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119Reducing 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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75While 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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13The 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 Gabbay (ed.), The Handbook of the History of Logic, Elsevier. pp. 719--772. 2009.
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103I—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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112Timothy Williamson, knowledge and its limits. Oxford: Oxford university press, 2000Grazer Philosophische Studien 65 (1): 195-205. 2002.
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308Beliefs 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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101A 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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172Possible-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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203What 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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73Hodges’ 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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100The 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
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33Vassar college, 124 Raymond avenue, poughkeepsie, ny 12604, usa. In a review, a reference “jsl xliii 148,” for example, refers either to the publication reviewed on page 148 of volume 43 of the journal, or to the review itself (which contains full bibliographical information for the reviewed publication). Analogously, a reference “bsl VII 376” refers to the review beginning on page 376 in volume 7 of this bulletin, or (review)Bulletin of Symbolic Logic 15 (4). 2009.
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On the metatheory of Field's `Solving the paradoxes, escaping revenge'In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.
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562Finitistic and Frequentistic Approximation of Probability Measures with or without σ-AdditivityStudia Logica 89 (2): 257-283. 2008.In this paper a theory of finitistic and frequentistic approximations — in short: f-approximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a frequency limit forms a pre-Dynkin system $${{D\subseteq\wp(N)}}$$. The limiting probability measure over D can always be extended to a probability measure over $${{\wp(N)}}$$, but this measure is not always σ-additive. We conclude that probability …Read more
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82Inference on the Low Level: An Investigation Into Deduction, Nonmonotonic Reasoning, and the Philosophy of CognitionKluwer Academic Publishers. 2004.This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and a…Read more
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4Vincent F. Hendricks and John Symons, eds. Formal Philosophy Reviewed byPhilosophy in Review 27 (4): 266-268. 2007.
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203Criteria of Identity: Strong and WrongBritish Journal for the Philosophy of Science 64 (1): 61-68. 2013.We show that finitely axiomatized first-order theories that involve some criterion of identity for entities of a category C can be reformulated as conjunctions of a non-triviality statement and a criterion of identity for entities of category C again. From this, we draw two conclusions: First, criteria of identity can be very strong deductively. Second, although the criteria of identity that are constructed in the proof of the theorem are not good ones intuitively, it is difficult to say what ex…Read more
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115Truth as translation – part aJournal of Philosophical Logic 30 (4): 281-307. 2001.This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate - this is possi…Read more
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109A New Analysis of QuasianalysisJournal of Philosophical Logic 36 (2): 181-226. 2007.We investigate the conditions under which quasianalysis, i.e., Carnap's method of abstraction in his Aufbau, yields adequate results. In particular, we state both necessary and sufficient conditions for the so-called faithfulness and fullness of quasianalysis, and analyze adequacy as the conjunction of faithfulness and fullness. It is shown that there is no method of (re-)constructing properties from similarity that delivers adequate results in all possible cases, if the same set of individuals …Read more
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51Truth and the Liar in De Morgan-Valued ModelsNotre Dame Journal of Formal Logic 40 (4): 496-514. 1999.The aim of this paper is to give a certain algebraic account of truth: we want to define what we mean by De Morgan-valued truth models and show their existence even in the case of semantical closure: that is, languages may contain their own truth predicate if they are interpreted by De Morgan-valued models. Before we can prove this result, we have to repeat some basic facts concerning De Morgan-valued models in general, and we will introduce a notion of truth both on the object- and on the metal…Read more
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1319When betting odds and credences come apart: more worries for Dutch book argumentsAnalysis 66 (2): 119-127. 2006.If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. Hitchcock argues that this credence follows from calculating he…Read more