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Philosophy Compass 10/1 (2015): 10–23, 10.1111/phc3.12187

Moore’s Paradox in Speech: A Critical Survey

John N. Williams* Singapore Management University

Abstract It is raining but you don’t believe that it is raining. Imagine accepting this claim. Then you are committed to saying ‘It is raining but I don’t believe that it is raining’. This would be an ‘absurd’ thing to claim or assert, yet what you say might be true. It might be raining, while at the same time, you are completely ignorant of the state of the weather. But how can it be absurd of you to assert something about yourself that might be true of you? This is Moore’s paradox as it occurs in speech. What is the source of the absurdity? And why does it strike us that a contradiction is somehow at work when there is no contradiction in the content of what is asserted? In Section 2, I describe Moore’s formulation of the paradox and evaluate his own solutions. In Section 3, I discuss Wittgenstein’s influence in solving the paradox. In Section 4, I discuss Shoemaker’s priority thesis that once the absurdity in belief has been explained, then this will translate into an explanation of the absurdity in assertion. In Section 5, I discuss work on omissive and commissive Moore-paradoxical assertions, i.e. those of the forms p & I don’t believe that p and p & I believe that not-p. In Section 6, I discuss work on assertions of the form p & I don’t know that p.

1. The Paradox

It is raining but you don’t believe that it is raining.

Imagine accepting this claim. Then you are committed to saying, ‘It is raining but I don’t believe that it is raining’. This would be an ‘absurd’ thing to assert, yet what you say might be true. It might be raining, while at the same time, you are completely ignorant of the state of the weather. But how can it be absurd of you to assert something about yourself that might be true of you? This is Moore’s paradox. The paradox occurs in thought as well, since if you silently believe the content of that would-be assertion, then you seem no less absurd. Yet, as we have just seen, the content of such an absurd belief might be true. How is that possible? What is the source of the absurdity? And why does it strike us that a contradiction is somehow at work when there is no contradiction in the content of what is asserted or believed?1 Solving the paradox consists in explaining why such assertions or beliefs are absurd. Must the absurdity be a form of irrationality? In what follows, I survey some of the literature on the paradox in speech. In ‘Moore’s Paradox in Thought: A Critical Survey’, I survey some of it on the paradox in thought.

2. Moore on the Paradox

In two different works, G.E. Moore gave the following examples of assertions:

‘I went to the pictures last Tuesday but I don’t believe that I did’ (1942, 543)

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and

‘I believe that he has gone out, but he has not’ (1944, 204).

If we let ‘p’ stand for the proposition I went to the pictures last Tuesday, then the form of the first assertion is the conjunction

p & I do not believe that p.

Moore says of these utterances that ‘[i]t is a paradox that it should be perfectly absurd to utter assertively words of which the meaning is something which might well be true – is not a contradiction’ (Baldwin 1993, 209). Discussion of such conjunctions appears to have originated with A.M. MacIver (1938). Sorensen (2007) finds isolated approximations to this absurdity in Jean Buridan, Parmenides, Plato, Sextus Empiricus, Augustine, Descartes, Spinoza, and others. Moore also poses the paradox another way, noting that

… as a rule, if it’s not absurd for another person to say assertively a sentence expressing a given proposition to me or to a third person, it isn’t absurd for me to say assertively a sentence expressing the same proposition (Baldwin 1993, 208–209, see also Chan 2010).

Thus, you normally detect no absurdity if I assert

‘I went to the pictures last Tuesday but he doesn’t believe that I did’.2

Nor does the absurdity seem to arise when the assertion is not conjugated in the present tense. You detect no absurdity if I assert

‘I went to the pictures last Tuesday but I didn’t believe that I did’

‘I went to the pictures last Tuesday but I will not believe that I did’.

In the first case, I may have only just remembered going to the pictures. In the second, I may know that I will shortly experience loss of memory (however, for dissent about the second case, see Bovens 1995 and Van Fraassen 1995). Moore claims that in making a first-person present-tense indicative assertion, one ‘implies’, in

a ‘non-mysterious’ sense (1942, 542), that one believes it. Thus, Moore’s first principle is that

If one asserts that p, then one implies that one believes that p.3

So since asserting a conjunction involves asserting its conjuncts (‘assertion-distribution’), when I assert that (p & I don’t believe that p), I assert that p. Hence, I imply that I believe that p, which flatly contradicts the second conjunct of my assertion. So what I assert f latly contradicts what I imply by asserting it (Baldwin 1993, 210). Moore’s first example has the ‘omissive’ form

p & I don’t believe that p

so-called because it self-reports a specific lack of true belief. In contrast, his second example,

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‘I believe that he has gone out, but he has not’

may be formalized as

I believe that p & not-p.

This is equivalent to

not-p & I believe that p

which may just as well be represented as

p & I believe that not-p.

Following Sorensen (1988), this may be called the ‘commissive’ form, since it self-reports my specific mistake in belief. Williams (1979) was the first to draw attention to this difference, which stems from that between atheists and agnostics. Let us call assertions that are possibly true yet absurd in the way Moore exemplifies, ‘Moore-paradoxical’ and assertions that have the same form or syntax as these, ‘Moorean’. Moore’s examples are both Moore-paradoxical and Moorean, although we will see later that Moorean assertions are not always Moore-paradoxical, nor conversely. Moore (1944) deals with the commissive example by using Moore’s second principle:

If one asserts that p, then one implies that one doesn’t believe that not-p.

Given assertion-distribution, if I assert that (p & I believe that not-p), then I assert that p. So I imply that I don’t believe that not-p, which flatly contradicts the second conjunct of my assertion. So again, what I assert f latly contradicts what I imply by asserting it. This suggests the possibility that Moore himself may not have seen the difference between

the omissive and commissive forms, perhaps because his own examples disguise them. For in advancing the first principle (1942), he nowhere mentions the second (1944), nor visa versa. Moreover, his second principle fails to explain the omissive assertion. For if I assert that (p & I don’t believe that p), then I imply-and-assert that I neither believe that not-p nor believe that p, which is a possible state of sensible agnosticism. Let us suppose that Moore did see the difference but was content to apply the first principle to the omissive case and the second to the commissive case. Then I have implied-and-asserted a contradiction in either case (that I do and don’t believe that p, in the omissive case and that I do and don’t believe that not-p, in the commissive case) so now the two absurdities come out as conceptually identical. But since the omissive form, which reports a specific instance of my ignorance, is semantically distinct from the commissive, which reports my specific mistake, we might expect a resulting structural difference in the contradiction-like phenomena that constitute the resulting absurdity. A more serious problem is that of elucidating the ‘non-mysterious’ sense of ‘imply’. Moore

claims (1942, 542–543) that his first principle

… arises from the fact, which we all learn by experience, that in the immense majority of cases a man who makes such an assertion does believe or know what he asserts: lying, although common enough, is vastly exceptional.

But as Baldwin observes (1990, 228), this ‘suggests that … in the mouth of a known habitual liar paradoxical sentences should not sound at all absurd’. If you learn that I’m lying to you when

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I make Moore-paradoxical assertions, this knowledge does nothing to expunge the absurdity. Nor will any other context of communication expunge it (as Rosenthal notes in 1995, 203. See also Cargile 1967). Moore also says:

… the sense of ‘imply’ in question is similar to that in which, when a man asserts anything that might be true or false, he implies that he himself, at the time of speaking, believes or knows the thing in question (Moore 1942, 541).

So to assert

‘It is raining but I don’t know that it is raining’

would likewise be ‘absurd’. I will return to this ‘knowledge version’ of the paradox in Section 6.

3. Wittgenstein on the Paradox

Malcolm reports Wittgenstein as having

once remarked that the only work of Moore’s that greatly impressed him was his discovery of the peculiar kind of nonsense involved in such a sentence as ‘It’s raining but I don’t believe it’ (1984, 56).

In a letter to Moore, Wittgenstein notes the importance of Moore’s discovery of an absurdity ‘which is in fact similar to a contradiction, though it isn’t one’ and adds that Moore has ‘said something about the logic of assertion’ (1974, 177). In the Investigations, he coins the term ‘Moore’s paradox’, which he formulates in terms of supposition:

“I believe that this is the case” is used like the assertion “This is the case”; and yet the hypothesis that I believe that this is the case is not used like the hypothesis that this is the case. (1953, 190)

Accordingly, he elsewhere comments that “ ‘I believe p’ means roughly the same as ‘p’ ” (1980a, §472). On this view of it, the absurdity of Moore-paradoxical assertion lies in Wittgenstein’s principle:

If one asserts that one believes that p, then one asserts that p.

This explains the absurdity of the commissive assertion, for in asserting that (p & I believe that not-p) I assert that I believe that not-p and so assert that not-p, which contradicts my assertion that p. So although what I have asserted is not a contradiction, my assertion of it involves contradictory assertions. Contemporary followers of Wittgenstein (notably Heal 1994, also Goldstein 1993; Jacobsen 1966 and 1997; Malcolm 1995 and Linville and Ring 1991, see also Gombay 1988) have defended this sort of explanation (see Williams 1998, §§3–6). One difficulty with it is that it cannot explain the absurdity of the omissive assertion. For in asserting that (p & I don’t believe that p) I assert a lack of belief, to which the principle cannot apply. This suggests adding ‘Wittgenstein’s’ second principle:

If one asserts that one doesn’t believe that p, then one denies that p.

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But on that principle, an agnostic who truthfully reports, ‘I neither believe that God exists nor believe that he doesn’t’ would be making contradictory assertions. Plainly she isn’t. Another difficulty arises if you ask me whether the post office is open and I reply, ‘I wouldn’t like to say, but I think so’. You cannot reasonably blame me for having stated a falsehood, especially since I went to the trouble of clearly stating my reluctance to make an assertion.4

After Wittgenstein, writers on the paradox largely considered it only as occurring in speech (for example, Bonney 1965; Black 1952; Cohen 1950; Collins 1996; Deutscher 1965 and 1967; Doran 1995; Jones 1991; Welbourne 1992; Willis 1953 and Wolgast 1977, some of which are surveyed by Green and Williams 2007, Chapter 1). Then the focus was upon the pragmatic absurdity of a speech-act. Many of their writings are likewise faulted by a failure to distinguish the omissive from the commissive assertion. Wittgenstein also makes the important point that the absurdity is only present in speech when

the utterance is an assertion (1980a §§485–487, 1980b §290). No absurdity arises if I say, ‘It is raining but I do not believe that it is raining’ in order to test a microphone or say under duress, ‘The train will arrive at 5 pm’ and add, ‘but personally I don’t believe it’. Nor does it arise when delighted by the imminent arrival of a friend, I exclaim in amazement, ‘He’s coming to visit me but I still can’t believe it!’. (For other cases, see Williams 2001, §9. See also Cargile 1967). This suggests that assertion is an essentially pragmatic phenomenon, so an explanation of the absur- dity of Moore-paradoxical assertion purely in terms of the semantics of utterances (e.g. Lawlor and Perry 2008) is misguided (see Green and Williams 2011). Wittgenstein adds that it is ‘a most remarkable thing, that the verbs “believe”, “wish”, “will”

display all the inflections possessed by “cut”, “chew”, “run” ’ (1953, II, §X, 190). His remark, albeit unclear, prompts the conjecture that analogous absurdity may be found in terms of desire (see Wall 2012; Williams 2014). For example, suppose that as we approach a bar, you ask me what I want to drink. I report my desire by answering, ‘I want to drink stout while wanting not to drink it’. However, Adler and Armour-Garb (2007) argue that only cases involving belief generate Moorean absurdity.

4. The Relation of the Paradox in Belief to the Paradox in Assertion

Shoemaker remarks that given an explanation of why it is impossible for a rational person to have Moore-paradoxical beliefs, then

… an explanation of why one cannot assert a Moore-paradoxical sentence will come along for free, via the principle that what one can believe constrains what one can assert (1996, 213).

He adds that

If you have an explanation of why a putative content could not be coherently believed, you thereby have an explanation of why it cannot be coherently asserted. (1996, 227, note 1)

So one’s belief constrains one’s assertion in the sense that if one’s assertion that p is ‘coherent’ or rational, then so is one’s belief that p. Thus, by transposition,

If one’s belief that p is irrational then so is one’s assertion that p.5

Since then, the orthodoxy has been that an explanation of the absurdity should first start with belief, on the assumption that once the absurdity in belief has been explained, then this will translate into an explanation of the absurdity in assertion (for example Adler 2002, 74; Douven

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2009, 364; Kriegel 2004, 102 and Williamson 2000, 255). This idea is foreshadowed by Hintikka (1962), who claims that ‘the gist of Moore’s paradox may be said to lie in the fact that’ the omissive proposition p and I don’t believe that p ‘is necessarily unbelievable by the speaker’ (1962, 67). In other words, the assertor is absurd because it is impossible for her to believe the content of her assertion if she is rational. This makes the explanation of the absurdity of Moore-paradoxical assertion derivative from that of Moore-paradoxical belief. Let us call the principle above ‘the priority thesis’, since it gives explanatory priority to belief

over assertion. Williams (2013) argues against the priority thesis, that the absurdity of Moore-paradoxical assertion is not always a subsidiary product of the absurdity in belief, even when the absurdity is conceived as irrationality (see also Fernández 2005). To see this, we must distinguish the rationality of belief from that of assertion. The ‘epistemic’

rationality of a belief may be seen as that property of it, if true and not Gettierized, needed for it to be knowledge. In contrast, the rationality of one’s speech-act of assertion is the rationality of action. The ‘practical’ rationality of actions, including assertions, may be seen as one’s acting in a way that an epistemically rational believer, similarly placed, would believe best promotes one’s interests by satisfying one’s desires and fulfilling one’s intentions. Practically irrational assertions might include, in the right circumstances, attempting to compliment a stranger by telling him that he is stupid. This sense of the rationality of an assertion is close to an older tradition of discussions of Moore-paradoxical assertion (Baldwin 1990; Jones 1991 and Welbourne 1992) in terms of the point of an assertion, for example whether the speaker intends to impart knowledge, instill belief, or deceive one into accepting a falsehood. There also seems to be a sense in which an assertion might be said to be ‘epistemically rational’,

in which the assertor is judged to have a corresponding epistemically rational belief under the assumption that she is sincere.6 This seems close to Williamson’s sense of ‘warranted assertion’ (2000, 253). Applying this sense of ‘irrational assertion’ to the priority thesis turns it into

If one’s belief that p is epistemically irrational, then one’s assertion that p is irrational, in the sense that one’s belief that p is epistemically irrational, under the assumption that one is sincere.

Of course this is true, but only trivially so. This makes the thesis entirely empty of content. So it must be read as

If one’s belief that p is epistemically irrational then one’s assertion that p is practically irrational.

But I might purport to express to you an epistemically irrational belief that I do not have, as part of an attempt to deceive you into thinking mistakenly that I am mad. If I have a good practical reason for this attempt, such as avoiding legal culpability, purporting to express the irrational belief is practically rational. Alternatively, I might express to you an epistemically irrational belief that I really do have. Although I recognize that I have the belief, still I cannot rid myself of it, and so I express it to you in order to inform you that I have it, as part of an attempt to get psychiatric or legal help from you. If I have a good practical reason for this attempt, such as seeking cure or compensation, expressing the irrational belief is again practically rational. For example, suppose that I discover – perhaps as the result of a blow to the head – that I have

the belief that I mistakenly believe that people are following me. This belief is epistemically irrational. Nonetheless, it seems that I may report and thus express my belief to you, my ther- apist, by telling you, ‘People are not following me but I still can’t help believing that they are’. If you persist in reassuring me that I am not being followed, I might even strengthen this to, ‘Look, I jolly well know that people are not following me but I still can’t help believing that they are!’ My

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assertion is sensible because it is part of my sensible attempt to get further help from you as a form of epistemic damage-control. Thus, independent explanations of the absurdity in belief and in assertion seem to be needed.

However, in attempting a complete account of it, an explanation of the absurdity of belief is a sensible place to start first, because it looks likely that an elucidation of assertion will involve the notion of belief and so will be more complex, especially once one considers the myriad points or purposes of speech-acts of assertion. Nonetheless, I will continue to confine myself to examining the paradox in speech in this survey.

5. The Absurdity of the Omissive and Commissive Assertions

There are also non-verbal Moore-paradoxical assertions, as when you ask me if the pubs are still open and I nod my head in emphatic affirmation while saying, ‘I don’t believe so’. This shows the need for an account of the nature of an assertion that does not appeal entirely to the meanings of sentences, in order to show why the paradox does not arise in wholly non-assertoric utterance. Nonetheless, there is a class of partly non-assertoric utterances (following Black 1952, discussed by Heal 1977; Searle and Vanderveken 1985 and Shoemaker 1988) that have an air of Moore-paradoxicality, such as, ‘What time is it? But I don’t want to know what time it is’. On one major approach to the paradox in assertion, one expresses belief in what one asserts

(Rosenthal, 1995, 2001, 168). So in asserting that (p & I don’t believe that p) I assert that p and so express belief that p. But I have also asserted that I don’t believe that p. So I have asserted- and-expressed a flat contradiction. The explanation of the commissive assertion would go: in asserting that (p & I believe that not-p), I assert that p and so express belief that p. But I have also asserted that I believe that not-p. So I have asserted-and-expressed a contradiction in belief. What remains to be elucidated, however, is what expressing belief amounts to and how it is

involved in assertion. Green (2007, 43) argues that one expresses a cognitive state to which one can have introspective access just in case one is in it and one’s action or behavior both ‘shows and signals’ that state. On this account, one asserts that p just in case one performs an act intending that (a) in performing it, it be manifest that one is committed to believing that p and (b) it be manifest that (a). Williams (2013) argues that one purports to express a belief that p to one’s interlocutors just in case one offers them defeasible reason to think that one believes that p. One asserts that p just in case one purports to express a belief that p with the intention of changing the beliefs or knowledge of one’s actual or potential interlocutors in a relevant way. Kriegel (2004, 102) makes the interesting claim that assertions must express conscious beliefs.

Atlas (2007) argues that the paradox in speech requires an indirect reflexive pronoun such as ‘I myself’ to guarantee that the speaker knows that she is speaking of herself. Williams (1994, 2013 and 2014) gives an explanation of the absurdity of Moore-paradoxical

assertion in terms of believing the speaker. When I make an assertion to you, I normally intend you to believe me, in other words, think that I am sincerely telling the truth. If you think that I am sincere in asserting the first conjunct of ‘p & I don’t believe that p’, then you believe that I believe that p. But if you think that I am telling the truth in asserting the second conjunct, then you believe that I do not believe that p. So you must have overtly contradictory beliefs if you believe me. On my charitable presumption that you are rational, I am in a position to see that you cannot believe me. The commissive assertion comes out differently. If you think that I am sincere in asserting the

first conjunct of ‘p & I believe that not-p’, then again you believe that I believe that p. But if you think that I am telling the truth in asserting the second conjunct, then you believe that I believe that not-p. This time you must think that I have overtly contradictory beliefs, and so cannot believe me if you think that I am rational.

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Williams (2012) couples this account with his principle that conscious belief both distributes and collects over conjunction:

One consciously believes that (p & q) just in case one both consciously believes that p and one consciously believes that q.

I cannot sensibly aim to make you accept either the truth of my omissive assertion or my sincerity in making it, on the assumption that you are asleep or not concentrating on my assertion. If you are indeed conscious of each belief, then since conscious belief collects over conjunction, you are conscious of believing that I both do and do not believe that p. In other words, you are now fully aware of believing a self-contradiction. On my charitable assumption that you are epistemically rational, I should see that you will not believe me. Since making you believe me is normally my aim, I am practically irrational in attempting the assertion. In the commissive case, you are conscious of believing that I have overtly contradictory beliefs. In most cases, I will not want you to think that I am epistemically irrational, if I am practically rational myself. Pagin (2011) proposes and defends the informativeness of assertion:

An utterance u is an assertion just in case u is prima facie informative

and informativeness:

An utterance u is informative just in case u is made partly because it is true.

Pagin (2008) applies this idea to Moore-paradoxical assertions. Suppose that I assert that (p but I don’t believe that p). If the second conjunct of what I have asserted is true, then I don’t believe that p, so the fact that p is not even part of why I assert that p. Thus, by informativeness, my assertion that p is non-informative, and so also is my omissive assertion. As one might expect, the absurdity of the commissive assertion gets a slightly different diagnosis.

Suppose that I assert that (p but I believe that not-p). If the second conjunct of what I have asserted is true, then I believe that not-p, thus either I don’t believe that p, so the absurdity of the commissive assertion reduces to that of the omissive, or I have contradictory beliefs about whether p. If so, then my assertion that p is not a reliable indication that p, and Pagin adds that being informative requires both truth and reliability (2008, 48). So as before, my conjunctive assertion is not ultimately informative. One interesting feature of this account is that the absurdity of the assertion gets located not in

irrationality, but in uninformativeness. Pagin (2008) even gives ingenious examples of Moore’s paradox in arational human artifacts. Suppose that although you are unable to see its antenna lead directly, your TV apparently broadcasts a live image of you looking at the same TV while its lead is disconnected. The screen may be veridical. Yet – absurdly – if you think that the screen is informative and hence veridical, you should regard it as non-informative! A complete account of Moore-paradoxical assertionshould be able to deal with a number of puzzle

cases that have emerged. One is raised by Crimmins (1992), as discussed by Hájek and Stoljar (2001), Rosenthal (2001), and Williams (2001). Gonzales informs me that I’m acquainted with him when he is disguised as some other person whom I think idiotic, but does not tell me who this other person is. I accept his words on the strength of his reliability and intelligence. I now seem compelled to acknow- ledge my acceptance of his news with the reply, ‘I mistakenly believe that you are an idiot’.

Pruss (2012) supposes that I have programmed a robot to bring me a drink whenever I utter the sentence, ‘The robot will bring me a drink and I don’t believe that the robot will bring me a drink.’ Jones has a habit of interrupting me before I finish any sentence this long. Thus, when I try to assert to Jones, ‘The robot will bring me a drink and I don’t believe that the robot will bring me a drink’,

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I justifiably expect to fail. Surprisingly, I do make the assertion, because the word ‘robot’ makes Jones pay attention and refrain from interrupting. Yet my assertion does not seem absurd. Turri (2010a) gives the interesting example of Ellie, an eliminativist who, impressed by argu-

ments given by philosophers such as Paul Churchland (1981), holds that there are no contentful mental states such as beliefs. She joins our table for lunch and rehearses these arguments to us. Although we are unpersuaded, we do not thereby judge her irrational. Ellie now makes appar- ently sincere and reasonable omissive assertions such as, ‘The waiter brought the wrong dish but I do not believe that he did’. This kind of example is anticipated by Gallois (2007, 166). Hájek (2007) argues that a variety of philosophical positions are committed to Moorean assertions.

These include Kyburg-inspired solutions to the lottery paradox, skepticism about higher-order beliefs or about higher-order probabilities (De Finetti 1972 and Savage 1954), dialetheism (Priest, 1987), expressivism about moral discourse (Ayer 1946), supervaluational approaches to vagueness, and the thesis that conditionals lack truth-values (Adams 1975; Edgington 1995 and Bennett 2003). Whether these Moorean assertions are Moore-paradoxical seems worth investigating.

6. The Knowledge Version of the Paradox

So far we have confined ourselves to omissive and commissive cases exemplified by Moore. Yet Sorensen (1988) made a major contribution to the debate by observing that there are other examples of Moore-paradoxical assertions besides Moore’s own, such as

‘I have no beliefs now’

‘Although you think all my opinions mistaken, you are always right’

and

‘God knows that we are not theists’.

Sorensen also gives the mind-boggling example:

‘The atheism of my mother’s nieceless brother’s only nephew angers God’.

My mother’s nieceless brother’s only nephew can only be me. So there does seem to be a sense in which this would be an ‘absurd’ thing for me to assert. But since it is difficult to work through the web of relevant familial relationships, I may well be forgiven for conceiving of my mother’s nieceless brother’s only nephew as an existing relative other than myself. In that case, it seems harsh to judge that my assertion is irrational. Other assertions we should accommodate include the ‘self-referential’

‘I don’t believe that this sentence expresses a truth’

as well as cases of ‘iterated belief’ such as

‘It is raining but I don’t believe that I believe that it is raining’. (Sorensen 2000; Williams 2007)

plus their commissive and knowledge transpositions and permutations. Putting this aside, let us now return to assertions of the form

p but I don’t know that p.

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Prompted largely by Williamson (2000), this version of the paradox has been recently quite widely discussed. Most agree that an assertion of this form is always absurd, although some give putative counterexamples (Maitra and Weatherson 2010; Weiner 2005; Williams 1994). It is also widely agreed that the corresponding belief is also absurd (e.g. Huemer 2007). Williamson proposes the norm or rule – supposedly constitutive of the practice of assertion – that one should assert that p only if one knows that p (2000, 243).7 But it is impossible for me to know that (p & I don’t know that p). Since knowing a conjunction involves knowing each conjunct (‘knowledge-distribution’), I know that p. But knowledge is factive (whatever is known is true). So knowing the conjunction also means that both conjuncts are true, hence I don’t know that p. Thus, I do and don’t know that p. Contradiction.8 So one cannot have warrant to make the assertion (Williamson 2000, 253).9

This ‘knowledge account’ of assertion also accommodates the omissive assertion, since its content is likewise unknowable.10 How it will handle the commissive assertion is less clear. Is it impossible for me to know that (p & I believe that not-p)?11

Objectors have argued that the knowledge account forbids obviously permissible assertions, including Gettiered assertions and those related to testimony (e.g. Brown 2010; Douven 2006; Hill and Schechter 2007, 109; Kvanvig 2009 and 2011; Lackey 2007, 596, 598 ff and 2008; plus Levin 2008, 369–370). Those who defend it include Benton (2011 and 2012), Turri (2010b) and Blauuw (2012). Kvanvig (2009) gives a rival explanation of the absurdity by defending Kvanvig’s principle:

If one is justified in believing that p and one knows that one believes that p, then one is justified in believing that one knows that p

as well as Kvanvig’s norm of sincerity:

One should assert that p only if one believes that p

and Kvanvig’s norm of justification:

One should assert that p only if one is justified in believing that p.

Now suppose that I assert that (p & I don’t know that p). I have asserted that p. Given my conformity to the two norms, I am justified in believing that p, and given that I know whether I am sincere, I know that I believe that p. So by Kvanvig’s principle, I am justified in believing that I know that p. But this means that I am not justified in believing that I do not know that p, yet I have also asserted that I do not know that p and so have violated the norm of justification. Kvanvig could handle the omissive assertion as follows. Suppose that I assert that (p & I don’t

believe that p). I have asserted that p. Given my conformity to the norm of sincerity and given that I know whether I am sincere, I know – and hence believe – that I believe that p. But I have also asserted that I don’t believe that p, so I have violated the norm of sincerity after all. A similar argument seems able to deal with the commissive assertion, on the assumption that the speaker does not have overtly contradictory second-order beliefs. Stanley (2005) argues for the stronger constraint that one should assert that p only if one is

certain that p. Maitra and Weatherson (2010) give examples of assertions about ‘the thing to do’, such as

buying flood insurance or going to war. In these cases they argue, one may properly assert that such-and-such is the thing to do, although one does not know that it is the thing to do, because one’s belief that it is the thing to do isn’t safe, where roughly, one’s belief is safe just in case it could not be easily be false (i.e. in closest worlds to the actual world in which one has the belief,

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it is still true). Moreover, one may properly assert what one does not know in an academic context, otherwise ‘debate and discussion would atrophy’ (2010, 114). Given the older tradition of discussing the speech-act of assertion in terms of its point, i.e. the

speaker’s primary intention, one might be forgiven for wondering whether those who talk of norms of assertion since Williamson (2000) are really talking of assertion at all, especially since none of them seem to give any elucidation of what assertion is supposed to be. Cappelen (2011) argues against Williamson (2000) that the absurdity of saying ‘p but I don’t know that p’ is poor evidence that knowledge is a constitutive rule of assertion, since the oddity of saying ‘p but I don’t want you to believe that p’ isn’t evidence that the desire to be believed is needed for an utterance to count as an assertion. This seems correct, because I might say something contentious to you that I know you won’t believe, not because I want you to believe it, but because I want to ‘wind you up’ (Williams 1994 and 2001). Why couldn’t this count as a genuine assertion? Cappelen (2011) goes on to argue that what philosophers have tried to capture by the term ‘assertion’ is largely a philosophers’ invention. It fails to pick out a type of act in which we engage, and it is not a category we need in order to explain any significant component of our linguistic practice.

7. Concluding Remarks

I started by giving some of the historical emergence of the paradox, which considers it only as it arises in speech, and then I surveyed some of the literature on Moore-paradoxical assertion. There is also considerable literature on Moore-paradoxical belief, stemming from Sorensen’s Blindspots in 1988. I survey some of this in ‘Moore’s Paradox in Thought: A Critical Survey’.

Short Biography

John N. Williams (PhD Hull) works primarily in epistemology and paradoxes, especially episte- mic paradoxes. He also works in philosophy of language and applied ethics. He has published in Acta Analytica, American Philosophical Quarterly, Analysis, Australasian Journal of Philosophy, Journal of Philosophical Research, Philosophy East and West, Mind, Philosophia, Philosophical Studies, Religious Studies, Social Epistemology Review and Reply Collective, Synthese and Theoria. He is co-editor of Moore’s Paradox: New Essays on Belief, Rationality and the First Person, Oxford University Press together with Mitchell Green. He researches and teaches in the School of Social Sciences, Singapore Management University.

Notes

* Correspondence: School of Social Sciences, Singapore Management University, Singapore 178903. Email: [email protected]

1 DeRose (1991, 59) however, reports having no clear sense of inconsistency. See also Douven (2006, 475). 2 An exception occurs when you know that I am staring at my reflection in a mirror and I assert of myself, ‘It is raining but he doesn’t believe that it is raining’. 3 In what follows, I take the liberty of coining my own labels for principles others have used, which may or may not be their own. 4 Alternatively, one could deal with the commissive assertion via the converse of Wittgenstein’s first principle: If one asserts that p, then one asserts that one believes that p. Then in asserting that (p & I believe that not-p) I assert that p, so I have asserted that I believe that p. Yet I have also asserted that I don’t believe that p. This may prove too much however. Suppose that you know that I am insincerely telling the truth when I tell you that p, because I have got my facts backwards in an attempt to lie. In that case, you should judge that I have said something true. But if instead, I tell you, ‘I think that p’, then you should judge that I have said something false.

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5 The converse of this principle is: If one’s assertion that p is irrational, then so is one’s belief that p. This is easily falsified. My assertion, ‘I am not now making an assertion’ is irrational because making it falsifies its content, as anyone may recognize. But if I am silently meditating, it might be a rational thing to believe. 6 The practical rationality of one’s belief would be a matter of how well one’s acquisition or maintenance of it best promotes one’s interests – as would be judged by an epistemically rational believer, similarly placed – by satisfying one’s desires and fulfilling one’s intentions. When in a strange town, it might be rational in this sense to believe that there is at least one stranger who may be trusted, whatever the evidence. This is not the type of irrationality in belief that concerns Shoemaker, although it is one we should bear in mind. 7 Williamson (2000, 243, note 6) argues that this subsumes a previous proposal defended by Unger (1975, 253–270) and Slote (1979, 185, cf. Martin-Löf 1998) and maintained by DeRose (2002, 179), that in asserting that p, one represents oneself as knowing that p. See also Dudman (1992), DeRose (1996), and Hawthorne (2004, 21). 8 Sorensen (1988) argues similarly, calling this a ‘knowledge blindspot’. 9 On the Unger–Slote proposal, when one asserts that (p & I don’t know that p), one asserts that p and so represents it as being the case that one knows that p. But one also asserts that one doesn’t know that p. So what one asserts is contradicted by what one represents by asserting it (DeRose 2002, 181). 10 Suppose that I know that (p & I don’t believe that p). By knowledge-distribution, I know that p. I also know that I don’t believe that p so since knowledge is factive, I don’t believe that p. But since knowledge entails belief (whatever one knows, one believes), I don’t know that p. So I do and don’t know that p. Contradiction. 11 An affirmative verdict might appeal to anti-incoherence: If one knows that p, then one does not believe that not-p. But could I not deceive myself into believing what I really know is false? We could restrict the principle to rational thinkers, but against this, consider a commissive variant of an example given by Garvey (1997). I read a self-help booklet that lists symptoms of alcoholism. As I read each one I think, ‘That’s true of me, but I still believe that I am not an alcoholic’. The final symptom listed is that I believe that I am not an alcoholic. I read this and think ‘That’s true of me’ and then in dawning realization of the horrible truth, finish my thought with ‘and I am an alcoholic!’ Could I not, in this fleeting instant of dawning awareness, sensibly come to know that I have the mistaken belief that I am not an alcoholic? See also de Almeida’s anti-incoherence: If one believes that p and also believes that not-p, then one knows neither, nor is one justified in believing either (de Almeida 2012, 205). Suppose that I know that (p & I believe that not-p). Then since knowledge distributes over conjunction, I do know that p. So because knowledge entails belief, I believe that p. I also know that I believe that not-p, so since knowledge is factive, I believe that not-p. Thus, I believe that p and also believe that not-p, so by de Almeida’s anti-incoherence, I also do not know that p. Contradiction. However, the Garvey variant seems to also count against de Almeida’s anti-incoherence, since my dawning awareness seems to constitute my recognition that I am an alcoholic.

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