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Profile: Alexander Paseau (Oxford University)
  1. Alexander Paseau (forthcoming). Knowledge of Mathematics Without Proof. British Journal for the Philosophy of Science:axu012.
    Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support (for example, the Riemann hypothesis), they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical (...)
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  2. Alexander Paseau (2012). Against the Judgment-Dependence of Mathematics and Logic. Erkenntnis 76 (1):23-40.
    Although the case for the judgment-dependence of many other domains has been pored over, surprisingly little attention has been paid to mathematics and logic. This paper presents two dilemmas for a judgment-dependent account of these areas. First, the extensionality-substantiality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the substantiality condition (roughly: non-vacuous specification). Second, the extensionality-extremality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the extremality condition (...)
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  3. Alexander Paseau (2012). Resemblance Theories of Properties. Philosophical Studies 157 (3):361-382.
    The paper aims to develop a resemblance theory of properties that technically improves on past versions. The theory is based on a comparative resemblance predicate. In combination with other resources, it solves the various technical problems besetting resemblance nominalism. The paper’s second main aim is to indicate that previously proposed resemblance theories that solve the technical problems, including the comparative theory, are nominalistically unacceptable and have controversial philosophical commitments.
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  4. Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng (2012). Science and Mathematics: The Scope and Limits of Mathematical Fictionalism. [REVIEW] Metascience 21 (2):269-294.
    Science and mathematics: the scope and limits of mathematical fictionalism Content Type Journal Article Category Book Symposium Pages 1-26 DOI 10.1007/s11016-011-9640-3 Authors Christopher Pincock, University of Missouri, 438 Strickland Hall, Columbia, MO 65211-4160, USA Alan Baker, Department of Philosophy, Swarthmore College, Swarthmore, PA 19081, USA Alexander Paseau, Wadham College, Oxford, OX1 3PN UK Mary Leng, Department of Philosophy, University of York, Heslington, York, YO10 5DD UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  5. Alexander Paseau (2011). Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence. Studies in History and Philosophy of Science Part A 42 (1):140-149.
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  6. Alexander Paseau (2011). Proofs of the Compactness Theorem. History and Philosophy of Logic 31 (1):73-98.
    In this study, several proofs of the compactness theorem for propositional logic with countably many atomic sentences are compared. Thereby some steps are taken towards a systematic philosophical study of the compactness theorem. In addition, some related data and morals for the theory of mathematical explanation are presented.
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  7. Alexander Paseau (2010). A Puzzle About Naturalism. Metaphilosophy 41 (5):642-648.
    Abstract: This article presents and solves a puzzle about methodological naturalism. Trumping naturalism is the thesis that we must accept p if science sanctions p, and biconditional naturalism the apparently stronger thesis that we must accept p if and only if science sanctions p. The puzzle is generated by an apparently cogent argument to the effect that trumping naturalism is equivalent to biconditional naturalism. It turns out that the argument for this equivalence is subtly question-begging. The article explains this and (...)
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  8. Alexander Paseau (2010). Defining Ultimate Ontological Basis and the Fundamental Layer. Philosophical Quarterly 60 (238):169-175.
    I explain why Ross Cameron's definition of ultimate ontological basis is incorrect, and propose a different definition in terms of ontological dependence, as well as a definition of reality's fundamental layer. These new definitions cover the conceptual possibility that self-dependent entities exist. They also apply to different conceptions of the relation of ontological dependence.
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  9. Alexander Paseau (2010). Pure Second-Order Logic with Second-Order Identity. Notre Dame Journal of Formal Logic 51 (3):351-360.
    Pure second-order logic is second-order logic without functional or first-order variables. In "Pure Second-Order Logic," Denyer shows that pure second-order logic is compact and that its notion of logical truth is decidable. However, his argument does not extend to pure second-order logic with second-order identity. We give a more general argument, based on elimination of quantifiers, which shows that any formula of pure second-order logic with second-order identity is equivalent to a member of a circumscribed class of formulas. As a (...)
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  10. Alexander Paseau (2009). How to Type: Reply to Halbach. Analysis 69 (2):280-286.
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  11. Alexander Paseau (2008). Fitch's Argument and Typing Knowledge. Notre Dame Journal of Formal Logic 49 (2):153-176.
    Fitch's argument purports to show that if all truths are knowable then all truths are known. The argument exploits the fact that the knowledge predicate or operator is untyped and may thus apply to sentences containing itself. This article outlines a response to Fitch's argument based on the idea that knowledge is typed. The first part of the article outlines the philosophical motivation for the view, comparing it to the motivation behind typing truth. The second, formal part presents a logic (...)
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  12. Alexander Paseau (2008). Justifying Induction Mathematically: Strategies and Functions. Logique Et Analyse 51 (203):263.
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  13. Alexander Paseau (2008). Motivating Reductionism About Sets. Australasian Journal of Philosophy 86 (2):295 – 307.
    The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.
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  14. Alexander Paseau (2008). Naturalism in the Philosophy of Mathematics. In Stanford Encyclopedia of Philosophy.
    Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...)
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  15. Alexander Paseau (2008). Stanford Encyclopedia of Philosophy.
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  16. Mary Leng, Alexander Paseau & Michael D. Potter (eds.) (2007). Mathematical Knowledge. Oxford University Press.
    What is the nature of mathematical knowledge? Is it anything like scientific knowledge or is it sui generis? How do we acquire it? Should we believe what mathematicians themselves tell us about it? Are mathematical concepts innate or acquired? Eight new essays offer answers to these and many other questions. Written by some of the world's leading philosophers of mathematics, psychologists, and mathematicians, Mathematical Knowledge gives a lively sense of the current state of debate in this fascinating field. Contents 1. (...)
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  17. Alexander Paseau (2007). Boolos on the Justification of Set Theory. Philosophia Mathematica 15 (1):30-53.
    George Boolos has argued that the iterative conception of set justifies most, but not all, the ZFC axioms, and that a second conception of set, the Frege-von Neumann conception (FN), justifies the remaining axioms. This article challenges Boolos's claim that FN does better than the iterative conception at justifying the axioms in question. For comments on earlier versions, I am grateful to Alex Oliver, Mary Leng, Michael Potter, Øystein Linnebo, Paul Benacerraf, Peter Smith, and three journal referees.
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  18. Alexander Paseau (2006). Genuine Modal Realism and Completeness. Mind 115 (459):721-730.
    John Divers and Joseph Melia have argued that Lewis's modal realism is extensionally inadequate. This paper explains why their argument does not succeed.
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  19. Alexander Paseau (2006). The Subtraction Argument(S). Dialectica 60 (2):145–156.
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  20. Alexander Paseau (2005). Naturalism in Mathematics and the Authority of Philosophy. British Journal for the Philosophy of Science 56 (2):377-396.
    Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the (...)
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  21. Alexander Paseau (2005). On an Application of Categoricity. Proceedings of the Aristotelian Society 105 (3):411–415.
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  22. Alexander Paseau (2005). What the Foundationalist Filter Kept Out. Studies in History and Philosophy of Science Part A 36 (1):191-201.
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  23. Alexander Paseau (2002). Why the Subtraction Argument Does Not Add Up. Analysis 62 (1):73–75.
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  24. Alexander Paseau (2001). Should the Logic of Set Theory Be Intuitionistic? Proceedings of the Aristotelian Society 101 (3):369–378.
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