This category needs an editor. We encourage you to help if you are qualified.
Volunteer, or read more about what this involves.
Related

Contents
64 found
Order:
1 — 50 / 64
  1. Thomistic Foundations for Moderate Realism about Mathematical Objects.Ryan Miller - forthcoming - In Proceedings of the Eleventh International Thomistic Congress. Rome: Urbaniana University Press.
    Contemporary philosophers of mathematics are deadlocked between two alternative ontologies for numbers: Platonism and nominalism. According to contemporary mathematical Platonism, numbers are real abstract objects, i.e. particulars which are nonetheless “wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal.” While this view does justice to intuitions about numbers and mathematical semantics, it leaves unclear how we could ever learn anything by mathematical inquiry. Mathematical nominalism, by contrast, holds that numbers do not exist extra-mentally, which raises difficulties about how mathematical statements could be (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  2. On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundation of Number Concepts.Markus Pantsar - 2023 - Theoria 89 (3):298-313.
    Linnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter-argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  3. Mathematics as a science of non-abstract reality: Aristotelian realist philosophies of mathematics.James Franklin - 2022 - Foundations of Science 27 (2):327-344.
    There is a wide range of realist but non-Platonist philosophies of mathematics—naturalist or Aristotelian realisms. Held by Aristotle and Mill, they played little part in twentieth century philosophy of mathematics but have been revived recently. They assimilate mathematics to the rest of science. They hold that mathematics is the science of X, where X is some observable feature of the (physical or other non-abstract) world. Choices for X include quantity, structure, pattern, complexity, relations. The article lays out and compares these (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  4. Quine on naturalism, nominalism, and philosophy’s place within science.James Andrew Smith - 2021 - Synthese 198 (2):1549-1567.
    W.V. Quine is a well-known proponent of naturalism, the view on which reality is described only in science. He is also well-known for arguing that our current scientific theories commit us to the existence of abstract objects. It is tempting to believe that the naturalistic philosopher should think scientists outside of philosophy are in the best position to assess the merits of revising our current commitment to abstract objects. But Quine rejects this deferential view. On the reading of Quine’s philosophical (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5. Quine’s Intuition: Why Quine’s Early Nominalism is Naturalistic.James Andrew Smith - 2020 - Erkenntnis 85 (5):1199-1218.
    According to a growing consensus in the secondary literature on Quine, the judgment Quine makes in favor of the nominalism outlined in “Steps Toward a Constructive Nominalism” is in tension with the naturalism he later adopts. In this paper, I show the consensus view is mistaken by showing that Quine’s judgment is rooted in a naturalistic standard of clarity. Moreover, I argue that Quine late in his career is committed to accepting one plausible reading of his judgment in 1947. In (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  6. Philosophy’s Loss of Logic to Mathematics: An Inadequately Understood Take-Over.Woosuk Park - 2018 - Cham, Switzerland: Springer Verlag.
    This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  7. Dimension‐Based Statistical Learning Affects Both Speech Perception and Production.Matthew Lehet & Lori L. Holt - 2017 - Cognitive Science 41 (S4):885-912.
    Multiple acoustic dimensions signal speech categories. However, dimensions vary in their informativeness; some are more diagnostic of category membership than others. Speech categorization reflects these dimensional regularities such that diagnostic dimensions carry more “perceptual weight” and more effectively signal category membership to native listeners. Yet perceptual weights are malleable. When short-term experience deviates from long-term language norms, such as in a foreign accent, the perceptual weight of acoustic dimensions in signaling speech category membership rapidly adjusts. The present study investigated whether (...)
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  8. Is Realism about Consciousness Compatible with a Scientifically Respectable Worldview?P. Goff - 2016 - Journal of Consciousness Studies 23 (11-12):83-97.
    Frankish's argument for illusionism -- the view that there are no real instances of phenomenal consciousness -- depends on the claim that phenomenal consciousness is an 'anomalous phenomenon', at odds with our scientific picture of the world. I distinguish two senses in which a phenomenon might be 'anomalous': its reality is inconsistent with what science gives us reason to believe, its reality adds to what science gives us reason to believe. I then argue that phenomenal consciousness is not anomalous in (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  9. Restrictiveness relative to notions of interpretation.Luca Incurvati & Benedikt Löwe - 2016 - Review of Symbolic Logic 9 (2): 238-250.
    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 issues raised by Hamkins. Our work brings (...)
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  10. The Logical Must: Wittgenstein on LogicBy Penelope Maddy.David G. Stern - 2016 - Analysis 76 (3):391-393.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  11. An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure by James Franklin. [REVIEW]Jude P. Dougherty - 2015 - Review of Metaphysics 68 (3):658-660.
  12. When Do Some Things Form a Set?Simon Hewitt - 2015 - Philosophia Mathematica 23 (3):311-337.
    This paper raises the question under what circumstances a plurality forms a set, parallel to the Special Composition Question for mereology. The range of answers that have been proposed in the literature are surveyed and criticised. I argue that there is good reason to reject both the view that pluralities never form sets and the view that pluralities always form sets. Instead, we need to affirm restricted set formation. Casting doubt on the availability of any informative principle which will settle (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  13. An Aristotelian Realist Philosophy of Mathematics: Mathematics as the science of quantity and structure.James Franklin - 2014 - London and New York: Palgrave MacMillan.
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   35 citations  
  14. Motivating Maddy’s Naturalist to Adopt Pluralism.Michèle Friend - 2014 - In Pluralism in Mathematics: A New Position in Philosophy of Mathematics. Springer Verlag.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  15. Penelope Maddy. Defending the Axioms: On the Philosophical Foundations of Set Theory. Oxford: Oxford University Press, 2011. ISBN 978-0-19-959618-8 (hbk); 978-0-19-967148-9 (pbk). Pp. x + 150. [REVIEW]C. McLarty - 2013 - Philosophia Mathematica 21 (3):385-392.
  16. Review of P. Maddy, Defending the Axioms: on the Philosophical Foundations of Set Theory[REVIEW]Eduardo Castro - 2012 - Teorema: International Journal of Philosophy 31 (1):147-150.
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  17. On Some Considerations of Mathematical Physics: May we Identify Clifford Algebra as a Common Algebraic Structure for Classical Diffusion and Schrödinger Equations?Elio Conte - 2012 - Advanced Studies in Theoretical Physics 6 (26):1289-1307.
    We start from previous studies of G.N. Ord and A.S. Deakin showing that both the classical diffusion equation and Schrödinger equation of quantum mechanics have a common stump. Such result is obtained in rigorous terms since it is demonstrated that both diffusion and Schrödinger equations are manifestation of the same mathematical axiomatic set of the Clifford algebra. By using both such ( ) i A S and the i,±1 N algebra, it is evidenced, however, that possibly the two basic equations (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark  
  18. Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory[REVIEW]Luca Incurvati & Peter Smith - 2012 - Mind 121 (481):195-200.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  19. Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory[REVIEW]Øystein Linnebo - 2012 - Philosophy 87 (1):133-137.
  20. Review of P. Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory[REVIEW]S. Vineberg - 2012 - Analysis 72 (3):635-637.
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  21. Penelope Maddy , Defending the Axioms: On the Philosophical Foundations of Set Theory . Reviewed by.Manuel Bremer - 2011 - Philosophy in Review 31 (4):292-294.
    Remove from this list   Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  22. Does mathematics have a life of its own?: Review of P. Maddy, Second Philosophy: A Naturalistic Method[REVIEW]James Robert Brown - 2011 - Metascience 20 (3):487-493.
  23. Deferentialism.Chris Daly & David Liggins - 2011 - Philosophical Studies 156 (3):321-337.
    There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   17 citations  
  24. Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  25. Penelope maddyová medzi realizmom a naturalizmom.Ladislav Kvasz - 2010 - Filozofia 65 (6).
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   2 citations  
  26. Penelope MaddySecond Philosophy: A Naturalistic Method. [REVIEW]Harvey Siegel - 2010 - British Journal for the Philosophy of Science 61 (4):897-903.
    (No abstract is available for this citation).
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  27. Aristotelian realism.James Franklin - 2009 - In A. Irvine (ed.), The Philosophy of Mathematics (Handbook of the Philosophy of Science series). North-Holland Elsevier.
    Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity, or numerosity, or symmetry. Let us start with an example, as Aristotelians always prefer, an example that introduces the essential themes of the Aristotelian view of mathematics. A typical mathematical truth is (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   14 citations  
  28. The Philosophy of Mathematics (Handbook of the Philosophy of Science series).A. Irvine (ed.) - 2009 - North-Holland Elsevier.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  29. On Naturalizing the Epistemology of Mathematics.Jeffrey W. Roland - 2009 - Pacific Philosophical Quarterly 90 (1):63-97.
    In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  30. A scientific enterprise?: A critical study of P. Maddy, Second Philosophy: A Naturalistic Method[REVIEW]Stewart Shapiro & Patrick Reeder - 2009 - Philosophia Mathematica 17 (2):247-271.
    For almost twenty years, Penelope Maddy has been one of the most consistent expositors and advocates of naturalism in philosophy, with a special focus on the philosophy of mathematics, set theory in particular. Over that period, however, the term ‘naturalism’ has come to mean many things. Although some take it to be a rejection of the possibility of a priori knowledge, there are philosophers calling themselves ‘naturalists’ who willingly embrace and practice an a priori methodology, not a whole lot different (...)
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  31. Review of P, Maddy, Second Philosophy[REVIEW]B. Stroud - 2009 - Mind 118 (470):500-503.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  32. Second Philosophy: a Naturalistic Method. [REVIEW]Eduardo Castro - 2008 - Disputatio 2 (24):349-355.
    Remove from this list   Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  33. Too naturalist and not naturalist enough: Reply to Horsten.Luca Incurvati - 2008 - Erkenntnis 69 (2):261 - 274.
    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 (...)
    Remove from this list   Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  34. Penelope Maddy, Second Philosophy: A naturalistic method.Rafał Krzemianowski & Paweł Kawalec - 2008 - Roczniki Filozoficzne:528-534.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  35. Naturalism in the Philosophy of Mathematics.Alexander Paseau - 2008 - 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 (...)
    Remove from this list   Direct download  
     
    Export citation  
     
    Bookmark   12 citations  
  36. Kitcher, mathematics, and naturalism.Jeffrey W. Roland - 2008 - Australasian Journal of Philosophy 86 (3):481 – 497.
    This paper argues that Philip Kitcher's epistemology of mathematics, codified in his Naturalistic Constructivism, is not naturalistic on Kitcher's own conception of naturalism. Kitcher's conception of naturalism is committed to (i) explaining the correctness of belief-regulating norms and (ii) a realist notion of truth. Naturalistic Constructivism is unable to simultaneously meet both of these commitments.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  37. Penelope Maddy, Second Philosophy: A Naturalistic Method.J. Van Evra - 2008 - Philosophy in Review 28 (2):131.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  38. Penelope Maddy, Second Philosophy: A Naturalistic Method Reviewed by.James Van Evra - 2008 - Philosophy in Review 28 (2):131-133.
    Remove from this list  
     
    Export citation  
     
    Bookmark  
  39. Anti-nominalism reconsidered.David Liggins - 2007 - Philosophical Quarterly 57 (226):104–111.
    Many philosophers of mathematics are attracted by nominalism – the doctrine that there are no sets, numbers, functions, or other mathematical objects. John Burgess and Gideon Rosen have put forward an intriguing argument against nominalism, based on the thought that philosophy cannot overrule internal mathematical and scientific standards of acceptability. I argue that Burgess and Rosen’s argument fails because it relies on a mistaken view of what the standards of mathematics require.
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  40. Second philosophy: a naturalistic method.Penelope Maddy - 2007 - New York: Oxford University Press.
    Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy". Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second Philosopher". (...)
    Remove from this list   Direct download (4 more)  
     
    Export citation  
     
    Bookmark   130 citations  
  41. Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
    Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.
    Remove from this list   Direct download (6 more)  
     
    Export citation  
     
    Bookmark   129 citations  
  42. Naturalism, Truth and Beauty in Mathematics.Matthew E. Moore - 2007 - Philosophia Mathematica 15 (2):141-165.
    Can a scientific naturalist be a mathematical realist? I review some arguments, derived largely from the writings of Penelope Maddy, for a negative answer. The rejoinder from the realist side is that the irrealist cannot explain, as well as the realist can, why a naturalist should grant the mathematician the degree of methodological autonomy that the irrealist's own arguments require. Thus a naturalist, as such, has at least as much reason to embrace mathematical realism as to embrace irrealism.
    Remove from this list   Direct download (10 more)  
     
    Export citation  
     
    Bookmark  
  43. Maddy and Mathematics: Naturalism or Not.Jeffrey W. Roland - 2007 - British Journal for the Philosophy of Science 58 (3):423-450.
    Penelope Maddy advances a purportedly naturalistic account of mathematical methodology which might be taken to answer the question 'What justifies axioms of set theory?' I argue that her account fails both to adequately answer this question and to be naturalistic. Further, the way in which it fails to answer the question deprives it of an analog to one of the chief attractions of naturalism. Naturalism is attractive to naturalists and nonnaturalists alike because it explains the reliability of scientific practice. Maddy's (...)
    Remove from this list   Direct download (7 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  44. Mathematical fictionalism – no comedy of errors.Chris Daly - 2006 - Analysis 66 (3):208–216.
  45. Is there a good epistemological argument against platonism?David Liggins - 2006 - Analysis 66 (2):135–141.
    Platonism in the philosophy of mathematics is the doctrine that there are mathematical objects such as numbers. John Burgess and Gideon Rosen have argued that that there is no good epistemological argument against platonism. They propose a dilemma, claiming that epistemological arguments against platonism either rely on a dubious epistemology, or resemble a dubious sceptical argument concerning perceptual knowledge. Against Burgess and Rosen, I show that an epistemological anti- platonist argument proposed by Hartry Field avoids both horns of their dilemma.
    Remove from this list   Direct download (8 more)  
     
    Export citation  
     
    Bookmark   24 citations  
  46. What is neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
    In this paper, we investigate (1) what can be salvaged from the original project of "logicism" and (2) what is the best that can be done if we lower our sights a bit. Logicism is the view that "mathematics is reducible to logic alone", and there are a variety of reasons why it was a non-starter. We consider the various ways of weakening this claim so as to produce a "neologicism". Three ways are discussed: (1) expand the conception of logic (...)
    Remove from this list   Direct download (12 more)  
     
    Export citation  
     
    Bookmark   23 citations  
  47. Die Vertreibung aus dem Platonischen Paradies.Marcus Rossberg - 2006 - Erwägen – Wissen – Ethik 17 (Naturalism in Mathematics):387–389.
  48. Naturalism in mathematics and the authority of philosophy.Alexander Paseau - 2005 - 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 (...)
    Remove from this list   Direct download (10 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  49. Success by default?Augustín Rayo - 2003 - Philosophia Mathematica 11 (3):305-322.
    I argue that Neo-Fregean accounts of arithmetical language and arithmetical knowledge tacitly rely on a thesis I call [Success by Default]—the thesis that, in the absence of reasons to the contrary, we are justified in thinking that certain stipulations are successful. Since Neo-Fregeans have yet to supply an adequate defense of [Success by Default], I conclude that there is an important gap in Neo-Fregean accounts of arithmetical language and knowledge. I end the paper by offering a naturalistic remedy.
    Remove from this list   Direct download (10 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  50. Naturalism in Mathematics. [REVIEW]Adam Rieger - 2003 - Philosophical Review 112 (3):425-427.
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
    Remove from this list   Direct download (9 more)  
     
    Export citation  
     
    Bookmark  
1 — 50 / 64