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119Too naturalist and not naturalist enough: Reply to HorstenErkenntnis 69 (2). 2008.Leon Horsten has recently claimed that the class of mathematical truths coincides with the class of theorems of ZFC. I argue that the naturalistic character of Horsten’s proposal undermines his contention that this claim constitutes an analogue of a thesis that Daniel Isaacson has advanced for PA. I argue, moreover, that Horsten’s defence of his claim against an obvious objection makes use of a distinction which is not available to him given his naturalistic approach. I suggest a way out of the …Read more
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312How basic is the basic revisionary argument?Analysis 68 (4): 303-309. 2008.Anti-realists typically contend that truth is epistemically constrained. Truth, they say, cannot outstrip our capacity to know. Some anti-realists are also willing to make a further claim: if truth is epistemically constrained, classical logic is to be given up in favour of intuitionistic logic. Here we shall be concerned with one argument in support of this thesis - Crispin Wright's Basic Revisionary Argument, first presented in his Truth and Objectivity. We argue that the reasoning involved in…Read more
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260On the Concept of FinitismSynthese 192 (8): 2413-2436. 2015.At the most general level, the concept of finitism is typically characterized by saying that finitistic mathematics is that part of mathematics which does not appeal to completed infinite totalities and is endowed with some epistemological property that makes it secure or privileged. This paper argues that this characterization can in fact be sharpened in various ways, giving rise to different conceptions of finitism. The paper investigates these conceptions and shows that they sanction differen…Read more
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263How to be a minimalist about setsPhilosophical Studies 159 (1): 69-87. 2012.According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, I outline a different app…Read more
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83Restrictiveness relative to notions of interpretationReview of Symbolic Logic 9 (2). 2016.Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy's definition. We look at Maddy's formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy's original notion, but fixes the issu…Read more
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University of AmsterdamDepartment of Philosophy
Institute for Logic, Language and ComputationAssociate Professor
Amsterdam, North Holland, Netherlands
Areas of Specialization
Philosophy of Mathematics |
Philosophy of Language |
Logic and Philosophy of Logic |
Meta-Ethics |
Metaphysics |