Contradiction alone is the proof that we are not everything.
--Simone Weil, Gravity and Grace
The Paradox of Refutation and its Socratic Solution
Socrates refutes people by getting them to contradict
themselves. Socratic conversation not only contains but can rightly
be said to aim at such refutation (Apology 23b). He thinks that
refutation is possible, therefore he thinks that it is possible for
someone to contradict himself. And so do we. As philosophers, we
have firsthand experience of the phenomenon we also observe in the
Socratic dialgues, because we carry the Socratic torch. We are
refuters. The question of this paper is, what are we and what is
Socrates aiming at in the act of refutation? What is
self-contradiction?
Self-contradiction would be ill-named if it had nothing to do
with contradiction. One plausible account of what it is to
contradict oneself is to that one does so by asserting or believing
a logical contradiction. The simplest way to assert or believe such
a contradiction is to assert or believe both a proposition and its
negation. For purposes of brevity, I will use the word judge to
cover both asserting and believing, and I will describe the judging
of a contradiction as a judgment which fits the schema p and p. It
is, however, possible to judge contradictions in (indefinitely
many) more complicated ways, such as: (1) judging p and also
judging if p then q and also judging q or (2) judging p and q and
also judging p or q.
The problem with this account of self-contradiction is that its
not clear that anyone can judge a contradiction. If judging is just
our shorthand for asserting/believing, then judging X should be the
same as judging it to be true. But most of us are committed to the
impossibility of contradictions being true, and therefore to their
consequent unbelievability and unassertibilty. That is: we are
committed to the logical, psychological and lexical laws of
noncontradiction, respectively. Of course, not all of us are so
committed: dialetheists think that there are true contradictions.
But this is of no help, not even to them: true contradictions, if
there were any, would also be precisely those contradictions you
could not refute someone by getting him to assert! Refuters,
dialtheistic or otherwise, are faced with the problem that the
contradiction we need the person to judge if he is to be refuted is
one that he shouldnt be able to judge. Refutation would be quixotic
indeed if success required us to get the interlocutor to do
something we believed it impossible for him to do.
But am I overstating things? Here is a familiar cases in which
someone can be said to judge a contradiction: change of mind.
Someone might say pwait a minute (with the twisted face of one upon
whom realization dawns) scratch that, p! We might even suppose that
he says, pNo, let me contradict thatactually, p! We do sometimes
aim to get our interlocutor to change his mindif I know that p, I
might aim to get you to adopt this belief, knowing I will face some
resistance because you currently believe p. Speech aimed at change
of mind involves refutation at most incidentally, as one among many
means to getting you to the belief that p. For I can sometimes
produce conviction in you that p just by saying, Trust me, p. If I
have enough clout, that might be enough to get you to drop p and
adopt p, without any refutation having taken place. Refutation is
neither necessary nor sufficient for change of mind, and it is easy
to see why: in refutation, we are aiming to put the person into a
single problematic state, not into two distinct nonproblematic
states which would only be problematic if they were not insulated
from one another. Someone who changes his mind judges p, and he
judges p, but he does not judge p and not p. He does not assert a
contradiction in the way that our refutee would need to.
We need someone to judge a contradiction without changing his
mind midstream. Is this possible? Yes, so long as the one doing it
doesnt realize thats what hes doing. If I judge that the
Tanayama-Shimura conjecture is true but Fermats last theorem is
false, you could say of me, she is contradicting herself, though
she doesnt realize it. This is a way we use the term
self-contradiction, but it once more picks out a different
phenomenon than the one we are looking for as refuters. For
whatever it is we are trying to do to our interlocutors when we
refute them, we are also trying to get them to know that we are
doing it. It is typically unethical (because deceitful) to have the
goal of getting someone to unknowingly contradict himself.
Could we somehow compose knowing self-contradiction additively,
out of unknowing self-contradiction + the realization thereof? The
question is: what do I realize? It seems that the most I can build
up out of unknowing self-contradiction is the realization that, at
some earlier time, I was unknowingly contradicting myself. Now this
might be an interesting thing to learn about my own history, but is
not the kind of thing refutation aims at. Because what I realize in
such a case is that there is nothing wrong with the state Im in
now. And it could hardly be the goal of refutation to show someone
there is nothing wrong with his epistemic state. What the refuter
wants me to realize is that I am contradicting myself, but we get
no help trying to see how this is possible by thinking about the
phenomenon of unknowing self-contradiction, whether or not it is
later made known.
Socrates is no stranger to change of mind, or unknowing
self-contradiction. His victims self-contradiction is sometimes
preceded by the saying of two things he does not realize contradict
one another [e.g. Euthyph. 15c.] ; and it may be followed by his
changing his mind about (or simply putting out of mind) the one or
the other. But the refutation itself is neither identical to any
ignorance preceding it nor any change of mind which may follow it.
The problem isnt that we cannot make sense of the idea of judging a
contradictionthe problem is that we seem to be able to make sense
only of contradictions of which we can make no refutational use. We
havent really been able to find a case in which someone judges the
kind of contradiction we could refute him with.
In change of mind cases what is really asserted is p and then
not p rather than p and not p, and in ignorance cases what is
really asserted is p and q where unbeknownst to the speaker, p q .
What I now want to show is that even if we could get someone to
assert, at one time, in all seriousness, p and not p, this would
not solve our problem. Getting someone to assert (at one time, in
one respect etc.) p and not p is the same thing as getting him to
assert that that contradiction is true. (Because asserting =
asserting to be true) The one who thinks that there are some true
contradictions is the dialetheist. So what we would do if we
succeded at producing the relevant p and not p assertion is to turn
our interlocutor into a dialetheist. But that was not our goal! For
such a person will not take himself to have been refuted. He takes
his contradiction to be an accurate representation of the way the
world is. Its contradictoriness simply mirrors the
contradictoriness he thinks he sees in the things themselves. To
judge that p and not p, is to judge that in some way or other the
world is contradictory. But that is not the kind of thought we are
trying to produce in refuting someone. We want him to hold fixed
the idea that the world is fine, and trying to show him that his
thinking about it is broken. We are trying to show him that there
is a way of thinking properly, and it is not his.
We have been barking up the wrong tree in seeking to produce the
assertion of contradiction in our refuteenot because we cant do so,
but because we wouldnt want to if we could. What we are after in
refutation is something more self-referential and
humility-inducing. We would like to show him that he is in the
wrong, that he isnot wasin some kind of epistemically defective
condition. We are trying to put someone in the state Socrates
interlocutors described as aporia or being-at-a-loss, a state that
consists in the thinking that ones own thinking is wrong or broken
or defective. The refutee does not judge a contradiction, he judges
that the world is not really the way he thinks it is. And not in
the kind of general way that we do when we say, with an easy-won
humility, Im probably wrong about something-or-other. This kind of
generalized detachment from ones beliefs itself raises
paradoxes[footnoteRef:1], but it is not nearly so paradoxical as
when the offending belief is specified. [1: See below, where I
distinguish the paradox of refutation from the preface
paradox.]
This change of target raises two questions. The first question
(Q1) is whether weve made the project of refutation any more
feasible by replacing p and not p with Im wrong about p. How is it
possible for someone to hold on to a belief he acknowledges as
wrong? The second question (Q2) is, why is it still true (as I
think it is) to say that refuting someone involves getting him to
contradict himself?
I will start by addressing Q2. Contradicting is a two place
relation, but in English, as in Greek, it can relate two different
kinds of things. One of them is propositions: we can say, p
contradicts p. The other one is people: we can say Socrates
contradicts Euthyphro. In describing the self-contradicter as
asserting p and not p, we have been tacitly assuming that the
relata are propositions. Im wrong about p is a kind of
contradiction only if we shift over to the second model, and take
our bearings from one it is to contradict another person.
Of course the two kinds of relata are themselves not unrelated
to one another. To contradict another person is to speak against
him, but we can only distinguish contradicting from badmouthing if
we add that this is done by saying that he is wrong in what he
says, wrong about some proposition p. And unless we do distinguish
contradicting from badmouthing, we will surely be charged with
equivocation. We must make the case for the claim that
contradicting somebody has something to do with contradictions of
the form p and not p. To that end, consider these two
questions:
(1) What proposition contradicts proposition p?
(2) By asserting what proposition do I contradict you, who
assert that p?
The answer to the first question is, simply, not p. The answer
to the second question is more complicated, but it does involve not
p. Typically, we do not simply assert not p after someone asserts
pwe say, no, not p or I disagree or youre wrong about p. These are
things that I cannot say without having heard what you said. not p,
by contrast, is an assertion with which I could begin a
conversation. In order to contradict you, I have to hear what you
saybut that is not enough. I must also understand it, and take it
to be a sincere and accurate representation of what you believe. If
I think you are lying I can play into the charade and pretend to
contradict you by saying no, not p, but I cannot do so in
seriousness. If I doubt either your sincerity or accuracy I can
sincerely contradict not what you say but what you imply, by saying
you dont really believe p. But in order to contradict someone who
says p by means of the contradictory proposition, not p, I have to
think he is being sincere and accurate. I have to think that what
he is saying (p) really is the way he thinks the world is. This is
what is contained in any contradiction of a person over and above
not p: an acknowledgment that someone (namely, the one being
contradicted) believes that p. When I contradict you, I am not
simply informing you that not pthis would not be contradicting. I
am, in addition, telling you that you are wrong to think that p.
The thought I wish to express to you by contradicting you is that
the way your beliefs are is not the way the things themselves are.
I say to you, even though you believe that p, nonetheless, not p.
That is what is contained in the shorthand, no, not p or our many
more colorful ways of contradicting (balderdash!).
If what it is to contradict another person is to say to him, you
believe that p, but not p, or you are wrong to believe that p or p,
even though you dont believe it then I am not straining the meaning
of the verb contradict to say that someone can contradict himself
by saying, I believe that p, but not p or I am wrong to believe
that p or p, even though I dont believe it.[footnoteRef:2] To
generate self-contradiction, what we do is substitute Is for all
the yous. To contradict myself is to address to myself the
assertion I address to another when I contradict him. We have
solved Q2 (from p.3): moving the target of refutation from logical
contradiction to self-referential corrections still allows us to
call what were going for a contradiction. But we have thereby
sharpened Q1. For it is famously impossiblethough not logically
contradictoryto assert or believe any of those statements. [2: It
is not only insufficient to assert not p it is also unnecessary. I
can contradict you by saying q, as long as I believe, and know that
youll immediately see, that q is incompatible with p. In such a
case, by asserting q, I can express the thought you believe that p,
but not p.]
Or is it? Consider a (professed) dialetheist, D. D claims that
there are some true contradictions, though he denies that all
contradictions are true. If p and p is on Ds list, he can assert,
p, and I believe that not p, without any trouble. (Although he
cannot assert, p, and I dont believe it, unless I believe that p
and I dont believe that p is also on his list.) In form, this
counts as the assertion of a Moore-paradoxical sentence, but it
wont help us out any. For D does not assert such a sentence by way
of contradicting himself. We can see this if we turn to the
other-contradiction analog of this case. Suppose, I assert p, and D
follows up with not p. D is not contradicting me, rather, he is
making a friendly additionhe is saying to me, I see that you
(rightly) believe that p, and I would like to add to that something
you should also know: not p. His not p is not a criticism of what I
saidhe is not accusing me of being wrong. Similarly, in the first
personal analog, (p, and I believe that not p, ) he is not accusing
himself.[footnoteRef:3] [3: Note that my claims in this paragraph
require only that it is possible to sincerely profess dialetheism,
not that it is possible to actually believe it. It is important to
distinguish (as, e.g., Lawlor and Perry urge) between the question
of whether a speaker is being sincere and whether he is accurately
putting forward his own views. The possibility of professing
dialetheism is indisputable, being currently actual, and I see no
reason to doubt the sincerity of the speakers in question. I leave
open the question about whether dialetheism is coherent enough to
really be anyones view. If it isnt, then suppose that D sincerely
but inaccurately asserts dialetheism. He can, in the same vein,
sincerely but inaccurately assert p, and I believe that not p, and
sincerely but inaccurately assert you believe that not p, and p.
The point is that noting the inaccuracy of these last two
assertions does not turn them into, respectively, self- and other-
contradictions. What is absent from them both is recrimination of
any kind, and this is so as long as D professes dialetheism
sincerely. Nothing rests on whether anyone can in fact be a
dialetheist.]
The other-contradictor does not only say, p and you believe that
not p. It is crucial that he also connects these two claims with an
adversative such as but or although or expresses his disapproval
otherwiseby a hostile tone of voice, by a disapproving facial
expression, by slipping in a parenthetical, wrongly. The
other-contradictor is blaming his interlocutor for being in the
wrong; the self-contradictor must, likewise, blame himself. This
reveals why a whole slew of what might be good candidates for
Moore-paradoxical assertions wont work to vouchsafe the possibility
of the kind of self-contradiction we are interested in. For
instance, consider unconscious beliefs. I might discover that I
unconsciously believe that p, and yet it is clear to me that not p.
I can say, not p, although I believe that p. But I do not thereby
criticize myself, since I cant blame myself for having beliefs of
which I am not even directly aware. The other-contradiction analog
might be if I say to my dog, you think there are more treats in
this bag, but there arent. I am not criticizing my dog for digging
deeper into the bag to find treats. Similarly I might patronize my
child or student by failing to criticize their false but
developmentally-appropriate ideas. You believe that p, and not p,
but thats okin such a case, I dont contradict him.
Consider the case of correction. Recently I was walking down the
street with someone when a stranger asked us, Where is the Robie
House? My friend said, Its on 57th street. I said, correcting him,
Actually, its on 58th and Woodlawn. There was no hostility in my
voice, and I was not blaming my friend. What I said (The Robie
House is on 58th) contradicted what he said (the Robie House is on
57th), but I was not contradicting him. I was correcting him. The
difference between contradiction and correction is that when we
correct someone we do not expect their error to outlast our
utterance. We take it that as soon as they have heard and
understood our words, they will no longer have the false belief in
question. The expectation of the corrector is that once hes spoken,
theres no cause for blame. Often, in order to indicate that our aim
is to correct rather than contradict we use a marker such as
actually, or as a matter of fact,... or as it so happens,
I can only contradict someone whose beliefs I take to diverge
from the truth in a manner that is both persistent and problematic;
likewise, mutatis mutandis, for self-contradiction. If we hide
behind dialetheism or unconscious beliefs or the opinions of our
therapist or beliefs we attribute to ourselves by inference we
eliminate the very clash we are looking for. Contradiction
presupposes exactly the transparency that makes it impossible to
say, its raining, but I dont believe it or it isnt raining, but I
believe it is. The defender of refutation needs both to make room
for the asserting of Moore-paradoxical sentences and he needs to
think there is something wrong with the assertion of such
sentences. We have our work cut out for us.
X speaks of me to Y: Her beliefs are contradictory, but she
doesnt realize it. She believes that p and q, but she does not
realize p entails not q. Is it possible for me to come to learn
that what X says is true? I can come to learn that what he says was
true. But can it survive my realizationcan I come to learn that
what he says is true at the time I learn it? Yes, but not without
Xs help.
Of course it is possible for me to come on my own to the
realization that p not q. Perhaps I read it in a book, along with a
cogent argument that convinces me. At the moment I read this, do I
also realize that I believe that p and q? Perhaps notperhaps this
belief has slipped my attention at the moment. If so, my
contradiction is still unwitting. X will once again say of me, she
is contradicting herself, but she doesnt realize it, because she
doesnt know that she believes p & q. And it remains unwitting
if I do recall my belief that p and q but by a kind of mental
glitch I fail to recognize the incompatibility. (Imagine that p and
q each represent very complicated propositions, themselves full of
nested conjunctions, disjunctions and conditionals.) If I dont
realize that p & q and pq has the form of p & p, the
realization that p not q wont reveal anything further to me. It
wont teach me that I was (let alone am) contradicting myself. But
suppose I do realize that p not q, and that that is incompatible
with believing p & qwhich is to say, that it entails p & q.
Can I, at this time also believe, or believe that I believe, p
& q? No. What I can believe is that what I believed up until
now (p & q) is wrong. As soon as I come to know that it is
wrong, I dont believe it anymore.
In trying to describe a solo-self refuation, Ive ended up
describing a change of mind; for as soon as I accept that p not q,
and that p not q entails (p & q), which is to say, as soon as I
accept that (p & q), ipso facto I sever my erstwhile ties with
p & q. I will say, I used to believe that p & q, but now I
see that not p & q. There cannot be a moment at which I say to
myself, even though I believe p & q, I can see that not p.
We might put the point this way: the fact that I believed p at
some time in the past has no hold over me once I come to see the
decisive considerations against p. I can turn my back on my belief
in p at the drop of a hat. I dont need to do anything more to give
up my belief than to see that there isnt a reason to hold it
anymore, and synthesizing q and qr and rs and sp is seeing I dont
have reason to hold p anymore. Solo self-refutation is mere change
of mind, one that skips over that moment of crisis in which I
realize that what I believe now is wrong. My original belief is
relegated to an irretrievable past the instant I come to see its
falsity.
I am trying to draw out what we might call the slipperiness of
the lone reasoners thinking: to believe that I shouldnt believe
that p on the grounds of ps falsity is simply not to believe that p
anymore. Beliefs cannot knowingly violate the rule believe whats
true. There is a corresponding rule with practical reason, and it
is the rule, ought implies can. I am pondering whether to raise my
arm a moment from now, but its paralyzed or held down by a strong
weight. Upon learning this, my decision is made. Or I dont believe
the weight is strong enough to keep my hand down. I do not spend
any time knowingly mis-deliberating, considering whether I ought to
do something I know I wont be able to do. Prospective actions are
rarely revealed by subsequent events to be nomologically impossible
(let alone logically so). We should note that the idea of what I
cant do here is a legitimately practical concept, not reducible to
logical or nomological impossibility. We say, of an action, that it
is practically impossible: so costly or dangerous for it to make no
sense for us do it, or requiring skills that we dont possess and
cant readily acquire, or so difficult that the probability of our
success is too low to warrant an endeavour, or such a blatant
violation of our principles that it is excluded from deliberation a
priori. (We do say: I cannot do that, because its wrong.) If I
judge an action to be in this sense impossible, I am unable to
judge that I ought to do it; correlatively, to judge that I ought
to do it is to judge that it is, after all, possible.
As a theoretical reasoner, I must avoid the false; as a
practical reasoner I must avoid the impossible. Though of course I
can believe something that I think is true but is really false, or
consider doing something that is, unbeknownst to me, impossible.
For this reason, we could speak of the knowledge of erroneous
reasoning as a kind of blindspot[footnoteRef:4]an unbelievable
truth. The blindspot is produced by the fact that reasoning is
slippery: we lose hold of the thought (of doing X, that p) as soon
as we see its defect. [4: I borrow the term from Roy Sorensons
eponymous book.]
But in the practical case there is a way to see into the
blindspot, and that is what we do in a dilemma. Suppose I must do X
and Y, but I cannot do both. I think: I must do X, but I cannot do
X (because doing X means not doing Y, which I must also do).
Perhaps the agent resolves the dilemma. He can do so by giving up
on the necessity of doing either X or Y, or finding some way to do
both. Perhaps some dilemmas are unresolvable. Either way, during
the time before he has resolved the dilemma, he believes that he
ought to but cant do X. So, for instance, Agamemnon has a duty to
his brother to sail, but in order to make the winds come he must
sacrifice his daughter. Presumably, when originally faced with this
option he thought, I cant do that. But he also cant let Menelaus
down. Dilemmas of this kind neednt be tragic[footnoteRef:5]. Heres
a banal example: before the guests arrive, I need to cook, and I
need to clean. I must do both, but I cant do both. At some point I
decide that either I dont really have to do both (perhaps you can
clean while I cook), or that I somehow can do both (I can forgo
making dessert). Before that point, however, I might describe
myself as being in a bind, or being stuck. We say I am in an
impossible position. If I am right to suggest that when we are in
dilemmas (which is to say, before we have resolved them) we can
rightly be described as believing I ought to , but I cant, then
this should give us hope for a way out of beliefs slipperiness as
well. What we are looking for is this experience of being stuck, or
being in a bind, or there being no way out. [5: If ought implies
can is a principle about final as opposed to contributory reasons,
then my point will rest on irresolvable (tragic) dilemmas. Nothing
hangs on this, since the practical case is only an illustration for
me.]
There are theoretical analogs of such dilemmas in, for instance,
Zenos arguments against motion or Kants antinomies or paradoxes
such as the preface paradox, Newcombs problem etc. Do they afford a
way out of the theoretical blindspot that arises from the rule to
believe whats true? No. For when we get caught up in philosophical
paradoxes and find both sides compelling, we do so at first by
vacillating and eventually (after enough vacillation) by suspending
judgment. The paradoxes dont get us to believe one thing and (at
the same time) assert another. (Again, if they did, they would turn
us into dialetheists rather than stymieing us.) What makes the
practical dilemma compelling is that we believe that we ought to do
what we cant do, and that leaves us unsure about what to do; what
makes the theoretical dilemma compelling is that both sides have
good arguments, and that leaves us unsure about what to believe. We
are able to believe I ought to even though I cant , because that
belief puts us in a practical and not a theoretical bind. How can I
get myself, via belief, into a theoretical bind?
By talking to another person. Sometimes I say to you something
that I can see conflicts with what I said to you earlierso, for
instance, having said p, I say q, and qp. If it were you who had
asserted q, and qp in response to my assertion of p, you would be
contradicting what I said. You would be claiming that p is, despite
my assertion of it, false, because q is true. But when I say p, and
then without changing my mind about p in the interim assert q, and
qp, I am not contradicting what I said (p). I am contradicting
myself. This is the kind of thing Socrates interlocutors were
constantly doing.
Gregory Vlastos argued that Socratic refutations, as a class,
are failures. Socrates doesnt refute Euthyphros account of piety as
the love of the gods or Protagoras disunified picture of virtue or
Thrasymachus Nietzschean analysis of power or:
What Socratesdoes in any given elenchus is to convict p [the
interlocutors thesis] of being a member of an inconsistent
premise-set; and to do this is not to show that p is false but only
that either p is false or that some or all of the premises are
false. The question then becomes how Socrates can claim to have
proved that the refutand is false, when all he has established is
its inconsistency with premises whose truth he has not tried to
establish in that argument: they have entered the argument simply
as propositions on which he and the interlocutor are agreed. This
is the problem of the Socratic elenchus
Vlastos point is that all Socrates does is get his interlocutor
to assert something like the following series: p, q, pq. This is
not a refutation of p any more than a refutation of q, or of pq.
The interlocutor has to go back on one of the things he has said,
but it is open to him to pick which one (or ones).
Vlastos thought this was the problem of Socratic elenchus. But
really this open-endedness is the genius of Socratic elenchus.
Because until the interlocutor does go back on one of his
statementsand the dialogues in question typically end without his
having done sothe interlocutor is contradicting himself. That is,
he stands by each of his assertions, and his assertions are not
consistent. The fact that there is more than one way he could go
once he has said p, q, pq makes clear that he has not yet gone in
any one of these ways. He has not yet extricated himself from any
of his assertions, as he would if he said, the mistake was in
agreeing to pq. Thus Vlastos problem of the elenchus shows us that
there is such a thing as a time after one has uttered a
contradiction but before one has extricated oneself from itthe
state Socrates called being in aporia (literally: without a way).
And so there is a time during which one is contradicting oneself.
Vlastos is right that this means that p has not been refuted. But
Socrates was never interested in refuting propositionshe is a
refuter of men.
The only thing Vlastos gets wrong is the assumption that what he
calls the refutand is Thrasymachus Nietzscheanism, rather than
Thrasymachus. Vlastos is operating with a modern and unSocratic
conception of refutation, which is that refutation is first and
foremost refutation of views, and only thereby refutation of the
people who hold them. A belief cannot be refutedit is too slippery,
vanishing at the sight of counter-argument. Socratic
elenchus[footnoteRef:6] is personal: by a human being of a human
being. Once thought is alienated from the mind in the form of
speech, it is possible for me to be held up to and to fail by the
light of, my own words. [6: This is straightforwardly a fact about
the verb elenchein, that it means to disgrace someone or put him to
the testbut my point is also that S. makes it clear that this is
how he sees things in, e.g. Apol.]
Still, Socratic refutation is deritvatively a refutation of
views, Since Socrates refutes men by means of the views they
express. Socratic refutation rests on the idea that people can be
held to what they say, even after they say something incompatible
with it. How plausible is this? Why are we held to our past
assertions and not our past (unasserted) beliefs?
The relevant difference between assertion and belief is that I
do not believe in order to do or achieve anything further, but I
always speak with a further end in view. Speaking is not an end in
itself. At the very least, I am trying to be heard and understood,
and usually also to be believed or, at least taken seriously. These
goals introduce the possibility for new kinds of defects. Mistakes
arise for asserted beliefs that are not present for unasserted
beliefs. For instance, lies. If I assert that p without myself
believing that p, this is an error. We can put the error in terms
of assertion deviating from belief, or belief deviating form
assertion: you should say what you think is true; you should think
what you say is true. Lying introduces the possibility of beliefs
being held up to a standard other than the truth.
Is it always wrong to assert what I dont myself believe?
Consider an apparent counterexample: correcting someones inference
while disagreeing with his premises. I can sincerely say, Given
that you believe that p, you should believe that q, even though I
neither believe p nor q. Am I telling you to believe something I do
not myself believe? No. For what exactly do I assert in this case?
Exactly one thing, namely, if p then q. And I assert this in the
ordinary way, as something that I believe. I do not go beyond
asserting the conditional; I do not recommend that you go ahead and
accept q as opposed to backing up and dropping p. I cannot
(sincerely) go that far, since I do not in fact think you should
accept q. Even in hypothetical argumentation we are hamstrung by
our own beliefs and commitments. I can say to you, look where your
principles take you, they take you to p! But that is exactly what
Im saying: your principles lead to p. If I go ahead and assert p, I
either agree with you, or Im lying.
Another apparent counterexample arises when my aim is not for
you to believe p, but only to consider it. In this case, I am
allowed to assert it might be true that p or p is worth keeping in
mind or you ought to think seriously about whether pbut only if I
believe all of these things. (As I may, even without believing p.)
I am not allowed to assert p in order to get you to consider it, if
I dont myself believe that p.
I may only assert what I believe, on pain of breaking the rules
of conversationor at least, serious conversation. Sometimes I am
not asking you to take me seriously, and I know you wont be
deceived by my saying what I dont believe. Such jesting or ironic
speech is not lying, because it lacks conversational goals.
Unserious speech will have nonconversational further goals such as
entertaining you, or demonstrating my urbanity. These are
nonconversational goals because they do not aim by speech to
produce a response in kind (speech). But a conversation requires
more than the exchanging of speeches, as Socrates is wont to remind
people. When we converse, you and I are trying to do something
together by means of words.
Conversation is exchange of speeches with a shared
understandingand this in two senses. Our shared understanding about
p is both the endpoint or goal and the beginning point or opening
move of our conversation. It is the endpoint because I assert p to
you with the goal that p be something we think together: if you
dont already believe it, I want to convince you. It is the
beginning point because our conversation can only get going on the
basis of our common ground that we share in both accepting that I
believe that p. If you do not think Im being sincere, if you dont
think I really do believe that p, then my assertion that p does not
get our conversation going. In asserting that p, I express my goal
of having you believe that p, but also my request that you take
seriously the fact that I believe it. We can talk our way to the
first thing if we, from the outset, see eye to eye on the second
one. There is no common ground between us if we do not both believe
that I believe that p. A conversation is a sharing of thought and
speech. It begins when two people agree about something.
But what am I asking for in asking to be taken seriously as
believing that p? I mean for you to believe that I am sincerely and
accurately reporting my belief. For how long? Should you start to
have doubts about my believing that p the moment I close my mouth?
Or as you start offering your counter-argument? That wont workwe
must be able to both hold on to our agreement through our many
moments of disagreement. You must believe that I believe that p,
unless I tell you otherwise. And, likewise, I must believe that p,
unless I tell you otherwise: I have a conversational responsibility
to tell you if I change my mind that is akin to my conversational
responsibility to tell you the truth[footnoteRef:7]. [7: I find
much to agree with in Morans Getting Told and Being Believed. I
think he is right to insist that testimony is not a matter of
seeing the beliefs or assertions of others as evidence of their
truth but rather of trusting others. Nonetheless, I think one of
his central contentions in that paper, that testimony tells us
something about the essence of assertion, is wrong. Assertion is
not essentially testimonial. P, you can trust me on it, is not a
basic but a specialized form of assertion. What assertion is,
essentially, is conversational. I do not, in asserting p,
ordinarily suggest that you do anything wrong if you fail to
believe that p. What you do wrong is fail to take seriously my
assertionso if you disagree, you ought to say so. And you ought not
to think Im joking or lying or being ironic. If Moran were right,
the case in which I correct my friend as to the location of the
Robie house (see above, p5) would be a model for all objection. In
the world in which assertions are assurances, expression of
disagreement always contains the expectation of the immediate
dissolution of disagreement. This is not sosometimes we object
instead of correcting. Moran would, I think, grants the possibility
of objection, but he seems to think that this phenomenon is
relegated to a specialized form of assertionassertions made in the
context of persuasion, argument and demonstration. He classifies
these together with other marginal cases of assertion (therapeutic
treatment, oral examination, police investigation) which,
altogether are to be understood in terms of the more basic and
central discourse of telling. (p.8) He has, I contend, inverted the
relative importance of what I would call conversational assertion
and what he might call assurances or tellings. As a result, he has
the wrong account of the former. Moran writes that one who is
persuading is not expecting to be believed but is attempting to
provide independently convincing reasons for the truth of his view,
or laying out the steps of a proof. Telling someone something is
not simply giving expression to whats on your mind, but is making a
statement with the understanding that here it is your word that is
to be relied on. (p.8) I think the association with proof suggests
more technicality than is typical of persuasion, so let us set it
aside. Is the one who is giving reasons expecting to be believed?
It seem to me he is, or is at least hoping for this, even though he
is not expecting to be believed merely on his say so. The theorist
of assurances and tellings does not have a monopoly on the
distinction between believing a person and believing what he says.
Contrary to Morans suggestion, the persuader is not simply giving
expression to whats on [his] mind, any more than the one who tells.
For as we have seen, the one who speaks even without an assurance
is making normative demands on his listener that allow him (the
speaker) to be taken at and held to his word. ]
An unreported change of mind exhibits a conversational defect in
the interlocutor that is much like lying. Which is not to say there
cannot be reported changes of mind. I can extricate myself from my
earlier utterances by saying, I no longer think p is true. p. Or
more cautiously: Im now agnostic about p. I dont assert either p or
p. These moves are open to me to make. But extractions take some
doingat the very least, they take my uttering assertions such as
Ive changed my mind.. etc. If the extraction is on the point of
discussion, the conversation will be over (though another may
begin). If it isnt, there must be a retreat to some other common
ground. Someone who readily extracted himself from whatever he had
said would hardly be worth taking seriouslythe conversation would
be over before it got anywhere. But the main point is that
extraction takes work because conversation requires us to
charitably assume that our interlocutor hasnt changed his mind
without notice in the same way as it requires us to charitably
assume that our interlocutor is being sincere. It follows that I am
not automatically extricated from my assertion that p simply in
virtue of having said some things that conflict with p. Assuming
you are taking me seriously, you are stillrightlyattributing to me
the belief that p.
Can someone be taken seriously even when he has uttered
contradictory things? Socrates thought so. He thought that it was
not the case that all his aporetic interlocutors were violating the
conversational rule to reveal when you have changed your mind.
Instead, he charitably assumes his interlocutor hasnt changed his
mind, and still believes that p in addition to believing something
he takes to be incompatible with p. Let us label the offending
proposition as p though the interlocutor is likely to have come to
it in a more complicated form (e.g., q & qp). Consider these
two propositions:
(a) (I believe that p)[footnoteRef:8] and p [8: Parentheses
indicate narrow scope reading.]
(b) (I believe that p) and p
The interlocutor believes that either (a) or (b) is true,
therefore he believes :
(c) EITHER ((I believe that p), and p) OR ((I believe that p)
and p)
His dilemma is that he does not know which half of this
disjunction to affirmwhether (a) is the true one, or (b) is. Nor
will he, ever. To decide between them would be to come to a
decision about whether p, and at the instant he does, he ceases to
believe (c).
To be shown to believe such a disjunction is to contradict
oneself; the possibility of such belief is the solution to the
paradox of refutation. Note that nowhere is the refutee required to
contradict himself or to believe a contradiction. Indeed, in order
for the dilemma to have any force, he is required to believe that
it is not the case that p and p. Otherwise, he could believe (a)
and (b), and (c) would not be a dilemma that leaves him in
aporia.
(c) is the solution to the paradox of refutation. It is that
proposition, the believing of which is being refuted. To see why
this is so, compare (c) with either of the following two
propositions.
(d) I believe that snow is white and it is not.
(e) Some propositionI know not whichis both believed by me and
false
= p s.t.(p & I believe p)
(d) is the orthodox Moorean belief. It is what we have
repeatedly banged our heads against in the attempt to make room for
self-contradiction, only to be shown that even if it is assertible
or believable, it cannot be asserted or believed in the mode of
self-reproach. The first is of no use to the one who would explain
refutation. The second is the purview of philosophers who worry
about the preface paradox : I can know that Im most likely to have
said at least one false thing in the course of the 300 pages of my
book. What I know, if I know this, is that a sentence like (e) is
true. But this is a quite different and far less paradoxical way of
knowing that Im wrong than (c), in which I know exactly what it is
that Im wrong about. We can see this because it would be impossible
for someone to fit a realization such as (c) into the preface of
his book. Suppose I know that in chapter 3, I asserted both p and
not p. I had better fix this before publishing. I cannot wave it
aside with a humble gesture in the preface, alongside my
acknowledgements. Any writer who knowingly asserts a contradiction
in his book will not be read seriously. (Though he can, of course,
still be read as writing ironically or in jest.) And as soon as I
make the relevant correction (excising all my ps and replacing them
with ps) I will no longer have anything to be ignorant about.
Socrates would say that the humility of prefaces is cheap for
having been cheaply bought. It is no kind of achievement to know
youre wrong, and have no idea what youre wrong about.
The dilemma expressed in (c) corresponds to the practical
dilemma we considered above. To be in it is to be stuck, to not
know where ones thinking goes. In the ethical case, such a dilemma
is made possible because we think before we act. In the nonethical
case, it is made possible because we aim to share our thoughts. By
speaking, I set myself up for a fall. I give myself enough rope to
hang myself on.
We underspecify elenchus if we describe it as refutation of
people as opposed to arguments. Elenchus is that refutation of
people in which the people who are being refuted know they are
being refuted. And the one who refutes does so knowing that they
know this. The knowledge of refutation is shared knowledge,
something only known by either one because it is first of all known
by the two of them together. There is no saving face in a Socratic
elenchus because each persons knowledge is somehow already the
other persons knowledge as well. Some of the dialogues represent
this publicity of refutation dramatically by supplying spectators
whose presence underscores the humiliational aspects of the
elenchus: the refutands downfall is public knowledge. But even
unspectated refutations are shared knowledge, in the sense that
Socrates and, e.g., Euthyphro, both know well what has gone on
between them. In the world of Socrates, refutations are ad hominem,
and no one is unwittingly refuted.[footnoteRef:9] Refutation is
something that people do together. And this is just another way of
saying that contradicting myself is something I cannot do alone.
[9: This is true even of, e.g., the refutation of Anytus in the
Meno, where S. makes clear that Anytus has the wrong end of the
stick in a lot of ways and hasnt properly understood what happened
between them; nonetheless, its clear that Anytus knows, and knows
that S. knows, and knows that S. knows that he knows.that hes been
refuted. ]
If refutation is not to be the practice of sadists, we must ask
what the point of it is. What good does it do the self-contradictor
to believe (c)? What does he learn, by learning (c)? If we turn to
the Socratic corpus, we find it that it has been waiting for us to
ask this question. This question is the lock that anay, thekey
Socratic mantra turns. Socrates thinks that the self-contradictor
learns something about himself, namely, that he has fails to live
up to his own standards for belief and assertion. The
self-contradictor is not remarkable for his ignoranceremember, were
all ignorant, since human knowledge is worth little or nothing. The
self contradictor is remarkable in that he fails to know, with
reference to p, in a peculiarly conscious and aware mannerhis
failure to know is not escaping his own notice. The refutee
displays knowledge of his own failure to know, not in the
abstractas in the preface paradoxbut with reference to a particular
proposition. What the self-contradictor knows is that he is wrong
about whether p[footnoteRef:10]. He can know, of himself, that he
has the false view on the topic of whether or not p should be
negated. The knowledge of the self-contradictor is knowledge of his
own ignorance. This is what it is to see into the blindspot. [10: I
should at least mention two other famous Moore sentences:(d) p, but
I dont believe that p (d) p, but I dont know that p There is no p
but I know that p since that is a logical contradiction. I will
consider (d) first. Though (d) is just as unassertible/unbelievable
as our original (d), it produces less interesting variants on (e)
and (c):(e) there exists a p s.t. p, but I dont believe it (c)
EITHER ((I dont believe that p), and p) OR ((I dont believe that p)
and p)(e) is the analog to the thought of the preface writer,
except that the one who asserts it, instead of claiming that he
knows he is wrong about something, claims, with what barely amounts
to humility, that he knows he doesnt know everything. (c) is the
analog to the refutees thought, in which someone asserts that there
is a specific proposition of which he does not know whether it is
true or false. But, as with the original (c), he cannot affirm
either disjunct. This analog to the refutees thought picks out the
much weaker sense of knowing ones own ignorance that is realizing a
(particularized) absence of knowledge, as opposed to realizing that
one is wrong or believes falsely. Now let us turn to (d). It
produces another uninteresting weak variant on (e), which I wont
discuss, and:(c) EITHER ((I dont know that p), and p) OR ((I dont
know that p) and p)(c) is, I believe, at least a part what Socrates
knowledge of his own ignorance consists in. He believes (c) is true
for the proposition under discussion in the dialogue, which is why
his task is relegated to refuting his interlocutor. If he knew
whether p or not p, he could prove this to his interlocutor instead
of merely refuting what they say. To believe (c) to be true is to
be in a position to ask a question about p. The reason why I say
that this is only a part of Socrates ignorance, is that he seems
more fundamentally not to know what the terms inside p signify. So,
if p is virtue is teachable Socrates fundamental question is what
is virtue? He is asking not after the truth of a proposition but
the account of the being of something. Im not sure how to fit this
in with the purely propositional structures of self-knowledge of
ignorance Ive identified here.]
If Wittgensteins private language argument is right, all
thoughts can be made publicthere are no essentially private
thoughts; if Socrates is right, some thoughts cant be made
privatethere are some essentially public thoughts. I believethough
I cannot argue for it herethat Socrates identified, and was right
to identify, the set of essentially public thoughts with the set of
philosophical thoughts. The claim that there even is such a thing
as a thought that is built for two is bound to meet with
resistance. That is why chronologically, of all the philosophical
ideas, refutation must come first. Refutation is the beginning of
philosophy because it proves the very possibility of philosophy to
one who would deny itto refute someone is to show him that there is
something he can think with another that he could not have thought
alone. It shows him the futility of trying to think for himself.
(Human knowledge is worth little or nothing.) The Socratic
dialogues record the struggles of a man to think some things he
recognizes he cannot think alone. I believe that they all succeed,
not in spite of but because of the fact that so many of them end in
aporia.
Even though it is not possible to believe a contradiction, it is
possible to be in aporia by believing that you are wrong about
whether p. The refutee comes to this belief by availing himself of
two resources which are not available to the would be believer of a
contradiction: an extent of time and the mind of another. We can
contradict ourselves, but we cant do it alone, or in an
instant.
1
1
Contradiction alone is the proof that we are not everything.
--
Simone Weil,
Gravity and Grace
T
he Paradox of Refutation
and its Socratic Solution
Socrates refutes people by
getting
them
to
contradict
themselves
. Socratic conversation not only
contains but can rightly be said to
aim
at such refutation (
Apology
23b
).
He thinks that refutation is
possible, therefore he thinks that it is possible for someone
to
contradict himself.
And so do we. As
philosophers, we
have firsthand experience of the phenomenon we also observe in
the Socratic
dialgues, because we carry the Socratic torch
. We are refuters
. The question of this paper is, what
are we and what is Socrates
aiming at
in the act of
refut
ation
?
What is self
-
contradiction?
Self
-
contradiction
would
be ill
-
named if it had nothing
to do with contradiction.
One plausible
account of what it is to contradict oneself is to
that one does so by
assert
ing
or believ
ing
a
logical
contradiction. The simplest way to a
ssert
or believe
such a
contradiction is to assert
or believe
both
a proposition and it
s negation.
For purposes of brevity, I will use the word judge to cover
both
asserting and believing, and
I will describe the
judging
of a contradiction as
a judgment
which fits
the schema
p and
p
.
I
t is
, however,
possible to
judge
contradictions in (indefinitely many) more
complicated ways
, such as:
(1)
judging
p and also
judging
if p then q and also
judging
q
or
(2)
judging
p and q and also
judging
p
or
q
.
The problem with this account of
self
-
contradiction is that its not clear that
any
one
can
judge a
contradiction.
If judging is just our shorthand for asserting/believing, then
judging X should be the
same as judging it to be true. But most of
us are committed to the impossibility of contradictions
being true, and therefore to their consequent unbeli
evability and unassertibilty. That is: we are
committed to the
logical, psychological and lexical laws of
noncontradiction, respectively.
Of
cours
e, not all of us are so committed: dialetheists think that there
are true contradictions.
But this
is of no help, not even to them: true contradictions, if there
were any, would also be
precisely those
contradictions you
could not
refu
t
e s
omeone by gettin
g him to assert!
Refuters,
dialtheistic or
otherwise
,
are faced with the problem that the contradiction we need the
person to
judge
if he is to
be refuted is one that
he shouldnt be able to
judge
.
Refutation would be quixotic
indeed
if success
required
us to get the interlocutor to do something we believed
it
impossible for him to do.
But am I overstating things?
Here is a
familiar cases in which someone
can
be said to judge a
contradiction
:
change
of
mind. Someone might
say
p
wait a minute
(with
the twisted face of
one upon whom realization dawns)
sc
r
a
t
ch that,
p!
We might even suppose that he says, p
No, let me contradict that
actually, p! We do sometimes aim
to get our interlocutor to
change
his mind
if I know that p, I might aim to
get
you to adopt this belief,
kn
o
w
ing I will face some
resistance because
you
currently
believe p.
Speech aimed at change of mind
involves refutation
at
most
incidentally
,
as one among many means to getting you to the belief that p. For
I can
sometimes prod
uce conviction in you that p just by saying, Trust me, p. If I
have enough clout,
that might be enough to get you to drop p and adopt p, without
any refutation having taken place.
Refutation is neither necessary nor sufficient for change of
mind, and
it is easy to see why: in
refutation, we are aiming to put the person into a single
problematic state, not into two distinct
nonproblematic states which would only
be
problematic if they were not insulated from one another.
Someone who changes his mind ju
dges
p
, and he
judges
p,
but he
does
not
judge
p and not p.
He does not assert a contradiction in the way that
our refut
ee
would
need to.
