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27The Historical turn in Analytic Philosophy (edited book)Palgrave-Macmillan. 2013.During the last 25 years, a large number of publications on the history of analytic philosophy have appeared, significantly more than in the preceding period. As most of these works are by analytically trained authors, it is tempting to speak of a 'historical turn' in analytic philosophy. The present volume constitutes both a contribution to this body of work and a reflection on what is, or might be, achieved in it. The twelve new essays, by an international group of contributors, range from cas…Read more
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223Frege on Numbers: Beyond the Platonist PictureThe Harvard Review of Philosophy 13 (2): 25-40. 2005.Gottlob Frege is often called a "platonist". In connection with his philosophy we can talk about platonism concerning three kinds of entities: numbers, or logical objects more generally; concepts, or functions more generally; thoughts, or senses more generally. I will only be concerned about the first of these three kinds here, in particular about the natural numbers. I will also focus mostly on Frege's corresponding remarks in The Foundations of Arithmetic (1884), supplemented by a few asides o…Read more
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From Frege to Wittgenstein: Essays on Early Analytic Philosophy (edited book)Oxford University Press. 2002.
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23Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. II (edited book)Routledge. 2005.
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194Completeness and Categoricity. Part I: Nineteenth-century Axiomatics to Twentieth-century MetalogicHistory and Philosophy of Logic 23 (1): 1-30. 2002.This paper is the first in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully exte…Read more
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Introduction : Analytic philosophy and philosophical historyIn The Historical turn in Analytic Philosophy, Palgrave-macmillan. pp. 1-36. 2013.
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68Frege's natural numbers: Motivations and modificationsIn Michael Beaney & Erich Reck (eds.), Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. III, Routledge. pp. 270-301. 2005.Frege's main contributions to logic and the philosophy of mathematics are, on the one hand, his introduction of modern relational and quantificational logic and, on the other, his analysis of the concept of number. My focus in this paper will be on the latter, although the two are closely related, of course, in ways that will also play a role. More specifically, I will discuss Frege's logicist reconceptualization of the natural numbers with the goal of clarifying two aspects: the motivations for…Read more
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99Dedekind, structural reasoning, and mathematical understandingIn Bart Van Kerkhove (ed.), New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics, World Scientific. pp. 150--173. 2009.
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191Frege on truth, judgment, and objectivityGrazer Philosophische Studien 75 (1): 149-173. 2007.In Frege's writings, the notions of truth, judgment, and objectivity are all prominent and important. This paper explores the close connections between them, together with their ties to further cognate notions, such as those of thought, assertion, inference, logical law, and reason. It is argued that, according to Frege, these notions can only be understood properly together, in their inter-relations. Along the way, interpretations of some especially cryptic Fregean remarks, about objectivity, l…Read more
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461Frege's influence on Wittgenstein: Reversing metaphysics via the context principleIn Michael Beaney & Erich Reck (eds.), Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. I, Routledge. pp. 241-289. 2005.Gottlob Frege and Ludwig Wittgenstein (the later Wittgenstein) are often seen as polar opposites with respect to their fundamental philosophical outlooks: Frege as a paradigmatic "realist", Wittgenstein as a paradigmatic "anti-realist". This opposition is supposed to find its clearest expression with respect to mathematics: Frege is seen as the "arch-platonist", Wittgenstein as some sort of "radical anti-platonist". Furthermore, seeing them as such fits nicely with a widely shared view about the…Read more
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1Carnapian Explication : A Case Study and CritiqueIn Pierre Wagner (ed.), Carnap's Ideal of Explication and Naturalism, Palgrave-macmillan. pp. 96--116. 2012.
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87Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-first-Century SemanticsHistory and Philosophy of Logic 23 (2): 77-94. 2002.This paper is the second in a two-part series in which we discuss several notions of completeness for systems of mathematical axioms, with special focus on their interrelations and historical origins in the development of the axiomatic method. We argue that, both from historical and logical points of view, higher-order logic is an appropriate framework for considering such notions, and we consider some open questions in higher-order axiomatics. In addition, we indicate how one can fruitfully ext…Read more
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