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Penelope Maddy [64]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. (...)
  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". (...)
  4.  59
    Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - 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.
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  5. Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
  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. Does Mathematics Need New Axioms.Solomon Feferman, Harvey M. Friedman, Penelope Maddy & John R. Steel - 1999 - 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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  8.  29
    A Reconstruction of Steel’s Multiverse Project.Penelope Maddy & Toby Meadows - forthcoming - Bulletin of Symbolic Logic:1-79.
    This paper reconstructs Steel’s multiverse project in his ‘Gödel’s program’ (Steel [2014]), first by comparing it to those of Hamkins [2012] and Woodin [2011], then by detailed analysis what’s presented in Steel’s brief text. In particular, we reconstruct his notion of a ‘natural’ theory, describe his multiverse axioms and his translation function, and assess the resulting status of the Continuum Hypothesis. In the end, we reconceptualize the defect that Steel thinks CH might suffer from and isolate what it would take (...)
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  9.  60
    Three Forms of Naturalism.Penelope Maddy - 2005 - In Stewart Shapiro (ed.), 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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  10.  11
    The Logical Must: Wittgenstein on Logic.Penelope Maddy - 2014 - Oup Usa.
    The Logical Must is an examination of Wittgenstein's philosophy of logic, early and late, from an austere naturalistic perspective called "Second Philosophy.".
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  11. What Do Philosophers Do?: Skepticism and the Practice of Philosophy.Penelope Maddy - 2017 - Oxford University Press USA.
    What Do Philosophers Do? takes up the leading arguments for radical skepticism from an everyday point of view. A range of philosophical methods are examined and employed, for a revealing portrait of what philosophers do, and perhaps a quiet suggestion for what they should do, for what they do best.
     
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  12. Believing the Axioms. I.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):481-511.
  13. Perception and Mathematical Intuition.Penelope Maddy - 1980 - Philosophical Review 89 (2):163-196.
  14.  52
    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.
  15. Externalism, Naturalism, Nominalism, and Mathematics.William G. Lycan, Penelope Maddy, Gideon Rosen & Nathan Salmon - 2001 - Philosophical Perspectives 15:17-117.
     
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  16. Believing the Axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
  17. 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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  18. 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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  19. 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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  20.  36
    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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  21. 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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  22. 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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  23. Set Theoretic Naturalism.Penelope Maddy - 1996 - Journal of Symbolic Logic 61 (2):490-514.
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  24.  4
    The Nature of Mathematical Knowledge.Penelope Maddy - 1985 - Philosophy of Science 52 (2):312-314.
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  25.  82
    A Naturalistic Look at Logic.Penelope Maddy - 2002 - Proceedings and Addresses of the American Philosophical Association 76 (2):61 - 90.
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  26.  14
    Mathematics: Form and Function.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):643-645.
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  27.  85
    The Roots of Contemporary Platonism.Penelope Maddy - 1989 - Journal of Symbolic Logic 54 (4):1121-1144.
    Though many working mathematicians embrace a rough and ready form of Platonism, that venerable position has suffered a checkered philosophical career. Indeed the three schools of thought with which most of us began our official philosophizing about mathematics—Intuitionism, Formalism, and Logicism—all stand in fundamental disagreement with Platonism. Nevertheless, various versions of Platonistic thinking survive in contemporary philosophical circles. The aim of this paper is to describe these views, and, as my title suggests, to trace their roots.I'll begin with some preliminary (...)
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  28.  78
    Proper Classes.Penelope Maddy - 1983 - Journal of Symbolic Logic 48 (1):113-139.
  29. 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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  30.  34
    Saunders Mac Lane. 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.
  31.  98
    Mathematical Epistemology: What Is the Question?Penelope Maddy - 1984 - The Monist 67 (1):46-55.
    The tenor of much recent work in the philosophy of mathematics has been dictated by the popular assumption that Platonism is defunct. Some embrace that assumption and look for alternatives, others deny it and attempt to revive Platonism, but either way it is the starting point. The fate of Platonism took center stage with the appearance of Paul Benacerraf’s “Mathematical truth”, but a decade has passed since then, and the philosophical climate has changed. Most important, the quarter from which Platonism (...)
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  32.  58
    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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  33. 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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  34.  53
    Recent Work in Philosophy of Mathematics: Review of P. Maddy, Naturalism in Mathematics; S. Shapiro, Philosophy of Mathematics: Structure and Ontology; M. Resnik, Mathematics as a Science of Patterns.Jamie Tappenden, Penelope Maddy, Stewart Shapiro & Michael Resnik - 2001 - Journal of Philosophy 98 (9):488.
  35.  91
    Ontological Commitment: Between Quine and Duhem.Penelope Maddy - 1996 - Philosophical Perspectives 10:317 - 341.
  36.  54
    The Nature of Mathematical Knowledge. Philip Kitcher.Penelope Maddy - 1985 - Philosophy of Science 52 (2):312-314.
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  37. Mathematical Alchemy.Penelope Maddy - 1986 - British Journal of Philosophy of Science 46 (September):555-575.
  38. 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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  39.  82
    Sets and Numbers.Penelope Maddy - 1981 - Noûs 15 (4):495-511.
  40.  38
    Does V. Equal L?Penelope Maddy - 1993 - Journal of Symbolic Logic 58 (1):15-41.
    Does V = L? Is the Axiom of Constructibility true? Most people with an opinion would answer no. But on what grounds? Despite the near unanimity with which V = L is declared false, the literature reveals no clear consensus on what counts as evidence against the hypothesis and no detailed analysis of why the facts of the sort cited constitute evidence one way or another. Unable to produce a well-developed argument one way or the other, some observers despair, retreating (...)
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  41.  58
    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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  42.  68
    A Problem in the Foundations of Set Theory.Penelope Maddy - 1990 - Journal of Philosophy 87 (11):619-628.
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  43.  67
    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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  44.  24
    Stephen Pollard. Philosophical Introduction to Set Theory. University of Notre Dame Press, Notre Dame, Ind., and London, 1990, Xii + 180 Pp. [REVIEW]Penelope Maddy - 1991 - Journal of Symbolic Logic 56 (2):755-756.
  45.  11
    Naturalizing Mathematical Methodology.Penelope Maddy - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
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  46.  23
    Replies to Coliva, Leite, and Stroud.Penelope Maddy - 2018 - International Journal for the Study of Skepticism 8 (3):231-244.
    _ Source: _Volume 8, Issue 3, pp 231 - 244 Here I cast some doubt on Professor Coliva’s interpretive claim that Moore’s “Proof of an external world” is addressed to idealism, not skepticism, and explore the consequences for our understanding of the final paragraphs of the paper. In response to Professor Leite, I examine the disagreement between us on whether the global skeptical hypotheses can be refuted by ordinary evidence. Finally, after analyzing the logic of the skeptical argumentation, I attempt (...)
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  47.  56
    Is the Importance of Identity Derivative?Penelope Maddy - 1979 - Philosophical Studies 35 (February):151-70.
  48.  9
    Transcendentalism, and Therapy.Penelope Maddy - 2011 - In Joel Smith & Peter Sullivan (eds.), Transcendental Philosophy and Naturalism. Oxford University Press. pp. 120.
  49.  36
    How the Causal Theorist Follows a Rule.Penelope Maddy - 1984 - Midwest Studies in Philosophy 9 (1):457-477.
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  50.  20
    Introductory Overview.Penelope Maddy - 2018 - International Journal for the Study of Skepticism 8 (3):193-197.
    _ Source: _Volume 8, Issue 3, pp 193 - 197 This piece gives an overview of my book, _What Do Philosophers Do? Skepticism and the Practice of Philosophy_.
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