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The Semantical Paradoxes, the Neutrality of Truth and the Neutrality of the Minimalist Theory of TruthIn P. Cartois (ed.), The Many Problems of Realism (Studies in the General Philosophy of Science: Volume 3), Tilberg University Press. 1995.
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2Eindig, oneindig, meer dan oneindig. Grondslagen van de wiskundige wetenschappenTijdschrift Voor Filosofie 67 (1): 175-177. 2005.
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117Revision RevisitedReview of Symbolic Logic 5 (4): 642-664. 2012.This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.
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13A Note Concerning The Notion Of SatisfiabilityLogique Et Analyse 47. 2004.Tarski has shown how the argumentation of the liar paradox can be used to prove a theorem about truth in formalized languages. In this paper, it is shown how the paradox concerning the least undefinable ordinal can be used to prove a no go-theorem concerning the notion of satisfaction in formalized languages. Also, the connection of this theorem with the absolute notion of definability is discussed.
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Perceptual Indiscriminability and the Concept of a Color ShadeIn Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic, Oxford University Press. 2010.
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130Computational Structuralism &daggerPhilosophia Mathematica 13 (2): 174-186. 2005.According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations…Read more
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3Given any finite graph, which transitive graphs approximate it most closely and how fast can we find them? The answer to this question depends on the concept of “closest approximation” involved. In [8,9] a qualitative concept of best approximation is formulated. Roughly, a qualitatively best transitive approximation of a graph is a transitive graph which cannot be “improved” without also going against the original graph. A quantitative concept of best approximation goes back at least to [10]. A qu…Read more
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170Reflecting on Absolute InfinityJournal of Philosophy 113 (2): 89-111. 2016.This article is concerned with reflection principles in the context of Cantor’s conception of the set-theoretic universe. We argue that within such a conception reflection principles can be formulated that confer intrinsic plausibility to strong axioms of infinity.
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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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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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34Godel'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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17The Logic of Intensional PredicatesIn Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences II, Kluwer Academic Publishers. pp. 89--111. 2003.