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41Principles of truth (edited book)Hänsel-Hohenhausen. 2002.On the one hand, the concept of truth is a major research subject in analytic philosophy. On the other hand, mathematical logicians have developed sophisticated logical theories of truth and the paradoxes. Recent developments in logical theories of the semantical paradoxes are highly relevant for philosophical research on the notion of truth. And conversely, philosophical guidance is necessary for the development of logical theories of truth and the paradoxes. From this perspective, this volume …Read more
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109One Hundred Years of Semantic ParadoxJournal of Philosophical Logic (6): 1-15. 2015.This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade
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1409Fair infinite lotteriesSynthese 190 (1): 37-61. 2013.This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
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153Vom Zahlen zu den Zahlen: On the Relation Between Computation and Arithmetical StructuralismPhilosophia Mathematica 20 (3): 275-288. 2012.This paper sketches an answer to the question how we, in our arithmetical practice, succeed in singling out the natural-number structure as our intended interpretation. It is argued that we bring this about by a combination of what we assert about the natural-number structure on the one hand, and our computational capacities on the other hand
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Gomperts, M.C., Neeltje komt dinsdag in evakostuum (review)Tijdschrift Voor Filosofie 55 (3): 571. 1993.
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The layered structure of physics according to Peter GalisonTijdschrift Voor Filosofie 61 (4): 747-778. 1999.
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32Dennis E. hesseling. Gnomes in the fog: The reception of Brouwer's intuitionism in the 1920s. Basel, boston, Berlin: Birkhäu-ser verlag, 2003. Pp. XXIII + 448. ISBN 3-7643-6536- (review)Philosophia Mathematica 13 (1): 111-113. 2005.
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23Review of jc Beall (ed.), Revenge of the Liar: New Essays on the Paradox (review)Notre Dame Philosophical Reviews 2009 (5). 2009.
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20An Axiomatic Investigation of Provability as a Primitive PredicateIn Leon Horsten & Volker Halbach (eds.), Principles of Truth, De Gruyter. pp. 203-220. 2003.
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46Platonistic formalismErkenntnis 54 (2): 173-194. 2001.The present paper discusses a proposal which says,roughly and with several qualifications, that thecollection of mathematical truths is identical withthe set of theorems of ZFC. It is argued that thisproposal is not as easily dismissed as outright falseor philosophically incoherent as one might think. Some morals of this are drawn for the concept ofmathematical knowledge.
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197Non-Archimedean ProbabilityMilan Journal of Mathematics 81 (1): 121-151. 2013.We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolm…Read more
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84No futureJournal of Philosophical Logic 30 (3): 259-265. 2001.The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past…Read more
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85On the Exclusivity Implicature of ‘Or’ or on the Meaning of Eating StrawberriesStudia Logica 81 (1): 19-24. 2005.This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective ‘or’.Keywords: exclusivity implicature, Adaptive Logics.
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83In defense of epistemic arithmeticSynthese 116 (1): 1-25. 1998.This paper presents a defense of Epistemic Arithmetic as used for a formalization of intuitionistic arithmetic and of certain informal mathematical principles. First, objections by Allen Hazen and Craig Smorynski against Epistemic Arithmetic are discussed and found wanting. Second, positive support is given for the research program by showing that Epistemic Arithmetic can give interesting formulations of Church's Thesis.
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116The Undecidability of Propositional Adaptive LogicSynthese 158 (1): 41-60. 2007.We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decid…Read more
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23Formalizing Church's ThesisIn A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years, Ontos Verlag. pp. 1--253. 2006.
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88The church-Turing thesis and effective mundane proceduresMinds and Machines 5 (1): 1-8. 1995.We critically discuss Cleland''s analysis of effective procedures as mundane effective procedures. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland''s mundane procedures can enter the world of numbers. Hence her arguments against versions o…Read more
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53Bas C. van Fraassen, The Empirical Stance (review)International Studies in the Philosophy of Science 18 (1): 95-97. 2004.
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324Philosophy of mathematicsStanford Encyclopedia of Philosophy. 2008.If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case with respect to th…Read more
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The deflationists' axioms for truthIn J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox, Oxford University Press. 2005.
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85On the Quantitative Scalar or-ImplicatureSynthese 146 (1-2): 111-127. 2005.. Two simple generalized conversational implicatures are investigated :(1) the quantitative scalar implicature associated with ‘or’, and (2) the ‘not-and’-implicature, which is the dual to (1). It is argued that it is more fruitful to consider these implicatures as rules of interpretation and to model them in an algebraic fashion than to consider them as nonmonotonic rules of inference and to model them in a proof-theoretic way.
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32A Kripkean Approach to Unknowability and TruthNotre Dame Journal of Formal Logic 39 (3): 389-405. 1998.We consider a language containing partial predicates for subjective knowability and truth. For this language, inductive hierarchy rules are proposed which build up the extension and anti-extension of these partial predicates in stages. The logical interaction between the extension of the truth predicate and the anti-extension of the knowability predicate is investigated
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121Having an interpretation (review)Philosophical Studies 150 (3). 2010.I investigate what it means to have an interpretation of our language, how we manage to bestow a determinate interpretation to our utterances, and to which extent our interpretation of the world is determinate. All this is done in dialogue with van Fraassen's insightful discussion of Putnam's model-theoretic argument and of scientific structuralism
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29Two problems concerning Frege's distinction between concepts and objectsLogique Et Analyse 127 (27): 267-284. 1989.
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18De gelaagde structuur Van de natuurkunde volgens Peter GalisonTijdschrift Voor Filosofie 61 (4). 1999.This article discusses Peter Galison's views on the structure and evolution of experimental and instrumental cultures in 20th century particle physics, which are unfolded in his recent book Image and Logic. A Material Culture of Microphysics. First a description is given of the uncomfortable predicament in which the Kuhnian tradition finds itself in the past two decades. It is then explained how Galison distinguishes a layered structure in the practice of modern particle physics. Physics as a pr…Read more
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31Remarks on the content and extension of the notion of provabilityLogique Et Analyse 48 (189-192): 15-32. 2005.