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Acknowledgements
Foreword—MitchellGreenandAlanHájek
Introducing Moore’s Paradox
Moore on Moore’s Paradox
Wittgenstein on Moore’s Paradox
Some Salient Approaches to Omissive and Commissive MooreParadoxical Assertion
Expressing Belief and Knowledge, Assertion, and the Expressivist Approach
An Account of Belief
Some Salient Approaches to Moore’s Paradox in Belief
The Knowledge Version in Belief
The Knowledge Version in Assertion
The Priority of Belief Thesis and the Incredibility of the Assertor
Conscious Belief
The Self-falsification Account in Belief and Assertion, Rationality, and Absurdity
Eliminativism, Dialetheism, and Moore’s Paradox
Moore’s Paradox and Sorensen’s Iterated Cases
15. 16. 17. 18.
The Justification Approach to Moore-Paradoxical Belief
Defining Moore-Paradoxicality: The Preface Paradox and Rational Inconsistent Belief
Moore’s Paradox and Desire
Further Work References Index
Acknowledgements
I am grateful for various forms of research support from Singapore Management University, and especially the encouraging assistance of Professor James H. Tang, Dean of School of Social Sciences.
My colleagues, in particular, Brian T. Mooney and Mark Nowacki, shaped my ideas in unexpected ways. The same is true of Steven Burik, who shouldered some of my responsibilities in order to help me.
I am grateful to Associate Professor Michael Pelczar for inviting me to spend a sabbatical leave in the Philosophy Department at the National University of Singapore, and over many years, his incisive discussion. Loy Hui Chieh, Christopher Brown, Tang Weng Hong, and Ben Blumson have also provided insights.
A special word of thanks goes to Claudio de Almeida, Mitchell Green, and Mark D’Cruz.
Vera’s support was invaluable.
Foreword
ByMitchellGreenandAlanHájek
John Williams (1952–2019), who spent the bulk of his career as an active and cherished member of the philosophical community in Singapore, passed away soon after completing the manuscript of this book.1 John was a lifelong student of and the world’s leading authority on Moore’s Paradox, and this book is the most complete treatment of it ever written. Our role here is to introduce the topic and explain its significance, and to provide an overview of this book’s contributions, both to understanding the topic and to other philosophical problems for which it has implications.
1. What Moore’s Paradox is
Suppose Robin asserts with no apparent irony or mid-assertion change of mind:
M1. It’s raining, but I don’t believe that it’s raining.2
Such an assertion is puzzling in the extreme, and indeed many would find it absurd. Yet well-established tools for explaining the absurdity of assertions do not seem to apply to this case. After all, M1 could be true: it might be raining without Robin’s believing that it is. M1 is both logically and metaphysically possible.
For this reason, M1 is absurd in a way that assertion of ‘It’s raining, but it’s not raining’ is not. G. E. Moore introduced this type
of example, which not only fascinated Wittgenstein but has provided a steady source of inspiration to philosophers for the near-century since Moore’s discovery.3
Now consider:
M2: It’s raining, but I believe that it’s not raining.
It is standard practice to refer to M2 as a commissive form of Moorean absurdity, and M1 as an omissiveform. Moore did not seem to be aware of the difference between the omissive and commissive forms. We believe that John’s (1979) paper was the first to explicitly acknowledge the two different forms and to point out that they need separate treatment.
On the other hand, changes of tense or person do not produce any absurdity. The following could be asserted without raising any puzzlement:
M3: It was raining, but I didn’t believe that it was raining.
M4. Robin believes it is raining, but it isn’t.4
M5. You believe it’s raining, but it isn’t.
The problem is not limited to assertions. Hintikka (1962) observed that a similar absurdity occurs when an agent has beliefs whose contents are expressed by either M1 or M2. Suppose that Robin believes ‘it’s raining but I don’t believe it’s raining’. There is something defective about her believing the proposition that this sentence expresses, even though that proposition could well be true. For if she does believe it, then by straightforward reasoning (which John makes explicit for conscious belief in Chapter 11 and for belief in general in Chapter 12) she must also be in error. Believing the proposition expressed by M2 is also defective, yet it too could well be true. Assume that belief distributes over conjunction (one who believes P & Q believes P and believes Q); and that one who believes that she believes that P, also believes that P. Then if Robin
Accounting for the absurdity of cases such as M1 and M2 requires clarity about the notions of assertion, absurdity, belief, knowledge, and (ir)rationality, all of which receive close and illuminating treatment in this book. In John’s hands, the project also requires clarity on the notion of expression, since assertions of sentences such as M1 and M2 express or purport to express beliefs (Ch. 5). Further, because the absurdity in question may be exemplified in belief rather than in a speech act, explaining Moorean absurdity requires drawing on a plausible theory of belief (Ch. 6). Since the work of Shoemaker (1996), it has been recognized that such an explanation also requires an account of conscious belief (Ch. 11). Additionally, as suggested by M4 and M5, Moore’s paradox brings out a difference between what philosophers call the first-person perspective, on the one hand, and the second- and third-person perspectives, on the other (Ch. 3).
Throughout the book, John critiques other authors’ characterizations of Moore-Paradoxical beliefs and assertions, and he repeatedly refines them. This culminates in the following definition (Ch. 16):
A belief or assertion is Moore-paradoxical just in case its content is
(i)
(ii)
(iii)
(iv) believes M2, she believes both that it is raining and that it is not raining. (John gives a more nuanced and satisfying formulation of this reasoning in 11.4.) By contrast, one can rationally believe M3–M5.
conjugated in the present tense where one should be taken as conceiving of oneself in first-personal terms a possible truth, at least by one’s own lights, that does not impugn one’s rationality may be the antecedent or consequent of counterfactual conditionals that one sensibly asserts or believes such that believing it falsifies it unless one has overtly contradictory beliefs.
John’s account of Moore-Paradoxical beliefs and assertions adverts to a number of philosophically rich notions—the first-person, possibility, truth, rationality, counterfactuals, assertion, belief, and in particular contradictory beliefs. It is no surprise, then, that Moore’s Paradox provides a springboard to many important topics in philosophy, which animated much of John’s research.
2. Why Moore’s Paradox Matters
Moore’s paradox teaches us that there are limits to what a rational agent may learn. For suppose that in fact it is raining but Robin believes that it is not raining. She cannot, on pain of irrationality, come to be aware of this fact, namely that it is raining but she believes it is not.
Moore sentences provide instances of what Sorensen (1988) calls ‘blindspots’: sentences that can be true, but that cannot rationally be believed by certain believers. It is remarkable that Moore sentences seem to involve individual blindspots, each involving exactly one person. For example, ‘it is raining and Robin believes it is not raining’ could be true, and the proposition expressed by it could rationally be believed by everyone in the world exceptRobin.5 Nobody but Robin is thus ‘blind’ to its truth.
Moore sentences can also teach us lessons about propositional attitudes more generally, and their associated norms. There is nothing defective about ‘it is raining and I prefer that it not be raining’; but there is about ‘it is raining and I am not confident that is raining’, and even ‘it is raining and I am not certain that it is raining’.6
Moore sentences can be destructive, providing counterexamples to some important philosophical theses. We see this in arguments against functionalism in the philosophy of mind (Heal 1994, Milgram 1994). We will later discuss John’s ingenious deployment of Moore
sentences in his refutation of the ‘Ramsey test’ for the acceptability of conditionals. Relatedly, it is typically a strike against a philosophical position if it commits one to asserting or believing Moore sentences—see Hájek (2007) and Chalmers and Hájek (2007).
Moore sentences can also be constructive, providing arguments for philosophical positions. For example, they are central to one of Williamson’s (2000) main arguments that knowledge is the norm of assertion. (See John’s Ch. 9.) Moore sentences convey ‘higher-order’ thoughts—e.g. beliefs about one’s own beliefs. Some philosophers (e.g. Rosenthal 1995) think that such thoughts are constitutive of consciousness. Moore’s paradox has also influenced the literature on self-knowledge and introspection. For example, Shoemaker (1996, Ch. 4) uses it to argue against an ‘inner sense’ account of introspection (which regards introspection as a kind of perception), and in favour of his ‘constitutivist’ account.
Furthermore, Moore’s paradox has been used to argue for certain norms of rationality (somewhat parallel to Dutch Book arguments for probabilistic norms). Such arguments have the form: if you do not abide by such-and-such norm, you are susceptible to being Mooronic: believing a Moore sentence. For example, the Reflection Principle is a putative rationality norm, requiring one’s current subjective probabilities to be the expectation of one’s future subjective probabilities. Van Fraassen (1984, 1995) analogizes violations of this principle to the kind of ‘incoherence’ in which one believes a Moore sentence. (See Green and Hitchcock 1994 for a response.)
3. Contributions of this Book
Let us turn now to this book. John’s treatment of Moore’s Paradox is ‘unified’ (as promised in the title) in that he provides a consistent account of the two main forms that the paradox takes (in speech and in thought) while acknowledging the distinctive character of each form. He also provides a coherent perspective from which we may see ways in which Moorean absurdity can come in degrees, as well as the extent to which it may occur in attitudes other than belief, such as desire.
Concerning the two main forms that the paradox takes, John shows that contrary to one tradition in the literature on Moore’s Paradox, we cannot explain Moorean absurdity in speech in terms of Moorean absurdity in thought. Instead they must each be accounted for on their own terms. John accounts for Moorean absurdity in speech in terms of the idea that one who utters a sentence such as M1 or M2 is incredible in the sense that their interlocutor cannot rationally believe them (Ch. 10). In so doing, he grounds the absurdity of Moore’s paradox in speech in practicalrationality.
In his account of Moorean absurdity in thought, Williams builds on the work of Green (2007), who distinguishes between absurdity and irrationality. A person might hold views guaranteed to put her into error, but in a way that she could only discern with further empirical or logical investigation. This would make her epistemic position absurd. But for her to be irrational, it would have to be feasible for her to discern this fact, and it may well not be if unearthing the error in question requires extensive calculation or empirical investigation. John accounts for Moore-paradoxicality in thought in light of the idea that one who believes a sentence such as M1 or M2, or its content, must be in error in a way that she could discern with minimal calculation, and so has a position that is both absurd and irrational. More subtle Moorean cases (such as ‘The
atheism of my mother’s nieceless brother’s only nephew angers God’) will also yield absurdity but may not impugn the believer’s rationality.
The incredibility of the assertor, and self-falsification of the believer, constitute the core of John’s explanation of the source of Moorean absurdity. Along the way John argues for a range of interesting, related theses. For instance he argues (Ch. 9) that while knowledge is not the norm for assertion across the board, it is the norm for acts of informing. He argues further that it is not paradoxical when reference to belief is replaced by knowledge in Moore sentences, contrary to much literature. John’s account also has striking implications for philosophical theology. Specifically, he argues (Ch. 12.6) that there can be no omniscient being who is rational in all of its beliefs.
In developing his position John also addresses (Ch. 13) eliminativists about the mental who are wont to say such things as ‘It’s raining outside but I don’t believe it (because I have no beliefs)’, as well as dialetheists who are wont to say such things as ‘The Liar sentence is true but I believe it is false.’ (It is both true and false according to them.) John understands the eliminativists’ utterances as absurd but not irrational, while arguing that the dialetheists’ utterances are neither absurd nor irrational.
Chapter 16 offers his final definition of Moore-paradoxicality (see above), steering away from identifying it with inconsistency. Indeed, he argues forcefully that while Moorean assertions are consistentbut impermissible, it may be permissibletomakeinconsistentassertions. He supports the latter claim with a generalization of the preface paradox. The upshot is that inconsistency is neither necessary nor sufficient for absurd utterance.
John goes on to discuss how Moore’s Paradox generalizes to other propositional attitudes, such as desires. In Chapter 17, he defines a Moorean desire as one whose contents have the same syntax as the contents of Moorean beliefs. For example, it is paradoxical to desire anything of the form:
p& I do not desire that p.
This leads John to a trenchant discussion of lessons to be learned about desire.
4. John’s Broader Contributions: Moore’s Paradox and Beyond
While John was best known for his research on Moore’s Paradox, that research resonates with other themes in his work. Among other things, he was interested in the various ways in which statements and beliefs can be inconsistent in a broad sense. For example, an early publication of his, ‘Inconsistency and Contradiction’ (1981), is a sharp-witted article that distinguishes these two, easily conflated notions. It concludes with the salutary lesson that, while contradictory beliefs are properly subject to censure, inconsistent beliefs may not be. And throughout his career he studied the interplay between logic and rationality, commencing with another early paper, ‘Believing the Self-Contradictory’ (1982). Some authors have argued that self-contradictory beliefs are impossible, and as such, that rationality cannot proscribe them. John offers convincing examples of such beliefs and compellingly argues that they are indeed irrational.
Throughout his career, John did much to bring out how Moore’s Paradox has ramifications for various philosophical views. The final chapter of his manuscript gestures briefly at some of them, but it is worth looking at a few in more detail.
A particularly striking one concerns Ramsey’s ‘test’ for the rational acceptability of conditionals. In surely the most famous passage ever written on conditionals, Ramsey writes (1929, 247): ‘If two people are arguing “If p, then q?” and are both in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on
that basis about q.’ As Stalnaker (1968/1981, 32) puts it: ‘add the antecedent (hypothetically) to your stock of knowledge (or beliefs), and then consider whether or not the consequent is true.’
John has an incisive objection to this ‘test’ in his (2012). Consider the conditional with a Moore-paradoxical antecedent:
If I fail to believe the truth that it is raining, then I do not believe that it is raining.
This is true, and rationality requires me to accept it. But I cannot hypothetically add the antecedent to my stock of beliefs. That would require me hypothetically to believe boththat it is raining andthat I fail to believe this, which I cannot do on pain of irrationality.
Moore’s paradox generalizes from beliefs to other propositional attitudes, shedding light on those also. As John observes, it is Moore-paradoxical (in an extended sense) to assert:
(P1) It is raining but I assign a low probability to the proposition that it is raining.
We might add that it is Moore-paradoxical to assign high probability to P1.
More generally, there seems to be something Moore-paradoxical about any assertion of the form:
pand I assign probability less than 1 to p.
The second conjunct asserts one’s uncertainty about p—things could go either way with respect to p by one’s own lights—yet the first conjunct asserts which way they go: the p-way.
Indeed, Moore paradoxicality seems to come in degrees. Consider assertions of the form:
(P2) pand I assign probability xto p.
The lower the value of x, the more paradoxical this seems; but some paradoxicality remains unless x is 1. Among other things, it seems that a rational agent cannot learn a proposition of P2’s form with x< 1, as doing so plausibly requires the agent to assign both probability 1 and less than 1 to p.
Moore-paradoxical sentences are also subtly implicated in other philosophical paradoxes. John does a fine job of displaying this in the case of the ‘surprise exam paradox’—see his (2007).
5. Personal Reflections
John was a passionate philosopher and a delightful interlocutor— Tiger beer in one hand, smoke in the other and very intellectually generous. He was also a committed teacher. His lectures were crystal clear. He had a warm rapport with his students, who found him most approachable. He had a remarkable way of connecting with them as individuals, despite often having large audiences. After his classes, he was frequently besieged by students eager to discuss matters further. He co-authored two textbooks on logic and critical thinking with colleagues at Singapore Management University, which formed the bases of courses on those topics. He was a mainstay of his department.
AH recalls that John was instrumental in setting up a two-month visit for him at Singapore Management University in 2005, truly a wonderful experience. They co-taught a course on epistemology, and met regularly to discuss philosophy—the beginning of an ongoing philosophical relationship and friendship. Similarly, MG fondly recalls writing to John for the first time in 1998 with some questions concerning Moore’s Paradox. John replied swiftly and generously. Their ensuing correspondence resulted in multiple visits to Singapore by MG, as well as the 2007 volume edited by Green and Williams. We shall not forget John’s grace, philosophical acumen, and friendship.
Finally, we are most grateful to Michael Pelczar for taking over this project after John’s untimely death, and for the enormous amount of work he put into seeing it to completion. Many thanks also to Ben Blumson for all the help that he provided.
References
Chalmers, D. and A. Hájek (2007) ‘Ramsey + Moore = God’, Analysis, 67 (294), April, 170–2.
Green, M. (2007) ‘Moorean Absurdity & Showing What’s Within’, in Green, M., and J. Williams (eds.), Moore’s Paradox: New Essays on Belief, Rationality, and the First Person, Oxford University Press, 189–214.
Green, M. and C. Hitchcock (1994) ‘Reflections on Reflection: Van Fraassen on Belief’, Synthese 98, 297–324.
Green, M. and J. Williams (2007) ‘Introduction’, in Green, M., and J. Williams (eds.), Moore’s Paradox: New Essays on Belief, Rationality, and the First Person, Oxford University Press, 3–36.
Hájek, A. (2007) ‘My Philosophical Position Says “p”, and I Don’t Believe “p”’, in Green, M., and J. Williams (eds.), Moore’s Paradox: New Essays on Belief, Rationality, andthe First Person, Oxford University Press.
Heal, J. (1994) ‘Moore’s Paradox: A Wittgensteinian Approach’, Mind, 103(409), 5–24.
Hintikka, J. (1962) Knowledge and Belief: An Introduction to the Logic of the Two Notions, Ithaca, NY: Cornell University Press.
Milgram, E. (1994) ‘An Apprentice Argument’, Philosophy and Phenomenological Research, 54, 913–16.
Moore, G. E. (1942) ‘A Reply to My Critics’, in P. Schilpp (ed.), The Philosophy ofG. E. Moore, La Salle, Ill.: Open Court, 535–677.
Moore, G. E. (2013) G. E. Moore: Selected Writings, T. Baldwin (ed.), Abingdon: Taylor & Francis.
Ramsey, F. P. (1929) ‘General Propositions and Causality’, in R. B. Braithwaite (ed.), The Foundations of Mathematics and Other Logical Essays, Kegan Paul, Trench, Trubner, & Co.
Rosenthal, D. M. (1995) ‘Moore’s Paradox and Consciousness’, Philosophical Perspectives, 9, AI, Connectionism, and Philosophical Psychology.
Shoemaker, S. (1996) The First-Person Perspective and Other Essays, Cambridge: Cambridge University Press.
Sorensen, R. (1988) Blindspots, Oxford: Oxford University Press.
Stalnaker, R. (1968/1981) ‘A Theory of Conditionals’, Studies in Logical Theory, American Philosophical Quarterly Monograph Series, No. 2, Oxford: Blackwell. In Harper, W. L., Stalnaker, R., and Pearce, G. (eds.) (1981): Ifs, Dordrecht: Reidel. (Page reference to Ifs.)
Van Fraassen, B. (1984) ‘Belief and the Will’, JournalofPhilosophy, 81, 235–56.
Van Fraassen, B. (1995) ‘Belief and the Problem of Ulysses and the Sirens’, PhilosophicalStudies, 77(1), 7–37.
Williams, J. (1979) ‘Moore’s Paradox: One or Two?’, Analysis, 39(3), 141–2.
Williams, J. (1981) ‘Inconsistency and Contradiction’, Mind, 90 (360), 600–2.
Williams, J. (1982) ‘Believing the Self-contradictory’, American Philosophical Quarterly, 19(3), 279–85.
Williams, J. (2007) ‘The Surprise Exam Paradox: Disentangling Two Reductios’, JournalofPhilosophicalResearch, 32, 67–94.
Williams, J. (2012) ‘Moore-Paradoxical Belief, Conscious Belief and the Epistemic Ramsey Test’, Topics in Contemporary Epistemology, a special issue of Synthese, 188 (2), 231–46.
Williamson, T. (2000) Knowledge: Its Scope and Limits, Oxford: Oxford University Press.
1 The manuscript was complete but was missing some references and other details. His former colleagues at the National University of Singapore, Michael Pelczar and Ben Blumson, have done their best to fill in these gaps.
2 We also assume that the second conjunct of M1 is not used as an expression of surprise, as in ‘Luke ate all those eggs; I can’t believe it!’
3 Calling an example like M1 a paradox is out of step with current usage which tends to characterize the notion as a set of premises, each of which is seemingly plausible, but which yield an implausible conclusion by seemingly acceptable reasoning. It is unclear what are the premises that would constitute ‘Moore’s paradox’. That said, Moore sentences have a number of surprising features and consequences, as we will see, so in that sense they may be regarded as ‘paradoxical’.
4 We assume that (M4) is uttered by someone other than Robin, or at least that if Robin does utter it, she is not aware of the fact that she is Robin.
5 In line with our earlier qualifications, we assume that in the case being excepted Robin thinks of herself as herself.
6 Moore (2013, 211) writes that Wittgenstein ‘pointed out that there is a similar absurdity in saying: “Possibly it isn’t raining, but as a matter of fact it is”. And this may be put in the form: “It isn’t certain that it’s raining, but as a matter of fact it is”.’
1
Introducing Moore’s Paradox
1.1 A Very Brief History
It is raining but you don’t believe that it is raining.
Imagine accepting this claim. Then you appear to be committed to saying
It is raining but I don’t believe that it is raining.
This would be an ‘absurd’ thing for you 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? Most people who are confronted with such an assertion hear contradiction, yet are puzzled to find no contradiction in what has been asserted. This is Moore’s paradox as it occurs in speech. Let us call an assertion that is paradoxical in this way ‘Moore-paradoxical’ and its form ‘Moorean’. Let us also call the form of such an assertion ‘omissive’ since its content is that one lacks a specific true belief.
From G. E. Moore himself, after whom of course the paradox is named, through Wittgenstein until Jaakko Hintikka, the paradox was considered only as it occurs in speech. With Roy Sorensen’s Blindspots came the widespread recognition that a similar paradox occurs in thought as well. For if you silently believe that
It is raining but I don’t believe that it is raining
then you seem no less ‘absurd’.1 Yet, the content of such a belief might be true. Let us also call a belief that is Moore-paradoxical in this way ‘Moore-paradoxical’. Solving the paradox consists in explaining why such assertions or beliefs are absurd. Must the absurdity be a form of irrationality?
Much the same absurdity seems to be found in asserting or believing
It is raining but I believe that it is not raining.
Let us call the form of such an assertion or belief ‘commissive’, since its content is that one has a specific false belief. Many of the attempts to explain the absurdity of the omissive assertion or belief fail to explain that of the commissive, or vice versa.
Sorensen made a second major contribution in showing that there are assertions or beliefs that although not Moorean, also seem Moore-paradoxical, including
I have no beliefs and God knows that we are not theists.
Sorensen also gives examples in which belief operators are iterated, such as the omissive
God exists but I don’t believe that I’m a theist and the commissive
God exists but I believe that I’m an atheist
and claims that as iteration increases, as in
God exists but I don’t believe that I believe that I believe…that I’m a theist
omissive absurdity appears to decrease, while commissive absurdity, as in
God exists but I believe that I believe that I believe…that I’m an atheist does not. Call these ‘Sorensen’s iterated cases’.
Many, but by no means all, commentators find absurdity in asserting or believing
It is raining but I don’t know that it is raining.
Moore himself seems to find assertions of this form ‘absurd’. Let us call its form the ‘knowledge version’. Following Timothy Williamson, this has recently been the subject of intense debate, particularly as the content of assertion. Williamson supports the ‘knowledge account’ that assertion is the only speech-act that is governed by the single ‘rule’ or ‘norm’ that one must know its content, partly by appealing to the alleged absurdity or ‘impropriety’ of such an assertion.
With the switch of focus after Sorensen from the absurdity in assertion to the absurdity in belief came Sydney Shoemaker’s influential work on the paradox, which approaches it in terms of conscious belief. This engendered the current orthodoxy, anticipated by Hintikka, 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. This assumption gives explanatorypriority to belief over assertion. Call this the priority(ofbelief)thesis. Although I will reject this thesis, nonetheless it will turn out that an
explanation of the absurdity in belief is the best place to start to explain the absurdity, since assertion is to be explicated in terms of the less complex notion of belief.
1.2 Aims
The absurdity in belief may be seen as a form of epistemic irrationality while the paradox in assertion may be seen as a form of practical irrationality. Although these forms of irrationality are arguably the most important forms of absurdity, I follow Mitchell Green in maintaining that absurdity can come apart from irrationality. In particular, Moorean beliefs or assertions may be absurd without being irrational. The absurdity in any case may be seen as a violation of various norms.
In line with my rejection of the priority thesis, I will give explanations of the absurdity in assertion that are independent of explanations of the absurdity in belief. To deal with the absurdity in assertion, I consider an expressivistapproach, broadly suggested by Wittgenstein, that starts with the idea that one purports to express belief in what one asserts. I ultimately reject this approach as incomplete. Instead I argue for the incredibility of the assertor approach, which turns upon the idea that in believing the assertor, one believes that she is sincerely telling the truth. The incredibility of the assertor approach may be deepened by coupling it with the conscious belief approach, an improvement on Shoemaker’s treatment of the paradox. This is based on the idea that in becoming conscious of one’s omissive belief, one becomes aware that one believes a contradiction.
But suppose that there are such things as unconscious Mooreparadoxical beliefs, in other words, those one has but is unaware of having. Then it will turn out that the conscious belief approach cannot be applied. I argue that such cases are better dealt with on
the self-falsification approach, based on the idea that the adoption or maintenance of the belief falsifies its content.
Cohering with this is the justification approach, that it is impossible for someone to justifiably believe a Moore-paradoxical content.
Here is how I will proceed. In Chapter 2 I examine Moore’s formulation of the paradox and his two attempts to solve it. In Chapter 3 I examine Wittgenstein’s reaction to the paradox, his alternative formulation of it, and his two approaches to it. Wittgenstein intimates that the paradox is found in speech only when assertion, rather than when mere utterance is present, thus indicating the need for an account of assertion. In Chapter 4 I discuss some interesting approaches to omissive and commissive Moore-paradoxical assertion. I note along the way other putative examples of Moore-paradoxical assertion that any complete account of the paradox should accommodate. In Chapter 5 I propose and defend an analysis of assertion. Since this proceeds in terms of expressing belief and knowledge, I start with an account of what such expression constitutes. This account lays the foundation for an expressivist approach that resembles Wittgenstein’s. In Chapter 7 I examine some interesting attempts to explain the absurdity of omissive and commissive Moore-paradoxical beliefs, noting other putative examples of Moore-paradoxical belief. As a preparation for that, in Chapter 6 I first give what seems to be a fairly standard account of belief, broadly influenced by Robert Audi.
At this point I will have also noted puzzling cases such as Turri’s example of an eliminativist who sincerely makes omissive assertions such as ‘The waiter brought the wrong dish but I don’t believe that he did’, as well as the case of a dialetheist who sincerely asserts, ‘The Russell set includes itself but I believe that it is not the case that the Russell set includes itself.’ In Chapters 8 and 9 I turn to the knowledge version, arguing in Chapter 8 that there need be nothing absurd or irrational in a belief of the form ‘pand I don’t know that p’. In Chapter 9 I argue that some, but not all, assertions of the form ‘p and I don’t know that p’ are absurd. In this I oppose the knowledge
account. I argue that focusing exclusively on the sincerity of the speech-act of letting one know engenders a category mistake about the nature of constraints on assertion. Assertion is an act and therefore falls under the constraints of practical, not epistemic rationality. I propose that the norm of a type of assertion is the epistemic state one needs for one’s speech-act to succeed in being an assertion of that type and that the epistemic state in question is determined by the point of the type of assertion. One is practically irrational in violating the norm. This lays part of the ground for Chapter 10, in which I show against the priority thesis that even if one’s Moore-paradoxical belief is epistemically irrational, asserting its content may be a practically rational thing to do. The absurdity in belief is not a reliable guide to that in assertion. The expressivist approach also appears to be incomplete because there are exceptional circumstances in which one may sensibly purport to express a Moore-paradoxical belief.
In Chapters 11 and 12 I develop the conscious belief and the selffalsification approaches to Moore-paradoxical belief and show, with two exceptions, that these accommodate all the cases I have considered so far. The first exception is the examples of the eliminativist and the dialetheist that I deal with in Chapter 13. The second exception is Sorensen’s iterated cases that I deal with in Chapter 14. In Chapter 15 I develop the justification approach to Moore-paradoxical belief and show that it accommodates all the cases I have considered so far.
In Chapter 16 I explain how my proposed definition of MooreParadoxicality accommodates the possibility of holding inconsistent beliefs without irrationality.
In Chapter 17 I consider Moore-Paradoxical desires.
I end in Chapter 18 by noting phenomena related to Moore’s paradox that might be fruitful lines of future investigation.
1 DeRose (1991, 59) however reports having no clear sense of inconsistency. See also Douven (2006, 475).
Moore on Moore’s Paradox
2.1 Moore’s Omissive and Commissive Paradox
In two different works, ‘A Reply to My Critics’ (1942) and ‘Russell’s Theory of Descriptions’ (1944), 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) 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.
Symbolizing ‘I believe that p’ as ‘Bp’ allows us to represent this as p& ~Bp
(Bp may also be read as ‘One believes that p’.) Following Sorensen (1988) we may call the form of Moore’s first example ‘omissive’
because it self-reports a specific omission of true belief (By ‘selfreport’ here I denote an assertion about one’s own mental states). In contrast, his secondexample,
I believe that he has gone out, but he has not, may be formalized as I believe that p& not-p.
This is equivalent by commutation to not-p& I believe that p We may represent this as p& I believe that not-p. p& B~p
Formalizing Moore’s two examples in this way allows us to see more clearly that the difference between them is that between not believing that p and believing that not-p. This crucial difference is disguised by Moore’s examples. Sorensen (1988) calls the form of Moore’s second example ‘commissive’ since it self-reports the commission of one’s specific mistake in belief. I was the first to draw attention to this difference, which stems from that between atheists and agnostics (Williams 1979).
Not believing that p neither entails nor is entailed by believing that not-p. Suppose for reductiothat if one believes that not-p then one does not believe that p. Then overtly contradictory beliefs (those with contents that are syntactic negations of each other) would be impossible, since if one believes that p and believes that not-p then one does and doesn’t believe that not-p.1 Yet I take it that it is possible to have overtly contradictory beliefs (Sorensen 1988, 27). I will defend this possibility in 6.6. And the converse entailment
prohibits agnosticism, since if one neither believes that p nor believes that not-p, then it would again follow that one does and doesn’t believe that not-p.2 The difference between the omissive and commissive forms is partly obscured by the fact that if you ask me, ‘Is it raining?’ and I truthfully reply, ‘I don’t believe so,’ then you are usually justified in taking me to believe that it is not raining, unless I then qualify my self-report with ‘but then I’ve no beliefs about it either way’.
Let us call assertions that have the same basic form or syntax as Moore’s examples ‘Moorean’. Moore’s first two examples are both Moore-paradoxical and Moorean, although we will see later that Moorean assertions are not always Moore-paradoxical, nor conversely.
Moore says of the utterances in his first two examples 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)
In fact, 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.
Of course it is a distinguishing feature of the paradox that what one asserts or believes might be true. Thus the relevant absurdity, whatever else it is, is not to be found in assertions or beliefs such as
I believe that it is raining and I don’t believe that it is raining Bp& ~Bp or 2 + 2 = 5 but I don’t believe that 2 + 2 = 5 or
It is raining but I know that it is not raining.
p& K~p
2.2 Moore’s Problem as Paradox
At first sight Moore’s use of ‘paradox’ does not appear to fit Sainsbury’s orthodox definition of a paradox as an argument with ‘an apparently unacceptable conclusion, which is derived by apparently acceptable reasoning from apparently acceptable premises’ (Sainsbury 1995, 1). We might try to fit Moore’s use of ‘paradox’ into this definition by arguing that assertions of possible truths are not absurd (in a way that involves some contradiction-like phenomenon) and Moore’s examples are assertions of possible truths, so these assertions are not absurd (in a way that involves some contradictionlike phenomenon).
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, 208–9, 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.
The absurdity normally seems to arise only when the content of assertion (or belief) is conjugated in the first person. It also normally seems to arise only when the content is conjugated in the grammatical present tense. You detect no absurdity if, knowing that I have only just remembered going to the pictures, I assert,
I went to the pictures last Tuesday but I didn’t believe that I did.
