76 found
Order:
Disambiguations
Penelope Maddy [75]Penelope J. Maddy [2]Penelope Jo Maddy [1]
  1. Realism in mathematics.Penelope Maddy - 1990 - New York: 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. (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   266 citations  
  2. Naturalism in mathematics.Penelope Maddy - 1997 - New York: 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.
  3. 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". (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   134 citations  
  4. 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.
  5.  44
    Defending the Axioms: On the Philosophical Foundations of Set Theory.Penelope Maddy - 2011 - Oxford, England: 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   46 citations  
  6. Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
  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 (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   79 citations  
  8.  36
    The Logical Must: Wittgenstein on Logic.Penelope Maddy - 2014 - Oxford, England: 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.".
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  9.  29
    A Plea for Natural Philosophy: And Other Essays.Penelope Maddy - 2022 - New York, NY: Oxford University Press.
    A plea for natural philosophy --On the question of realism --Hume and Reid --Moore's hands --Wittgenstein on hinges --A note on truth and reference --The philosophy of logic --A Second Philosophy of logic --Psychology and the a priori sciences --Do numbers exist? --Enhanced if-thenism.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  10. Believing the axioms. I.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):481-511.
  11. Perception and mathematical intuition.Penelope Maddy - 1980 - Philosophical Review 89 (2):163-196.
  12. Nominalism, Naturalism, Epistemic Relativism.William G. Lycan, Penelope Maddy, Gideon Rosen & Nathan Salmon - 2001 - Philosophical Perspectives 15:69–91.
  13. What Do We Want a Foundation to Do?Penelope Maddy - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 293-311.
    It’s often said that set theory provides a foundation for classical mathematics because every classical mathematical object can be modeled as a set and every classical mathematical theorem can be proved from the axioms of set theory. This is obviously a remarkable mathematical fact, but it isn’t obvious what makes it ‘foundational’. This paper begins with a taxonomy of the jobs set theory does that might reasonably be regarded as foundational. It then moves on to category-theoretic and univalent foundations, exploring (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   11 citations  
  14. Believing the axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
  15.  24
    What Do Philosophers Do? Skepticism and the Practice of Philosophy.Penelope Maddy - 2017 - New York, US: 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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  16. Three Forms of Naturalism.Penelope Maddy - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: 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.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   39 citations  
  17.  84
    Naturalism and the A Priori.Penelope Maddy - 2000 - In Paul Artin Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori. Oxford, GB: Oxford University Press. pp. 92--116.
  18. A Naturalistic Look at Logic.Penelope Maddy - 2002 - Proceedings and Addresses of the American Philosophical Association 76 (2):61 - 90.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   33 citations  
  19.  95
    Set-theoretic Foundations.Penelope Maddy - 2016 - In Andrés Eduardo Caicedo, James Cummings, Peter Koellner & Paul B. Larson (eds.), Foundations of Mathematics. American Mathematical Society.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  20. Proper classes.Penelope Maddy - 1983 - Journal of Symbolic Logic 48 (1):113-139.
  21. 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 (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   14 citations  
  22.  25
    The Nature of Mathematical Knowledge.Penelope Maddy - 1985 - Philosophy of Science 52 (2):312-314.
  23. 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 (...)
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  24. 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.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   21 citations  
  25. 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.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  26. Set theoretic naturalism.Penelope Maddy - 1996 - Journal of Symbolic Logic 61 (2):490-514.
    My aim in this paper is to propose what seems to me a distinctive approach to set theoretic methodology. By ‘methodology’ I mean the study of the actual methods used by practitioners, the study of how these methods might be justified or reformed or extended. So, for example, when the intuitionist's philosophical analysis recommends a wholesale revision of the methods of proof used in classical mathematics, this is a piece of reformist methodology. In contrast with the intuitionist, I will focus (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  27. A reconstruction of steel’s multiverse project.Penelope Maddy & Toby Meadows - 2020 - Bulletin of Symbolic Logic 26 (2):118-169.
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  28.  26
    Mathematics: Form and Function.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (2):643-645.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   19 citations  
  29. What Do We Want a Foundation to Do?Penelope Maddy - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag.
    No categories
     
    Export citation  
     
    Bookmark   4 citations  
  30. 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.
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  31.  76
    A Second Philosophy of Arithmetic.Penelope Maddy - 2014 - Review of Symbolic Logic 7 (2):222-249.
    This paper outlines a second-philosophical account of arithmetic that places it on a distinctive ground between those of logic and set theory.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  32.  63
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  33. Physicalistic Platonism.Penelope Maddy - 1990 - In A. D. Irvine (ed.), Physicalism in Mathematics. Dordrecht: Kluwer. pp. 259-290.
  34.  85
    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.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  35. Sets and numbers.Penelope Maddy - 1981 - Noûs 15 (4):495-511.
  36.  61
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  37.  57
    How the Causal Theorist Follows a Rule.Penelope Maddy - 1984 - Midwest Studies in Philosophy 9 (1):457-477.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  38. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  39. Mathematical alchemy.Penelope Maddy - 1986 - British Journal of Philosophy of Science 46 (September):555-575.
  40.  58
    Mathematical Epistemology.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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  41.  85
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  42. 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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  43.  19
    Mathematical Alchemy.Penelope Maddy - 1986 - British Journal for the Philosophy of Science 37 (3):279-314.
  44.  24
    Naturalizing mathematical methodology.Penelope Maddy - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   5 citations  
  45. Ontological commitment: Between Quine and Duhem.Penelope Maddy - 1996 - Philosophical Perspectives 10:317 - 341.
  46.  41
    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.
  47.  31
    Mathematical Realism.Penelope Maddy - 1988 - Midwest Studies in Philosophy 12 (1):275-285.
  48.  68
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  49.  44
    Psychology and the A Priori Sciences.Penelope Maddy - 2018 - In Naturalizing Logico-Mathematical Knowledge Approaches from Philosophy, Psychology and Cognitive Science. London: Routldge. pp. 15-29.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  50.  65
    Is the importance of identity derivative?Penelope Maddy - 1979 - Philosophical Studies 35 (February):151-70.
1 — 50 / 76