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15Terugkeer van het subject? Verslag van de 23e Vlaams-Nederlandse filosofiedag, Kortrijk, 27 oktober 2001Algemeen Nederlands Tijdschrift voor Wijsbegeerte 94 (2): 155-158. 2002.
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Kessels, J., van der Dam, A., Tollenaar, J., De zaak Arlet. Inleiding in de kennistheorie (review)Tijdschrift Voor Filosofie 53 (1): 167. 1991.
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16The Logic of Intensional PredicatesIn Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences Ii, Kluwer Academic Publishers. pp. 89--111. 2003.
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30Godel's Disjunction: The Scope and Limits of Mathematical Knowledge (edited book)Oxford University Press UK. 2016.The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that in…Read more
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5Reflecting in Epistemic ArithmeticJournal of Symbolic Logic 61 (2): 788-801. 1996.An epistemic formalization of arithmetic is constructed in which certain non-trivial metatheoretical inferences about the system itself can be made. These inferences involve the notion of provability in principle, and cannot be made in any consistent extensions of Stewart Shapiro's system of epistemic arithmetic. The system constructed in the paper can be given a modal-structural interpretation.
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52Canonical naming systemsMinds and Machines 15 (2): 229-257. 2004.This paper outlines a framework for the abstract investigation of the concept of canonicity of names and of naming systems. Degrees of canonicity of names and of naming systems are distinguished. The structure of the degrees is investigated, and a notion of relative canonicity is defined. The notions of canonicity are formally expressed within a Carnapian system of second-order modal logic.
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2PrefaceIn Leon Horsten & Volker Halbach (eds.), Principles of Truth: [Conference "Truth, Necessity and Provability", Which Was Held in Leuven, Belgium, From 18 to 20 November 1999], De Gruyter. pp. 7-8. 2004.
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127An argument concerning the unknowableAnalysis 69 (2): 240-242. 2009.Williamson has forcefully argued that Fitch's argument shows that the domain of the unknowable is non-empty. And he exhorts us to make more inroads into the land of the unknowable. Concluding his discussion of Fitch's argument, he writes: " Once we acknowledge that [the domain of the unknowable] is non-empty, we can explore more effectively its extent. … We are only beginning to understand the deeper limits of our knowledge. " I shall formulate and evaluate a new argument concerning the domain o…Read more
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18Mathematical Philosophy?In Hanne Andersen, Dennis Dieks, Wenceslao González, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science, Springer Verlag. pp. 73--86. 2013.
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2523Cantorian Infinity and Philosophical Concepts of GodEuropean Journal for Philosophy of Religion 5 (3): 117--138. 2013.It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, …Read more
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128Infinitesimal ProbabilitiesBritish Journal for the Philosophy of Science 69 (2): 509-552. 2016.Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ Fir…Read more
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57The Tarskian Turn: Deflationism and Axiomatic TruthMIT Press. 2011.The work of mathematician and logician Alfred Tarski (1901--1983) marks the transition from substantial to deflationary views about truth.
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Hughes, R.I.G., The Structure and Interpretation of Quantum Mechanics (review)Tijdschrift Voor Filosofie 54 (4): 735. 1992.
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12Scope and rigidityCommunication and Cognition: An Interdisciplinary Quarterly Journal 25 (4): 353-372. 1992.
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62Provability in principle and controversial constructivistic principlesJournal of Philosophical Logic 26 (6): 635-660. 1997.New epistemic principles are formulated in the language of Shapiro's system of Epistemic Arithmetic. It is argued that some plausibility can be attributed to these principles. The relations between these principles and variants of controversial constructivistic principles are investigated. Special attention is given to variants of the intuitionistic version of Church's thesis and to variants of Markov's principle
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22Book Review: Stewart Shapiro. Vagueness in Context (review)Notre Dame Journal of Formal Logic 50 (2): 221-226. 2009.
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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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1394Fair 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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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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152Vom 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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The layered structure of physics according to Peter GalisonTijdschrift Voor Filosofie 61 (4): 747-778. 1999.
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Gomperts, M.C., Neeltje komt dinsdag in evakostuum (review)Tijdschrift Voor Filosofie 55 (3): 571. 1993.
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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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31Dennis 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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45Platonistic 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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20An Axiomatic Investigation of Provability as a Primitive PredicateIn Leon Horsten & Volker Halbach (eds.), Principles of Truth, De Gruyter. pp. 203-220. 2003.