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Philosophia Mathematica 11 (3):305-322 (2003)

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  1. (3 other versions)Elusive Knowledge.David Lewis - 2000 - In Sven Bernecker & Fred I. Dretske (eds.), Knowledge: readings in contemporary epistemology. New York: Oxford University Press.
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  • (1 other version)Solving the Skeptical Problem.Keith DeRose - 1999 - In Keith DeRose & Ted A. Warfield (eds.), Skepticism: a contemporary reader. New York: Oxford University Press.
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  • The Limits of Abstraction.Bob Hale - 2006 - Philosophy and Phenomenological Research 72 (1):223-232.
    Kit Fine’s book is a study of abstraction in a quite precise sense which derives from Frege. In his Grundlagen, Frege contemplates defining the concept of number by means of what has come to be called Hume’s principle—the principle that the number of Fs is the same as the number of Gs just in case there is a one-to-one correspondence between the Fs and the Gs. Frege’s discussion is largely conducted in terms of another, similar but in some respects simpler, (...)
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  • (2 other versions)Review of Crispin Wright: Frege's conception of numbers as objects[REVIEW]Gregory Currie - 1985 - British Journal for the Philosophy of Science 36 (4):475-479.
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  • Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
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  • The Philosophy of Mathematics Today.Fraser MacBride - 2003 - Mind 112 (448):792-799.
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  • The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.
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  • Meaning and Method: Essays in Honor of Hilary Putnam.George Boolos (ed.) - 1990 - Cambridge and New York: Cambridge University Press.
    In this festschrift for the eminent philosopher Hilary Putnam, a team of distinguished philosophers write on a broad range of topics and thus reflect the remarkably fertile and provocative research of Putnam himself. The volume is not merely a celebration of a man, but also a report on the state of philosophy in a number of significant areas. The essays fall naturally into three groups: a central core on the theme of conventionality and content in the philosophy of mind, language, (...)
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  • New Essays on the A Priori.Paul Artin Boghossian & Christopher Peacocke (eds.) - 2000 - Oxford, GB: Oxford University Press.
    A stellar line-up of leading philosophers from around the world offer new treatments of a topic which has long been central to philosophical debate, and in ...
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  • (1 other version)Is Hume's principle analytic?G. Boolos - 1998 - Logic, Logic, and Logic:301--314.
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  • Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
    Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
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  • The limits of abstraction.Kit Fine - 2002 - New York: Oxford University Press. Edited by Matthias Schirn.
    Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits ofion breaks new ground both technically and philosophically.
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  • The reason's proper study: essays towards a neo-Fregean philosophy of mathematics.Crispin Wright & Bob Hale - 2001 - Oxford: Clarendon Press. Edited by Crispin Wright.
    Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...)
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  • 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.
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  • Frege's conception of numbers as objects.Crispin Wright - 1983 - [Aberdeen]: Aberdeen University Press.
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  • Nominalism through de-nominalization.Agustin Rayo & Stephen Yablo - 2001 - Noûs 35 (1):74–92.
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  • The skeptic and the dogmatist.James Pryor - 2000 - Noûs 34 (4):517–549.
    Consider the skeptic about the external world. Let’s straightaway concede to such a skeptic that perception gives us no conclusive or certain knowledge about our surroundings. Our perceptual justification for beliefs about our surroundings is always defeasible—there are always possible improvements in our epistemic state which would no longer support those beliefs. Let’s also concede to the skeptic that it’s metaphysically possible for us to have all the experiences we’re now having while all those experiences are false. Some philosophers dispute (...)
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  • Grundlagen §64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (3):243–261.
    Bob Hale; XII*—Grundlagen §64, Proceedings of the Aristotelian Society, Volume 97, Issue 1, 1 June 1997, Pages 243–262, https://doi.org/10.1111/1467-9264.00015.
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  • (3 other versions)Elusive knowledge.David Lewis - 1996 - Australasian Journal of Philosophy 74 (4):549 – 567.
    David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers.
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  • (1 other version)Implicit definition, analytic truth, and aprior knowledge.Paul Horwich - 1997 - Noûs 31 (4):423-440.
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  • (1 other version)Epistemic operators.Fred I. Dretske - 1970 - Journal of Philosophy 67 (24):1007-1023.
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  • (1 other version)Solving the skeptical problem.Keith DeRose - 1995 - Philosophical Review 104 (1):1-52.
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  • (3 other versions)Elusive Knowledge.David Lewis - 1999 - In Keith DeRose & Ted A. Warfield (eds.), Skepticism: a contemporary reader. New York: Oxford University Press.
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  • Frege's Conception of Numbers as Objects. [REVIEW]John P. Burgess - 1984 - Philosophical Review 93 (4):638-640.
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  • Word and objects.Agustín Rayo - 2002 - Noûs 36 (3):436–464.
    The aim of this essay is to show that the subject-matter of ontology is richer than one might have thought. Our route will be indirect. We will argue that there are circumstances under which standard first-order regimentation is unacceptable, and that more appropriate varieties of regimentation lead to unexpected kinds of ontological commitment.
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  • New V, ZF and Abstraction.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293-321.
    We examine George Boolos's proposed abstraction principle for extensions based on the limitation-of-size conception, New V, from several perspectives. Crispin Wright once suggested that New V could serve as part of a neo-logicist development of real analysis. We show that it fails both of the conservativeness criteria for abstraction principles that Wright proposes. Thus, we support Boolos against Wright. We also show that, when combined with the axioms for Boolos's iterative notion of set, New V yields a system equivalent to (...)
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  • Externalism and armchair knowledge.Martin Davies - 2000 - In Paul Artin Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori. Oxford, GB: Oxford University Press. pp. 384--414.
    [I]f you could know a priori that you are in a given mental state, and your being in that state conceptually or logically implies the existence of external objects, then you could know a priori that the external world exists. Since you obviously _can.
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  • Frege's Conception of Numbers as Objects. [REVIEW]Donald Gillies - 1984 - Mind 93 (372):613-617.
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  • (1 other version)Grundlagen der Arithmetik: Studienausgabe mit dem Text der Centenarausgabe.Gottlob Frege - 1988 - Meiner, F.
    Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.
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  • The problem stated.Paul Boghossian - 2000 - In Paul Artin Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori. Oxford, GB: Oxford University Press. pp. 229.
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  • Realism and Anti-Realism about Mathematics.Hartry Field - 1982 - Philosophical Topics 13 (1):45-69.
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  • Finitude and Hume’s Principle.Richard G. Heck - 1997 - Journal of Philosophical Logic 26 (6):589-617.
    The paper formulates and proves a strengthening of ‘Frege’s Theorem’, which states that axioms for second-order arithmetic are derivable in second-order logic from Hume’s Principle, which itself says that the number of Fs is the same as the number ofGs just in case the Fs and Gs are equinumerous. The improvement consists in restricting this claim to finite concepts, so that nothing is claimed about the circumstances under which infinite concepts have the same number. ‘Finite Hume’s Principle’ also suffices for (...)
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  • ‘Neo-logicist‘ logic is not epistemically innocent.Stewart Shapiro & Alan Weir - 2000 - Philosophia Mathematica 8 (2):160--189.
    The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemically innocent. We conclude that the epistemic innocence of mathematics has not been (...)
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  • (1 other version)Epistemic Operators.Fred Dretske - 1999 - In Keith DeRose & Ted A. Warfield (eds.), Skepticism: a contemporary reader. New York: Oxford University Press.
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  • Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
    Neo-Fregeans argue that substantial mathematics can be derived from a priori abstraction principles, Hume's Principle connecting numerical identities with one:one correspondences being a prominent example. The embarrassment of riches objection is that there is a plurality of consistent but pairwise inconsistent abstraction principles, thus not all consistent abstractions can be true. This paper considers and criticizes various further criteria on acceptable abstractions proposed by Wright settling on another one—stability—as the best bet for neo-Fregeans. However, an analogue of the embarrassment of (...)
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  • Science without Numbers.Michael D. Resnik - 1983 - Noûs 17 (3):514-519.
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  • A Subject with no Object.Zoltan Gendler Szabo, John P. Burgess & Gideon Rosen - 1999 - Philosophical Review 108 (1):106.
    This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...)
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  • On the philosophical significance of Frege's theorem.Crispin Wright - 1997 - In Richard G. Heck (ed.), Language, thought, and logic: essays in honour of Michael Dummett. New York: Oxford University Press. pp. 201--44.
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  • On the consistency of second-order contextual definitions.Richard Heck - 1992 - Noûs 26 (4):491-494.
    One of the earliest discussions of the so-called 'bad company' objection to Neo-Fregeanism, I show that the consistency of an arbitrary second-order 'contextual definition' (nowadays known as an 'abstraction principle' is recursively undecidable. I go on to suggest that an acceptable such principle should satisfy a condition nowadays known as 'stablity'.
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  • Frege's unofficial arithmetic.Agustín Rayo - 2002 - Journal of Symbolic Logic 67 (4):1623-1638.
    I show that any sentence of nth-order (pure or applied) arithmetic can be expressed with no loss of compositionality as a second-order sentence containing no arithmetical vocabulary, and use this result to prove a completeness theorem for applied arithmetic. More specifically, I set forth an enriched second-order language L, a sentence A of L (which is true on the intended interpretation of L), and a compositionally recursive transformation Tr defined on formulas of L, and show that they have the following (...)
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  • (1 other version)Grundlagen der Arithmetik: Studienausgabe mit dem Text der Centenarausgabe.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner Verlag.
    Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.
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  • (1 other version)Grundgesetze Der Arithmetik Vol. (Band 1).Friedrich Ludwig Gottlob Frege - 1893 - Verlag Hermann Pohle.
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  • Crispin Wright, Frege's Conception of Numbers as Objects. [REVIEW]Boguslaw Wolniewicz - 1986 - Studia Logica 45 (3):330-330.
    The book is an attempt at explaining to the nation the ideas of Frege's Grundlagen. It is wordy and trite, a paradigm case of a redundant piece of writing. The reader is advised to steer clear of it.
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  • Implicit definition and the a priori.Bob Hale & Crispin Wright - 2000 - In Paul Artin Boghossian & Christopher Peacocke (eds.), New Essays on the A Priori. Oxford, GB: Oxford University Press. pp. 286--319.
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  • (1 other version)The Philosophy of Mathematics Today.M. Schirn - 2000 - Studia Logica 64 (1):146-146.
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  • The standard of equality of numbers.George Boolos - 1990 - In Meaning and Method: Essays in Honor of Hilary Putnam. Cambridge and New York: Cambridge University Press. pp. 261--77.
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  • (1 other version) Grundlagen §64.Bob Hale - 1997 - Proceedings of the Aristotelian Society 97 (1):243-262.
    Bob Hale; XII*—Grundlagen §64, Proceedings of the Aristotelian Society, Volume 97, Issue 1, 1 June 1997, Pages 243–262, https://doi.org/10.1111/1467-9264.00015.
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  • (2 other versions)The Limits of Abstraction.Kit Fine - 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.
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  • (2 other versions)The Limits of Abstraction.Kit Fine - 2005 - Philosophical Studies 122 (3):367-395.
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  • (1 other version)The Philosophy of Mathematics Today.Matthias Schirn - 2000 - Tijdschrift Voor Filosofie 62 (1):180-181.
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