“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 it’s 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 shouldn’t 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) “…scratch 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, 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.
1
We need someone to judge a contradiction without changing his mind midstream. Is this possible?
Yes, so long as the one doing it doesn’t realize that’s what he’s doing. If I judge that the TanayamaShimura conjecture is true but Fermat’s last theorem is false, you could say of me, ‘she is
contradicting herself, though she doesn’t realize it.’ This is a way we use the term ‘selfcontradiction,’ 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 selfcontradiction + 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 I’m 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 victim’s selfcontradiction 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 isn’t that we
cannot make sense of the idea of judging a contradiction—the problem is that we seem to be able to
make sense only of contradictions of which we can make no refutational use. We haven’t 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
refutee—not because we can’t do so, but because we wouldn’t want to if we could. What we are
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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 is—not was—in some kind of epistemically defective condition.
We are trying to put someone in the state Socrates’ interlocutors described as ‘aporia’ or being-at-aloss, a state that consists in the thinking that one’s 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, ‘I’m
probably wrong about something-or-other.’ This kind of generalized detachment from one’s beliefs
itself raises paradoxes1, but it is not nearly so paradoxical as when the offending belief is specified.
This change of target raises two questions. The first question (Q1) is whether we’ve made the
project of refutation any more feasible by replacing ‘p and not p’ with ‘I’m 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 selfcontradicter as asserting ‘p and not p,’ we have been tacitly assuming that the relata are propositions.
‘I’m 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 “p”—we say, “no, not p” or “I disagree” or “you’re 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 say—but 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 don’t 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 p—this would not be contradicting. I
1
See below, where I distinguish the paradox of refutation from the preface paradox.
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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 don’t 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 don’t believe it.”2 To generate
self-contradiction, what we do is substitute “I’s” for all the “you’s.” 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 we’re going for a contradiction. But we have thereby sharpened Q1. For
it is famously impossible—though not logically contradictory—to assert or believe any of those
statements.
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 D’s list, he can assert, ‘p, and I
believe that not p,’ without any trouble. (Although he cannot assert, ‘p, and I don’t believe it,’ unless
‘I believe that p and I don’t believe that p’ is also on his list.) In form, this counts as the assertion of
a Moore-paradoxical sentence, but it won’t 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 addition—he 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
said—he 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.3
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 otherwise—by 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 won’t work to vouchsafe the possibility of the
kind of self-contradiction we are interested in. For instance, consider unconscious beliefs. I might
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 you’ll 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.’
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 anyone’s view. If it isn’t,
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.
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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 can’t 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 aren’t.’ 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 that’s ok”—in such a case, I don’t 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, “It’s on 57th street.” I said,
correcting him, “Actually, it’s 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 he’s
spoken, there’s 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, ‘it’s raining, but I don’t believe it’ or ‘it
isn’t 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 doesn’t 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 realization—can I
come to learn that what he says is true at the time I learn it? Yes, but not without X’s 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 not—perhaps 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 doesn’t realize it, because she doesn’t 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 don’t realize that ‘p & q and p¬q’ has
the form of p & ¬p, the realization that p not q won’t reveal anything further to me. It won’t
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 & q—which 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 don’t believe it anymore.
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In trying to describe a solo-self refuation, I’ve 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 don’t need to do anything more to give up my belief than to see that there isn’t a
reason to hold it anymore, and synthesizing q and q→r and r→s and s→¬p is seeing I don’t 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 reasoner’s thinking: to believe
that I shouldn’t believe that p on the grounds of p’s falsity is simply not to believe that p anymore.
Beliefs cannot knowingly violate the rule ‘believe what’s 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 it’s paralyzed or held down by a strong weight. Upon learning this, my
decision is made. Or I don’t 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
won’t 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 ‘can’t’ 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 don’t possess and can’t 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 it’s 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 blindspot4—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.
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 can’t 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 can’t do that.” But he also can’t let Menelaus
4
I borrow the term from Roy Sorenson’s eponymous book.
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down. Dilemmas of this kind needn’t be tragic5. Here’s a banal example: before the guests arrive, I
need to cook, and I need to clean. I must do both, but I can’t do both. At some point I decide that
either I don’t 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 can’t,’ then this should give us hope for a way out of belief’s
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.
There are theoretical analogs of such dilemmas in, for instance, Zeno’s arguments against motion or
Kant’s antinomies or paradoxes such as the preface paradox, Newcomb’s problem etc. Do they
afford a way out of the theoretical blindspot that arises from the rule to believe what’s 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
don’t 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 can’t 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
can’t ,’ 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 earlier—so, for instance, having said p, I say q, and q→¬p. If it were you who had
asserted q, and q→¬p 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 q→¬p, 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 doesn’t refute
Euthyphro’s account of piety as the love of the gods or Protagoras’ disunified picture of virtue or
Thrasymachus’ Nietzschean analysis of power or…:
What Socrates…does in any given elenchus is to convict p [the interlocutor’s 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, p→¬q. This is not a refutation of p any more than a refutation of q, or of p→¬q. The
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.
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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 statements—
and the dialogues in question typically end without his having done so—the 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, p→¬q”
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 p→¬q’. 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 it—the 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
propositions—he 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 ‘refuted’—it is
too slippery, vanishing at the sight of counter-argument. Socratic elenchus6 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.
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 don’t myself believe? Consider an apparent counterexample:
correcting someone’s 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
This is straightforwardly a fact about the verb elenchein, that it means to disgrace someone or put him to the test—but
my point is also that S. makes it clear that this is how he sees things in, e.g. Apol.
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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 I’m saying: your principles lead to p. If I go ahead and assert p, I either
agree with you, or I’m 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 p’—but 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 don’t myself believe that p.
I may only assert what I believe, on pain of breaking the rules of conversation—or at least, serious
conversation. Sometimes I am not asking you to take me seriously, and I know you won’t be
deceived by my saying what I don’t 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 understanding—and 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 don’t 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 I’m being sincere, if you don’t 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 won’t work—we 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 truth7.
I find much to agree with in Moran’s “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 assertion—so if you disagree,
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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: ‘I’m now agnostic
about p. I don’t assert either p or ¬p.’ These moves are open to me to make. But extractions take
some doing—at the very least, they take my uttering assertions such as ‘I’ve changed my mind..’ etc.
If the extraction is on the point of discussion, the conversation will be over (though another may
begin). If it isn’t, 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 seriously—the
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 hasn’t 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 still—
rightly—attributing 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 hasn’t 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 & q¬p). Consider
these two propositions:
(a) (I believe that p)8 and ¬ p
(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)
you ought to say so. And you ought not to think I’m 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 so—sometimes 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 assertion—assertions 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 what’s 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 Moran’s suggestion, the persuader is not ‘simply giving expression to what’s 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.
8 Parentheses indicate narrow scope reading.
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His dilemma is that he does not know which half of this disjunction to affirm—whether (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 proposition—I know not which—is 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 I’m 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 I’m wrong than (c), in
which I know exactly what it is that I’m 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 p’s and replacing them with ¬p’s) 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 you’re wrong, and have no idea what you’re 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 one’s 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 person’s
knowledge is somehow already the other person’s knowledge as well. Some of the dialogues
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represent this publicity of refutation dramatically by supplying spectators whose presence
underscores the humiliational aspects of the elenchus: the refutand’s 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.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.
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 a—nay, the—key 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 ignorance—remember, we’re 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 manner—his failure to know is not
escaping his own notice. The refutee displays knowledge of his own failure to know, not in the
abstract—as in the preface paradox—but with reference to a particular proposition. What the selfcontradictor knows is that he is wrong about whether p10. 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.
If Wittgenstein’s ‘private language argument’ is right, all thoughts can be made public—there are no
essentially private thoughts; if Socrates is right, some thoughts can’t be made private—there are
some essentially public thoughts. I believe—though I cannot argue for it here—that Socrates
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 hasn’t properly understood what happened between them; nonetheless, it’s clear that
Anytus knows, and knows that S. knows, and knows that S. knows that he knows….that he’s been refuted.
10 I should at least mention two other famous Moore sentences:
(d’) p, but I don’t believe that p
(d’’) p, but I don’t 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 don’t believe it
(c’) EITHER ((I don’t believe that p), and p) OR ((I don’t 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 doesn’t know
everything. (c’) is the analog to the refutee’s 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 refutee’s thought picks out the much weaker sense of knowing one’s 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 won’t discuss, and:
(c’’) EITHER ((I don’t know that p), and p) OR ((I don’t 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. I’m not sure how to fit this in with the purely propositional structures of selfknowledge of ignorance I’ve identified here.
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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 it—to 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 can’t do it alone, or in an instant.
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