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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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129Computational 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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167Reflecting 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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33Godel'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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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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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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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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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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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.