Of course, to get these results we are still making assumptions about the behavior of ⇢ in infinite sets, but I take it that the assumptions required are quite abstemious.2 John L. Pollock Philosophy, University of Arizona, Tucson, AZ A Note on Kripke's Puzzle about Belief In his recent contribution to this gazette, Jesse Steinberg (2007: "Pierre may be ignorant, but he's not irrational", The Reasoner 1(3): 2-3) discusses the following rendition of Kripke's puzzle, due to Sosa: 1. Pierre is rational. (assumption) 2. Pierre, on reflection, assents to "Londres est jolie". (assumption) 3. "London is pretty" is a translation of "Londres est jolie". (assumption) 4. Pierre, on reflection, assents to "London is not pretty". (assumption) 5. Pierre believes that London is pretty. (2, 3, D) 6. Pierre believes that London is not pretty. (4, D) 7. Pierre believes that London is pretty and Pierre believes that London is not pretty. (5, 6, I) 8. If Pierre believes that London is pretty and Pierre believes that London is not pretty, then Pierre has contradictory beliefs. (analytic?) 9. Pierre has contradictory beliefs. (7, 8, MP) 10. If Pierre has contradictory beliefs, then Pierre is not rational. (analytic?) 11. Pierre is not rational. (9, 10, MP) Steinberg aims to provide a solution to this purported paradox, by denying premise (10). According to him, the mere fact that an agent has contradictory beliefs is not a su cient condition to count that agent as irrational. Steinberg supports this claim with the example of Tim, a student who rightfully believes that the form of a certain argument (modus ponens) is valid, but then fails to recognise the validity of a di↵erent argument of the same form. Now, Steinberg asks: "Would we consider Tim to be irrational? Tim is surely not astute. One might be tempted to call him obtuse, but he is certainly not irrational. [. . . ] What would make Tim irrational is his believing a contradiction, his being aware that he 2 This work was supported by NSF grant no. IIS-0412791. Thanks to Stephen Fogdall for his comments. believes that contradiction, and his obstinacy in continuing to believe the contradiction even in the face of this awareness." (2007: 2-3) The intended moral of this example is that an agent A might have contradictory beliefs and yet continue to be rational. According to Steinberg that may happen if (i) A has two contradictory beliefs, (ii) A is ignorant of having beliefs that are contradictory, and (iii) A is disposed, or able, to revise his belief system upon becoming aware of the contradiction. My intention here is not to criticise this suggestion. Though some further qualification may be needed (e.g., to the e↵ect that A's ignorance must not be due to any obvious fault in A's reasoning capacities), the idea that rational agents might have contradictory beliefs is not so unintuitive, and has in fact received compelling support from various philosophers (e.g., Dummett 1973: Frege: Philosophy of Language, London: Duckworth). What I do intend to argue, in e↵ect, is that this idea is not necessary-and, indeed, not even adequate-for the task of solving Kripke's puzzle. To see this, let us follow Steinberg's suggestion and grant that Pierre is ignorant, but not irrational. In other words, Pierre has contradictory beliefs, but is unaware of the contradiction, and therefore (at least potentially) rational. Now the question is: What is Pierre actually ignorant of? Presumably, it is the fact that there is only one city which he calls 'Londres' in French and 'London' in English. Obviously, there is no irrationality involved in this cognitive shortcoming: one may fully rationally employ di↵erent idiolects, without having to know all the correspondences (i.e., standard translations) between those idiolects. But let us imagine next that Pierre somehow learns that the names 'Londres' and 'London' in fact denote the same city and reports his discovery (of an a posteriori piece of knowledge) in French: "Incroyable! Après tout, Londres est London!". Now, applying Kripke's translation principle, together with his remark that the translation of 'Londres' as 'London' "[i]s a standard one, learnt by students together with other standard translations of French into English" (Kripke 1979: "A Puzzle about Belief", in Meaning and Use, p. 128), we should have no qualms about translating Pierre's words into English as: "Incredible! After all, London is London!" Yet, it seems pretty clear that this translation would be inadequate, since it would have Pierre foolishly rejoicing in the discovery of a trivial a priori identity statement-which is clearly not what his French utterance reports. This suggests to me that in cases like Pierre's-i.e., when the speaker is unaware of certain facts about translation between idiolects-our own translation of the speaker's utterances should be guided, and appropriately constrained, not only by what Kripke calls the translation principle, but also by a principle of charity which implies, among other things, that we should aim 8 at preserving both the truth-value of the speaker's assertions, and their cognitive content. (There are other imaginary examples that support this diagnosis. Suppose, for instance, that Pierre is blindfoldedly taken to a (fictional)Quartier Français in London. Without knowing where he is, Pierre sees a placard that reads: "Bienvenus à Londres!". As he enjoys the neighbourhood a lot, he says to himself: "Allors, ça c'est Londres! C'est une ville merveilleuse! J'aimerais bien vivre ici! Quel dommage que j'habite à London!" If we were to translate Pierre's assertions in the standard way, we would get the following result: "So, this is London! What a wonderful city! I'd love to live here! Too bad I live in London!" It goes without saying that this is not an adequate translation of Pierre's words, since it has him contradict himself, which is not what he's doing in French.) The preceding remarks, if correct, suggest a di↵erent way of tackling Kripke's puzzle, which enables us to block the apparent paradox before it even gets o↵ the ground. If the translation of 'Londres' (in Pierre's idiolect) as 'London' is unwarranted, as I have argued, then premise (3) of the argument is false (N.B. as applied to Pierre's idiolect, not as a rule of standard translation). And this, in turn, blocks the derivation of line (5). Not only is Pierre "merely ignorant and not some sort of bizarre irrational being", as Steinberg argues. He is not even committed to any contradiction in the first place. Cristian Constantinescu Philosophy, Trinity College, Cambridge §3 News Calls for Papers Introducing . . . The Reasoner would like to publish very short introductions to key terms, people and texts in logic and reasoning. Selected pieces will also be published in a book "Key Terms in Logic" by Continuum. If you would like to contribute, please contact TheReasoner@kent.ac.uk TheoreticalComputer Science: Special issue in honour of Jean-Yves Girard on the occasion of his 60th birthday year, deadline 30 September. Connection Science Journal: Special issue on Social Learning in Embodied Agents, alberto.acerbi@istc.cnr.it, deadline: 30 October 2007. Special Issue of Foundations of Science: Mathematics and Argumentation, deadline 1 November 2007. Erkenntnis: Special Issue on Conditionals and Ranking Functions, franz.huber@uni-konstanz.de, Deadline for submissions: May 31, 2008. §4 Events LORI: Logic, Rationality and Interaction, Beijing, 5-9 August 2007. TANCL'07: Algebraic and topological methods in non-classical logics III, 5-9 August 2007, Oxford. Workshop: Construction and properties of Bayesian nonparametric regression models, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, August 6-10 2007. LMPS: 13th International Congress of Logic, Methodology and Philosophy of Science, Beijing, 9-15 August 2007. IJCNN2007: 2007 International Joint Conference on Neural Networks, Orlando, Florida, August 12-17, 2007. Uni-Log: 2ndWorld Congress and School on Universal Logic, Xi'an, 16-19 August 2007. C&O:RR-2007: The Third International Workshop on Contexts and Ontologies: Representation and Reasoning, August 21, 2007, CONTEXT Workshop Program, Roskilde University, Denmark. LSFA'07: Second Workshop on Logical and Semantic Frameworks, with Applications, August 28th, 2007, Ouro Preto, Minas Gerais, Brazil. ASAI 2007: IX Argentine Symposium on Artificial Intelligence Mar del Plata, Argentina, August 27-28, 2007. Progic 2007 The Third Workshop on Combining Probability and Logic, University of Kent, 5-7 September 2007. BLC 2007: British Logic Colloquium, London, September 6-8, 2007. IDA 2007: The 7th International Symposium on Intelligent Data Analysis, Ljubljana, Slovenia, September 6-8, 2007. Dynamics of Knowledge and Belief: Workshop at KI-2007, 30th Annual German Conference on Artificial Intelligence, Osnabrück, 10 September 2007. CSL 2007: Computer Science Logic, 11-15 September, 2007, Lausanne (CH). International Conference on Normative Concepts: Zurich University, 21 22 September 2007. AIPL-07: Workshop on Artificial Intelligence Planning and Learning, Providence, Rhode Island, September 22, 2007, organized in conjunction with the International Conference on Automated Planning and Scheduling (ICAPS-07). SymCon'07: The Seventh International Workshop on Symmetry and Constraint Satisfroblems, Providence, RI, USA, September 23rd 2007. ICAPS 2007: Workshop on Planning in Games, Providence, Rhode Island, USA, September, 23, 2007.