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Penelope Maddy [68]Penelope Jo Maddy [1]Penelope J. Maddy [1]
  1. Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford University Press.
    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.
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  2. Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...)
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  3. Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - 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". (...)
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  4. Does Mathematics Need New Axioms?Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel - 2000 - Bulletin of Symbolic Logic 6 (4):401-446.
    Part of the ambiguity lies in the various points of view from which this question might be considered. The crudest di erence lies between the point of view of the working mathematician and that of the logician concerned with the foundations of mathematics. Now some of my fellow mathematical logicians might protest this distinction, since they consider themselves to be just more of those \working mathematicians". Certainly, modern logic has established itself as a very respectable branch of mathematics, and there (...)
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  5. Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275-289.
  6. Defending the Axioms: On the Philosophical Foundations of Set Theory.Penelope Maddy - 2011 - Oxford University Press.
    Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of (...)
     
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  7. Externalism, Naturalism, Nominalism, and Mathematics.William G. Lycan, Penelope Maddy, Gideon Rosen & Nathan Salmon - 2001 - Philosophical Perspectives 15:17-117.
     
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  8. Believing the Axioms. I.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):481-511.
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  9.  48
    Second Philosophy.Penelope Maddy - unknown
    Perhaps some of the movie-goers among you have had the experience of sitting through a film with no discernable plot and no significant action, only to be accused by your companions of having missed the point. 'It's not supposed to be dramatic', they tell you, 'it's a Character Study! ' The conventions of this genre seem to require that it centre on an otherwise inconspicuous person who undergoes some familiar life passage or other with terribly subtle, if any, reactions or (...)
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  10.  21
    Three Forms of Naturalism.Penelope Maddy - 2005 - In Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press.
    This chapter compares and contrasts Quine’s naturalism with the versions of two post-Quineans on the nature of science, logic, and mathematics. The role of indispensability in the philosophy of mathematics is treated in detail.
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  11.  4
    Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
  12. Perception and Mathematical Intuition.Penelope Maddy - 1980 - Philosophical Review 89 (2):163-196.
  13.  27
    Naturalism and the A Priori.Penelope Maddy - 2000 - In Paul Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori. Oxford University Press. pp. 92--116.
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  14. Set Theoretic Naturalism.Penelope Maddy - 1996 - Journal of Symbolic Logic 61 (2):490-514.
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  15.  78
    Believing the Axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
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  16. Naturalism and Ontology.Penelope Maddy - 1995 - Philosophia Mathematica 3 (3):248-270.
    Naturalism in philosophy is sometimes thought to imply both scientific realism and a brand of mathematical realism that has methodological consequences for the practice of mathematics. I suggest that naturalism does not yield such a brand of mathematical realism, that naturalism views ontology as irrelevant to mathematical methodology, and that approaching methodological questions from this naturalistic perspective illuminates issues and considerations previously overshadowed by (irrelevant) ontological concerns.
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  17. Naturalism and Common Sense.Penelope Maddy - 2011 - Analytic Philosophy 52 (1):2-34.
    My topic here is metaphilosophy, the question of how philosophy is properly done. For some years now, I've been developing a particularly austere, roughly naturalistic approach to philosophical questions that I call 'second philosophy'. It has seemed to me that one effective way to convey the spirit of second philosophy is to compare and contrast it with other more familiar methods, like transcendental or therapeutic philosophy. Here I hope to pursue this sort of engagement with two other venerable schools of (...)
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  18.  49
    Proper Classes.Penelope Maddy - 1983 - Journal of Symbolic Logic 48 (1):113-139.
  19. Mathematical Existence.Penelope Maddy - 2005 - Bulletin of Symbolic Logic 11 (3):351-376.
    Despite some discomfort with this grandly philosophical topic, I do in fact hope to address a venerable pair of philosophical chestnuts: mathematical truth and existence. My plan is to set out three possible stands on these issues, for an exercise in compare and contrast.' A word of warning, though, to philosophical purists (and perhaps of comfort to more mathematical readers): I will explore these philosophical positions with an eye to their interconnections with some concrete issues of set theoretic method.
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  20.  48
    A Problem in the Foundations of Set Theory.Penelope Maddy - 1990 - Journal of Philosophy 87 (11):619-628.
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  21. Some Naturalistic Reflections on Set Theoretic Method.Penelope J. Maddy - 2001 - Topoi 20 (1):17-27.
    My ultimate goal in this paper is to illuminate, from a naturalistic point of view, the significance of the application of mathematics in the natural sciences for the practice of contemporary set theory.
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  22.  27
    A Second Philosophy of Arithmetic.Penelope Maddy - 2014 - Review of Symbolic Logic 7 (2):1-28.
    This paper outlines a second-philosophical account of arithmetic that places it on a distinctive ground between those of logic and set theory.
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  23.  2
    Set-Theoretic Foundations.Penelope Maddy - 2016 - In Andrés Eduardo Caicedo, James Cummings, Peter Koellner & Paul B. Larson (eds.). American Mathematical Society.
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  24.  84
    Naturalism: Friends and Foes.Penelope Maddy - 2001 - Noûs 35 (s15):37-67.
    The goal of this paper is to sketch a distinctive version of naturalism in the philosophy of science, both by tracing historical antecedents and by addressing contemporary objections.
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  25.  20
    Psychology and the A Priori Sciences.Penelope Maddy - unknown
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  26.  49
    A Naturalistic Look at Logic.Penelope Maddy - 2002 - Proceedings and Addresses of the American Philosophical Association 76 (2):61 - 90.
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  27. The Philosophy of Logic.Penelope Maddy - 2012 - Bulletin of Symbolic Logic 18 (4):481-504.
    This talk surveys a range of positions on the fundamental metaphysical and epistemological questions about elementary logic, for example, as a starting point: what is the subject matter of logic—what makes its truths true? how do we come to know the truths of logic? A taxonomy is approached by beginning from well-known schools of thought in the philosophy of mathematics—Logicism, Intuitionism, Formalism, Realism—and sketching roughly corresponding views in the philosophy of logic. Kant, Mill, Frege, Wittgenstein, Carnap, Ayer, Quine, and Putnam (...)
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  28.  45
    The Roots of Contemporary Platonism.Penelope Maddy - 1989 - Journal of Symbolic Logic 54 (4):1121-1144.
  29.  80
    How Applied Mathematics Became Pure.Penelope Maddy - 2008 - Review of Symbolic Logic 1 (1):16-41.
    My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...)
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  30.  85
    Mathematical Alchemy.Penelope Maddy - 1986 - British Journal of Philosophy of Science 46 (September):555-575.
  31. The Legacy of Mathematical Truth.Penelope Maddy - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 60--72.
     
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  32.  54
    Mathematical Epistemology.Penelope Maddy - 1984 - The Monist 67 (1):46-55.
  33.  71
    Ontological Commitment: Between Quine and Duhem.Penelope Maddy - 1996 - Philosophical Perspectives 10:317 - 341.
  34.  44
    Logic and the Discursive Intellect.Penelope Maddy - 1999 - Notre Dame Journal of Formal Logic 40 (1):94-115.
    The effort to fit simple logical truths–like `if it's either red or green and it's not red, then it must be green'–into Kant's account of knowledge turns up a position more subtle and intriguing than might be expected at first glance.
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  35.  2
    Realism in Mathematics.Penelope Maddy - 1990 - Journal of Philosophy 89 (6):321-326.
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  36.  3
    Transcendentalism, and Therapy.Penelope Maddy - 2011 - In Joel Smith & Peter Sullivan (eds.), Transcendental Philosophy and Naturalism. Oxford University Press. pp. 120.
  37.  49
    Philosophy of Mathematics: Prospects for the 1990s.Penelope Maddy - 1991 - Synthese 88 (2):155 - 164.
    For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers of (...)
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  38.  64
    Sets and Numbers.Penelope Maddy - 1981 - Noûs 15 (4):495-511.
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  39.  73
    Skepticism, Naturalism, and Therapy.Penelope Maddy - unknown
    Our goal in this course is to investigate radical skepticism about the external world, primarily to compare and contrast various naturalist and therapeutic reactions to it. We’ll largely side-step attempts to refute the skeptic and focus instead on naturalistic and therapeutic ways of reacting without refuting (though the boundary between these isn’t always sharp). The hope is that this exercise will help differentiate various strains of naturalism and clarify their interrelations with a range of therapeutic approaches.
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  40. The Reality of Numbers: A Physicalist's Philosophy of Mathematics.John Bigelow, Penelope Maddy, Yvette Solomon & Jean Paul van Bendegem - 1994 - British Journal for the Philosophy of Science 45 (1):305-340.
     
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  41.  6
    Realism in Mathematics.Joan Weiner & Penelope Maddy - 1993 - Philosophical Review 102 (2):281.
  42.  38
    Is the Importance of Identity Derivative?Penelope Maddy - 1979 - Philosophical Studies 35 (February):151-70.
  43.  12
    Mathematical Realism.Penelope Maddy - 1988 - Midwest Studies in Philosophy 12 (1):275-285.
  44.  47
    Romanell Lecture.Penelope Maddy - unknown
    There’s a tendency to suppose that a naturalist is automatically, by virtue of her naturalism, committed to some particular view of logic. These days, for example, the classical Quinean picture is sometimes taken to be the naturalistic standard: logic lies at the center of the web of belief; remote from sense experience, but widely confirmed by its role in all our successful theorizing; a posteriori like the rest, but also the most resistant to change, given the principle of minimum mutilation; (...)
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  45.  3
    Recent Work in Philosophy of MathematicsNaturalism in MathematicsPhilosophy of Mathematics: Structure and OntologyMathematics as a Science of Patterns.Jamie Tappenden, Penelope Maddy, Stewart Shapiro & Michael Resnik - 2001 - Journal of Philosophy 98 (9):488.
  46.  7
    Naturalizing Mathematical Methodology.Penelope Maddy - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
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  47. Charles Parsons, Mathematics in Philosophy Reviewed By.Penelope Maddy - 1985 - Philosophy in Review 5 (3):125-126.
     
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  48.  24
    How the Causal Theorist Follows a Rule.Penelope Maddy - 1984 - Midwest Studies in Philosophy 9 (1):457-477.
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  49.  22
    Does V. Equal L?Penelope Maddy - 1993 - Journal of Symbolic Logic 58 (1):15-41.
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  50. Lane Saunders Mac. Mathematics: Form and Function. Springer-Verlag, New York, Berlin, Heidelberg, and Tokyo, 1986, Xi + 476 Pp. [REVIEW]Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):643-645.
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