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371The Stability Theory of BeliefPhilosophical Review 123 (2): 131-171. 2014.This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so…Read more
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135A way out of the preface paradox?Analysis 74 (1). 2014.The thesis defended in this article is that by uttering or publishing a great many declarative sentences in assertoric mode, one does not actually assert that their conjunction is true – one rather asserts that the vast majority of these sentences are true. Accordingly, the belief that is expressed thereby is the belief that the vast majority of these sentences are true. In the article, we make this proposal precise, we explain the context-dependency of belief that corresponds to it, we point ou…Read more
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196Scientific Philosophy, Mathematical Philosophy, and All ThatMetaphilosophy 44 (3): 267-275. 2013.This article suggests that scientific philosophy, especially mathematical philosophy, might be one important way of doing philosophy in the future. Along the way, the article distinguishes between different types of scientific philosophy; it mentions some of the scientific methods that can serve philosophers; it aims to undermine some worries about mathematical philosophy; and it tries to make clear why in certain cases the application of mathematical methods is necessary for philosophical progr…Read more
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102An impossibility result on semantic resemblanceDialectica 62 (3): 293-306. 2008.We show that a set of prima facie plausible assumptions on the relation of meaning resemblance – one of which is a compositionality postulate – is inconsistent. On this basis we argue that either there is no theoretically useful notion of semantic resemblance at all, or the traditional conception of the compositionality of meaning has to be adapted. In the former case, arguments put forward by Nelson Goodman and Paul Churchland in favor of the concept of meaning resemblance are defeated. In the …Read more
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121On the Ramsey Test without TrivialityNotre Dame Journal of Formal Logic 51 (1): 21-54. 2010.We present a way of classifying the logically possible ways out of Gärdenfors' inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramsey test—we determine which of the assumptions in three different versions of Gärdenfors' theorem turn out to be false. This is done by constructing ranked models in which such Ramsey-test conditionals are evaluated and wh…Read more
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176How Serious Is the Paradox of Serious Possibility?Mind 121 (481): 1-36. 2012.The so-called Paradox of Serious Possibility is usually regarded as showing that the standard axioms of belief revision do not apply to belief sets that are introspectively closed. In this article we argue to the contrary: we suggest a way of dissolving the Paradox of Serious Possibility so that introspective statements are taken to express propositions in the standard sense, which may thus be proper members of belief sets, and accordingly the normal axioms of belief revision apply to them. Inst…Read more
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Logic and Philosophy of MathematicsJournal of the Indian Council of Philosophical Research 27 (2). 2010.
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2What is a self-referential sentence? Critical remarks on the alleged mbox(non-)circularity of Yablo's paradoxLogique and Analyse 177 (178): 3-14. 2002.
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93God − Moore = Ramsey (A Reply to Chalmers and Hájek)Topoi 30 (1): 47-51. 2011.Famously, Frank P. Ramsey suggested a test for the acceptability of conditionals. Recently, David Chalmers and Alan Hájek (2007) have criticized a qualitative variant of the Ramsey test for indicative conditionals. In this paper we argue for the following three claims: (i) Chalmers and Hájek are right that the variant of the Ramsey test that they attack is not the correct way of spelling out an acceptability test for indicative conditionals. But there is a suppositional variant of the Ramsey tes…Read more
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96Theories of truth which have no standard modelsStudia Logica 68 (1): 69-87. 2001.This papers deals with the class of axiomatic theories of truth for semantically closed languages, where the theories do not allow for standard models; i.e., those theories cannot be interpreted as referring to the natural number codes of sentences only (for an overview of axiomatic theories of truth in general, see Halbach[6]). We are going to give new proofs for two well-known results in this area, and we also prove a new theorem on the nonstandardness of a certain theory of truth. The results…Read more
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476An Objective Justification of Bayesianism I: Measuring InaccuracyPhilosophy of Science 77 (2): 201-235. 2010.One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts to f…Read more
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116Reducing belief simpliciter to degrees of beliefAnnals of Pure and Applied Logic 164 (12): 1338-1389. 2013.Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there…Read more
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74While the Gödel centenary year 2006 triggered a lot of conference and workshop activity on Gödel, the years leading to it stand out by exhibiting several excellent publications on Gödel's life and work, most notably the completion of the Kurt Gödel Collected Works series . The two volumes of Kurt Gödel. Wahrheit & Beweisbarkeit, written in German and edited by E. Köhler et al., constitute something like the ‘German-Austrian contribution’ to this renewal of interest in Gödel's legacy, even though…Read more
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12The Association for Symbolic Logic publishes analytical reviews of selected books and articles in the field of symbolic logic. The reviews were published in The Journal of Symbolic Logic from the founding of the Journal in 1936 until the end of 1999. The Association moved the reviews to this Bulletin, beginning in 2000. The Reviews Section is edited by Steve Awodey (Managing Editor), John Baldwin, John (review)Bulletin of Symbolic Logic 16 (1). 2010.
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32On formal and informal provabilityIn Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics, . pp. 263--299. 2009.
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Mechanizing InductionIn Dov Gabby, Hartmann M., Woods Stephan & John (eds.), Handbook of the History of Logic: Inductive Logic, Elsevier: Amsterdam. pp. 719--772. 2009.
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102I—The Humean Thesis on BeliefAristotelian Society Supplementary Volume 89 (1): 143-185. 2015.This paper suggests a bridge principle for all-or-nothing belief and degrees of belief to the effect that belief corresponds to stably high degree of belief. Different ways of making this Humean thesis on belief precise are discussed, and one of them is shown to stand out by unifying the others. The resulting version of the thesis proves to be fruitful in entailing the logical closure of belief, the Lockean thesis on belief, and coherence between decision-making based on all-or-nothing beliefs a…Read more
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111Timothy Williamson, knowledge and its limits. Oxford: Oxford university press, 2000Grazer Philosophische Studien 65 (1): 195-205. 2002.
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306Beliefs in conditionals vs. conditional beliefsTopoi 26 (1): 115-132. 2007.On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representa…Read more
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18Towards a logic 0f type-free modality and truthIn Costas Dimitracopoulos (ed.), Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28-August 3, 2005, Cambridge University Press. pp. 28--68. 2008.
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99A Lottery Paradox for Counterfactuals Without AgglomerationPhilosophy and Phenomenological Research 89 (3): 605-636. 2013.We will present a new lottery-style paradox on counterfactuals and chance. The upshot will be: combining natural assumptions on the truth values of ordinary counterfactuals, the conditional chances of possible but non-actual events, the manner in which and relate to each other, and a fragment of the logic of counterfactuals leads to disaster. In contrast with the usual lottery-style paradoxes, logical closure under conjunction—that is, in this case, the rule of Agglomeration of counterfactuals—w…Read more
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170Possible-worlds semantics for modal notions conceived as predicatesJournal of Philosophical Logic 32 (2): 179-223. 2003.If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for p…Read more
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122Logic in general philosophy of science: old things and new thingsSynthese 179 (2). 2011.This is a personal, incomplete, and very informal take on the role of logic in general philosophy of science, which is aimed at a broader audience. We defend and advertise the application of logical methods in philosophy of science, starting with the beginnings in the Vienna Circle and ending with some more recent logical developments
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199What Truth Depends onJournal of Philosophical Logic 34 (2): 155-192. 2005.What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of Φ in/from the extension of the tr…Read more
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68Hodges’ Theorem Does not Account for Determinacy of Translation. A Reply to WerningErkenntnis 62 (3): 411-425. 2005.Werning applies a theorem by Hodges in order to put forward an argument against Quine's thesis of the indeterminacy of translation and in favour of what Werning calls 'semantic realism'. We show that the argument rests on two critical premises both of which are false. The reasons for these failures are explained and the actual place of this application of Hodges' theorem within Quine's philosophy of language is outlined.
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95The Review Paradox: On The Diachronic Costs of Not Closing Rational Belief Under ConjunctionNoûs 48 (4): 781-793. 2013.We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions