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35Correction to: HYPE: A System of Hyperintensional LogicJournal of Philosophical Logic 48 (2): 407-407. 2019.The original version of the article unfortunately contained a mistake. The author missed to mention the support by a EU-funded research network that he is involved in. See below. This work was supported by the Marie-Sklodowska-Curie Innovative Training Network DIAPHORA.
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15Why pure mathematical truths are metaphysically necessary: a set-theoretic explanationSynthese 197 (7): 3113-3120. 2020.Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.
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41HYPE: A System of Hyperintensional LogicJournal of Philosophical Logic 48 (2): 305-405. 2019.This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositio…Read more
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28Imaging all the peopleEpisteme 14 (4): 463-479. 2017.It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out…Read more
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Inference on the Low Level: An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of CognitionJournal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 38 (2): 393-395. 2007.
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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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12God − 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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36An 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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20Theories 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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5While 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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18Reducing 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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7The 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, Palgrave-macmillan. 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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11I—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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21Beliefs 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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8Timothy Williamson, knowledge and its limits. Oxford: Oxford university press, 2000Grazer Philosophische Studien 65 (1): 195-205. 2002.
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10A 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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3Towards a logic 0f type-free modality and truthIn C. Dimitracopoulos, L. Newelski & D. Normann (eds.), 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. 2007.
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17Possible-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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15Logic 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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20What 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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21Hodges’ 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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8The 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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7Vassar 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.