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