25 found
Order:
See also:
Profile: Alexander Paseau (Oxford University)
  1.  24
    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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   11 citations  
  2.  97
    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. (...)
    Direct download  
     
    Export citation  
     
    My bibliography   5 citations  
  3. 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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  4.  98
    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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  5. 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 (...)
    Direct download (10 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  6.  43
    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.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  7.  40
    Alexander Paseau (2002). Why the Subtraction Argument Does Not Add Up. Analysis 62 (1):73–75.
    Gonzalo Rodriguez-Pereyra (1997) has refined an argument due to Thomas Baldwin (1996), which claims to prove nihilism, the thesis that there could have been no concrete objects, and which apparently does so without reliance on any heavy-duty metaphysics of modality. This note will show that on either reading of its key premiss, the subtraction argument Rodriguez-Pereyra proposes is invalid.
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography   6 citations  
  8.  62
    Alexander Paseau (2015). Knowledge of Mathematics Without Proof. British Journal for the Philosophy of Science 66 (4):775-799.
    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, 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 proposition. We also show that (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  9.  23
    Alexander Paseau (2011). Proving Induction. Australasian Journal of Logic 9:1-17.
    The hard problem of induction is to argue without begging the question that inductive inference, applied properly in the proper circumstances, is conducive to truth. A recent theorem seems to show that the hard problem has a deductive solution. The theorem, provable in zfc, states that a predictive function M exists with the following property: whatever world we live in, M correctly predicts the world’s present state given its previous states at all times apart from a well-ordered subset. On the (...)
    Direct download  
     
    Export citation  
     
    My bibliography  
  10.  26
    Alexander Paseau (2006). The Subtraction Argument(S). Dialectica 60 (2):145–156.
    The subtraction argument aims to show that there is an empty world, in the sense of a possible world with no concrete objects. The argument has been endorsed by several philosophers. I show that there are currently two versions of the argument around, and that only one of them is valid. I then sketch the main problem for the valid version of the argument.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  11.  41
    Alexander Paseau (2011). Mathematical Instrumentalism, Gödel's Theorem, and Inductive Evidence. Studies in History and Philosophy of Science Part A 42 (1):140-149.
    Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of mathematical instrumentalism (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  12.  50
    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.
    Direct download (8 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  13.  89
    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.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  14. 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.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  15.  50
    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 (...)
    Direct download  
     
    Export citation  
     
    My bibliography   1 citation  
  16.  50
    Alexander Paseau (2009). How to Type: Reply to Halbach. Analysis 69 (2):280-286.
    In my paper , I noted that Fitch's argument, which purports to show that if all truths are knowable then all truths are known, can be blocked by typing knowledge. If there is not one knowledge predicate, ‘ K’, but infinitely many, ‘ K 1’, ‘ K 2’, … , then the type rules prevent application of the predicate ‘ K i’ to sentences containing ‘ K i’ such as ‘ p ∧¬ K i⌜ p⌝’. This provides a motivated response (...)
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  17.  51
    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.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  18.  61
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  19.  8
    Alexander Paseau (2008). Justifying Induction Mathematically: Strategies and Functions. Logique Et Analyse 51 (203):263.
    If the total state of the universe is encodable by a real number, Hardin and Taylor have proved that there is a solution to one version of the problem of induction, or at least a solution to a closely related epistemological problem. Is this philosophical application of the Hardin-Taylor result modest enough? I advance grounds for doubt.
    Direct download  
     
    Export citation  
     
    My bibliography  
  20.  23
    Alexander Paseau (2001). Should the Logic of Set Theory Be Intuitionistic? Proceedings of the Aristotelian Society 101 (3):369–378.
    It is commonly assumed that classical logic is the embodiment of a realist ontology. In “Sets and Semantics”, however, Jonathan Lear challenged this assumption in the particular case of set theory, arguing that even if one is a set-theoretic Platonist, due attention to a special feature of set theory leads to the conclusion that the correct logic for it is intuitionistic. The feature of set theory Lear appeals to is the open-endedness of the concept of set. This article advances reasons (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  21.  35
    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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  22.  29
    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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  23.  20
    Alexander Paseau (2005). On an Application of Categoricity. Proceedings of the Aristotelian Society 105 (3):411–415.
    James Walmsley in “Categoricity and Indefinite Extensibility” argues that a realist about some branch of mathematics X (e.g. arithmetic) apparently cannot use the categoricity of an axiomatisation of X to justify her belief that every sentence of the language of X has a truth-value. My note corrects Walmsley’s formulation of his claim, and shows that his argument for it hinges on the implausible idea that grasping that there is some model of the axioms amounts to grasping that there is a (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography  
  24.  14
    Alexander Paseau (2005). What the Foundationalist Filter Kept Out. Studies in History and Philosophy of Science Part A 36 (1):191-201.
    From title to back cover, a polemic runs through David Corfield's "Towards a Philosophy of Real Mathematics". Corfield repeatedly complains that philosophers of mathematics have ignored the interesting and important mathematical developments of the past seventy years, ‘filtering’ the details of mathematical practice out of philosophical discussion. His aim is to remedy the discipline’s long-sightedness and, by precept and example, to redirect philosophical attention towards current developments in mathematics. This review discusses some strands of Corfield’s philosophy of real mathematics and (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  25. Alexander Paseau (2008). Stanford Encyclopedia of Philosophy.
    No categories
     
    Export citation  
     
    My bibliography