Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. (Halpern, 2001) The jury is still out concerning the epistemic conditions for backward induction, the “oldest idea in game theory ” (Aumann, 1995, p. 635). Aumann (1995) and Stalnaker (1996) take conflicting positions in the debate: the former claims that common “knowledge ” of “rationality ” in a game of perfect information entails the backwardinduction solution; the latter that it does not. 1 Of course there is nothing wrong with any of their relevant formal proofs, but rather, as pointed out by Halpern (2001), there are differences between their interpretations of the notions of knowledge, belief, strategy and rationality. Moreover, as pointed out by Binmore (1987; 1996),

When I have a conscious experience of the sky, there is a bluish way it is like for me to have that experience. We may distinguish two aspects of this “bluish way it is like for me”: (i) the bluish aspect and (ii) the for-me aspect. Let us call the bluish aspect of the experience its qualitative character and the for-me aspect its subjective character. What is this elusive for-me-ness, or subjective character, of conscious experience? In this paper, I examine six different attempts to account for subjective character in terms of the functional and representational properties of conscious experiences. After arguing against the first five, I defend the sixth. There is something at least prima facie mysterious about conscious experience. The problem of consciousness is the problem of demystifying whatever it is that accounts for the prima facie mysteriousness of conscious experience. This would involve showing that the prima facie mysterious aspects of conscious experience are not super-natural phenomena. That is, it would require “naturalizing ” the relevant aspects of conscious experience, presumably by showing how they could exist in a purely physical world. 1 It is useful to refer to the prima facie mysterious element in conscious experience in terms of what it is like for the subject to have or undergo a conscious experience. 2 When I have a conscious experience of the sky, there is a bluish way it is like for me to have or undergo my experience. 3 I suggest that we distinguish two aspects in this “bluish way it is like for me”: (i) the bluish aspect, which we may call the experience’s qualitative character, and (ii) the for-me aspect, which we may call its subjective character. Not only is the experience bluish, but I am also aware of its being bluish. Its being

The Sum-and-Product riddle was first published in [Fre69]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the riddle, that were previously (as far as we know) unknown. We then model the Sum-and-Product riddle in a modal logic called public announcement logic. This logic contains operators for knowledge, but also operators for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. We also provide characteristic formulas of the initial epistemic state of the riddle. Finally we analyze one of the announcements towards the solution of the riddle as a so-called unsuccessful update: a formula that become false because it is announced. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. The results are compared with other work in epistemic model checking.

Propositions such as <It is raining, but I do not believe that it is raining> are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore’s paradox. Sydney Shoemaker has recently argued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker’s own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account is the claim that conscious beliefs are always partly about themselves; it will be shown to follow from this that conscious beliefs in Moorean propositions are self-contradictory.

abstract. Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after arbitrary announcements. Intuitively, [!]ϕ expresses that ϕ is true after an arbitrary announcement ψ. We show completeness for a Hilbert-style axiomatization of this logic, and also provide a labelled tableau-calculus.

this paper was presented at the Second National Meeting of the Italian Society of Analytic Philosophy, Vercelli (Italy), September 1996. We are thankful to the audience for stimulating comments and discussion.

The Sum-and-Product riddle was first published in [Fre69]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the riddle, that were previously (as far as we know) unknown. We then model the Sum-and-Product riddle in a modal logic called public announcement logic. This logic contains operators for knowledge, but also operators for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. We also provide characteristic formulas of the initial epistemic state of the riddle. Finally we analyze one of the announcements towards the solution of the riddle as a so-called unsuccessful update: a formula that become false because it is announced. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. The results are compared with other work in epistemic model checking.

Abstract not found

Sidney Shoemaker (1995) has given an influential explanation of the absurdity of Mooreparadoxical belief in terms of conscious belief. Here I offer a novel account of the absurdity of Moore-paradoxical assertion in terms of an interlocutor’s fully conscious beliefs. This account starts with an original argument for the principle that fully conscious belief collects over conjunction. The argument is premised on the synchronic unity of consciousness and the transparency of belief. 1. Fully conscious belief and transparency: fully conscious belief collects as well as distributes over conjunction It is plausible that your fully conscious beliefs—beliefs that you are fully aware of having— distribute over conjunction: (D) If you are fully conscious at t of believing that p and q, then you are fully conscious at t of believing that p and fully conscious at t of believing that q. For illustration, suppose that in bad weather, you are fully conscious that you believe both that it is wet and that it is cold. At the same time you are fully conscious that you believe that it is wet. And at the same time you are fully conscious that you believe that it is cold.

THE SCHOOL OF ECONOMICS & SOCIAL SCIENCES, SMUSuperman, Wittgenstein and the disappearance of Moorean absurdity JOHN N. WILLIAMS (UNDER THE GUISE OF LOIS LANE) ‘You have known me for years, Lois ’ explains Superman, as I lay aside my copy of Crimmins’s example (1992). ‘But there is something you have not yet discovered. You also know me under a disguise. You have not yet realized that this person is I in disguise. On that way of thinking about me, you have different opinions of me. In fact you think me an idiot.’ I’ve just informed Superman that I accept his testimony on the strength of his intelligence. But I confess I don’t quite know how to acknowledge my acceptance of his final remark. Had he let me know the identity of the person with whom I’m acquainted and who I think idiotic, then I wouldn’t have this problem. For example, had he informed me that his alter ego is Clark then (since I know that Superman would lose his sex appeal but not his intelligence if disguised as Clark) I would have to stop believing that Clark is an idiot. For otherwise I would have to start believing that Superman is an idiot, but we