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134Infinitesimal 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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Hughes, R.I.G., The Structure and Interpretation of Quantum Mechanics (review)Tijdschrift Voor Filosofie 54 (4): 735. 1992.
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59The 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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12Scope and rigidityCommunication and Cognition: An Interdisciplinary Quarterly Journal 25 (4): 353-372. 1992.
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63Provability 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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110One 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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1438Fair 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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42Principles 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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155Vom 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
