms

a non-starter, ound to lose him the debate before t

has a chance

to get going. It is

necessarily loser because in a

dialectical

context B), contingent hough

t s, s in a sense guaran-

teed to hold; for here s no debate

without isagreement nd a clash

of views.But

if

B)

is

in

this ense

guaranteed

t

can be regarded, n

effect,s notcontributing ssentially othe refutation f A), some-

what

n

the

way necessary ruth an be dropped from n argument

without

mpairing

ts

validity.

And

that,

venture

o

suggest,

s

how

the

presumption

f a

dialectical ontext nables Sextus to

say

that

A)

is reversed or

self-refuted.

This suggestion nvolves further, ut

not, hope, indefensible

extension

of the notion

of self-refutation. e

began

with he

simple

and,

if

you

like, strictlyelf-refuting

ase of

a

thesis

falsified

y

ts

own content.Then came falsification y the waya proposition s

presented, the

scope of this notionbeing enlarged to take

in

sup-

porting rguments

s

part

of

the

advancing

of a

thesis.

Now

it s the

act

of

submitting

thesisfor debate or

maintaining

t

n

the face of

disagreement hatcauses itsreversaland

shows

t

up as false. One

mightcall this dialectical

self-refutation,nd

say

that

a thesis so

falsified

s

dialectically elf-refuting.

aking

the more

social

as

I

am

representing

he Greek) viewof what t s toadvance a thesis

has the

advantagenotmerely fgreaterrealism,butofcallingattention o

defects

n

a

doctrine ike

subjectivism

which

would

not

be disclosed

to a narrow tomistic

crutiny

f

Protagoras sserting

his doctrine

n

vacuo.

Subjectivism

enies

a

presupposition

of

debate,

the

possibility

f

genuine disagreement.

That

is

why

t s

self-refuting

n

a dialectical

Peripatetic n origin, since the context

s a defense of Aristotle'sdefinition f the

syllogism nd the Peripatetic chool did object to duplicated arguments ike

the

second specimen bove (cf.Benson Mates,

toic ogic Berkeley& Los Angeles, 1961],

p. 66; paperback ed.).

In

a

discussionof

the

passage Sullivan, op. cit.,pp. 159-161,

describesApuleius' rejectionof these forms f argument s motivated y considera-

tionsof utility atherhan f validity. ut

would this ontrast e so sharp forApuleius

himself,whose termfor ogic s arsdisserendi

PeriHerm. , p. 176,

1-4)-i.e.,

the art of

disputationor discussion? f it was, would he indeed have set down his (essentially

confused) criticism f the Stoics

n

the

first lace?

59




18/27

M. F.

BURNYEAT

context.

But

debate is

the

interpersonal

version of

something hat

can

go

on

in

the mind

of an

individual

deliberating n some

matter

that s

in

doubt

with him

when,

to

borrowPlato's

well-known e-

scriptionTheaetetus90a), the soul isquestioning tself nd answer-

ing

Yes - No,

Yes - No, until t

settles he

question

to itsown

satisfaction

ne

way or the

other.

We

conduct

internal

debates as

well as

external

nes,

and

if

this

fact s

gnored, o toowill

be the

role

of

reasons

in

the

formation f

views.

Debate of

eithervariety

resupposes

an open

issue,

withneither

Yes

nor

No given n

advance

as theright

nswer: that s what

the

requirement or

xternal

debate

that

genuine

disagreementbe pos-

sible amountsto, and without ttherewouldbenothing o debate. It

must

be

left

to the

considerations nd

reasons

contending for or

againstthe thesis

n

question,

in

external

debate

to the

reasoners

representing hem

on

either ide,

to

determineby

contending

with

each

otherwhat

the

answer

s.

Victory

n

debate is not truth ut t

s

the

subjective

ppearance of

truth-the

individual

debating with

himself

s

no longer,

as we

say, n

two

minds

about the

issue; the

disputants

who

disagreed

with ach

otherare

now,

as we

also say,of

one mindabout it. But on the subjectivistccount of truth et forth

in

A)

we

have toadmit

to

borrow

nother

well-known emark)

hat

whatever

s

going to seem

right ome is

right.

And

that

onlymeans

that here we can't talk

about

right.'

25

If

both Yes

and No

are

equally

valid

answers,debate which

eeks to

decide betweenthem s

pointless,

fraud.

There is

nothing

forreasons to

settle,

no

role for

them to

play

in

the

formation

f views.

It

was thusno

accident

thatthe

ancient

Greek

Skeptics

denied

reason itself.Their principle of equal strengthisostheneia) f op-

posed

assertions

does

say

precisely

hat

Yes and

No are

equally

valid

answers,

between which

no

decision can be made.

What is

more,

someone, whether from

the

Skeptic

school

itselfor a less

sympathetic historian of

another

following,

traced

the

equal-

strength

principle

to

Protagoras. We

find n

several later

sources

testimony

o

the effect hat

Protagoraswas the first

o

say

that

here

are two

opposed

sides that

may

be

taken on

everymatter;

he fullest

version s thatofthe Stoicwriter eneca, who has itthatProtagoras

said it s

possible

to

dispute

with

qual

validity

n

either ide of

every

question,

including the

question

whether

t is

possible

to

dispute

25

Ludwig

Wittgenstein,

hilosophical

nvestigations

Oxford, 1953),

? 258.

60




19/27


with qual validity n either ide of everyquestion.26 cholars have

had difficultyn reconciling his ttribution ith he relativism f the

historical rotagoras,27 ut t goes well enough with he subjectivist

doctrineforwhichProtagoras tands nthe doxographyof the ater

period.

In

fact, as we have just seen, the idea that there are two

equally

valid

sides

to

every uestion

s a

consequence

of that

ubjec-

tivism.

n this

ense

it

was fair o claim

thatProtagoras aid

first hat

the Skeptics said later.

There is a difference, f course, n that the Skepticsdo not hold

thatthe opposed assertions n a given question are both true; they

suspend judgment, being

unable

to determine

the

truth

of

the

matter cf.PH 1.216-219). But the Skeptic and the Protagorean

positions re equally nimical o the dea of reason.

If

therereally re

two

equally

valid sides to

every question,

the idea of a reason for

preferring ne to the othercollapses.

And

if, s the Stoicsurged

and

26

Seneca, Epistles

8,

43:

Protagoras

it de

omni e n

utramqueartem

isputariosse

x

aequo

et

de hac

psa, n omnis es n

utramqueartem

isputabilisit.For

Protagoras

s

the

first o

say

this

we turn

to

the other

reports DL IX,

51:

rp)Tros

e> &uo

Xoyovs

t'vat

7rept ccvros 7rpacyicros

aPTtKe6/ieVotL

&XXO',Xots:

Clement,

tromnateis

VI, 65: EXXPfe's

facrt

HpwTcayOpOV

rpOKaTp'Tavros

7ravcTt

Xo7y

Xo7yoV

'oCvrtKeLurac),

which

again

raise

the

question of how

xo'6yos

s to

be translated and

again

suggest

that

argument

s

wrong,

ontra, .g.,

W.

K.

C. Guthrie,A

Historyf Greek hilosphy,

II

(Cambridge,

1969), 182

(who,however, lso

gives

variantversion n a

footnote)

nd

Capizzi, op.cit.,p. 287. For

why

nly wo, nd what

does itmean

for wo

arguments o

be

opposed? The more

natural

ssumption

supported bythe

Senecan report)

would

be that

according to the

thesis ny

number

ofarguments an

be given

on behalf of

each member

of

the

contradictory air p

and not-p,

or any

p.

27

E.g., Ulrich von

Wilamowitz-Moellendorff,

laton

IJ2

(Berlin, 1920), p.

160,

claimed tneed have onlyrhetorical aliditywhatever hat s) since t s incompatible

withthe

Measure

doctrine. Of course,

those who

are prepared to

formulate

he

Measuredoctrine s the

thesis hat

llappearances are

true

period) have

nodifficulty

in

acceptingthat

Protagoras

nticipates heSkeptic

sostheneza:

hus

VictorBrochard,

Les

Sceptiques recs2

Paris,

1932),pp. 14-16;

cp. G. B.

Kerferd n Paul

Edwards

ed.),

The

Encyclopaedia f

Philosophy

New York and

London,

1967), sv Protagoras

of

A.dera.

What is

reliably ttested

for

Protagoras,but quite

distinct

rom heprinciple

hat

there re two

opposed

sides to be taken on

every

matter, s thathe

professed o

make

the weakercase (Xoyos) hestrongerAristotle,Rhetoric1402a23-26, K 80 A 21; to

which add

Cicero,

Brutlis

30,

who

translates

Xoyos

by

causa).

Notwithstanding

various

difficultiesf interpretationhis

involves,

ne

thing

s

clear.

It was not

a

thesis that

Protagoras

maintained but a

method

of

argument,

whether the

one

of

comparatively

restricted

cope

that

Aristotle llustrates

Rhet.

1402a17-23)

or

some

general

program

of

persuasion

more

apt

to evoke

the scandalized

reactions

which

got

transferred

on

to Socrates

(Aristophanes,

Clozids

112

ff.; Plato,

Apology 19b).

61




20/27

M. F.

BURNYEAT

the Skeptics dmitted, here s a sense n which hedenial of reason s

self-refuting,o too and in the same sense is subjectivism.

APPENDIX:

Two

QUESTIONS

OF

CHRONOIOGY

AND) A

PUZZ1,E

From Epicurus,to whom, o far

s

I

have been able to discover,we

owe theearliest xtant xample ofperitrepeinn tsdialectical ense of

reversal r self-refutation,o Sextus Empiricus s a span of some five

centuries.

t

is not

easy

to be

at

all

precise about when, within hat

very onsiderableperiod of time, he nteractions nd developments

brought o light n thispaper took place. But it s worth skingwhat

indications there are, both for its own interest nd because the

question bears on the evolution of the Hellenisticphilosophies.

(1) Take first heperitropergumentswhichthe Stoics devised to

refute he Skepticdenial of reason. Clearly, hese mustdate from

period

when

Skepticswere,

n

one

way

or

another,denying

reason.

When

was

that?

According

to what

is

still,perhaps,

the most au-

thoritative orkon the Skeptic movement Brochard,

Les

Sceptiques

Grecs, p. cit.,pp.

384

ff.,building

on Norman

Maccoll,

The

Greek

Scepticsfromyrrho

o extus

London-Cambridge, 1869], pp.

100

ff.),

so radical a skepticismdoes not precede Aenesidemus, who

was

active at the earliest

around

80-60

B.C. (Brochard, op. cit., pp.

242-246),

more

likely

after the death in 43 B.C. of

Cicero,

who

appears not to know his work A. Goedeckemeyer,

ie

Geschichte

er

griechischenkeptizismusLeipzig, 1905], pp. 211-212);

the

earlier,

Academic Skeptics Arcesilaus and Carneades

do not

take

the self-

refuting tep of demolishing he ogic on which heir wnreasoning

relies.

Now

it

is

true thatAenesidemus is the first keptic for

whom

arguments against signs

and

against

the

reasoning

embodied

in

causal explanation

aZtnov)

re

personally

itteste(I

PH

1.180

ff.;

M

8.215

ff.,

.218 ff.;Photius,

Biblioteca

12, 170b),

and these

would

suggest

that at least

part

of

the Skeptic critique

of

proof

was to be

found

in

Aenesidemus

also

(cf.

Leon

Robin,Pyrrhon

t e

Scepticisme

Grec [Paris, 1944], p. 164). But, given his date, it is a question

whether o late

in

the

day

the Stoics still etained

a

creative

nough

interest n matters ogical not only to construct he peritropergu-

ments

but also to

engage

in

their own controversy

bout the as-

sociated formaldilemma. As far s concerns heir ide of the

matter,

it

seems more plausible to refer he arguments nd the controversy

62




21/27

PROTAGORAS

AND

SELF-REFUTATION

to theearlier,

formative

eriodof Stoic

ogic,

whenChrysippus

circa

280-207

B.C.) and his

more mmediate

followerswere active

both

n

logic

and

in polemics against

Academic Skepticism.

Von

Arnim's

inclusionof thearguments nStoicorumeterumragmentaLeipzig,

1903-1924;

henceforthSVF)

I, 118,

223, 268,337

(cp. also

II, 121=

Clement,

StromateisIII, 5)

does

not necessarily

mply judgment

as

to

their

burnyeat, m. f._protagoras and self-refutation in later greek philosophy_phr, 85, 1_1976!44!69

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