Switch to: Citations

Add references

You must login to add references.
  1. The Foundations of Arithmetic.Michael J. Loux - 1970 - New Scholasticism 44 (3):470-471.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   559 citations  
  • The Possible and the actual: readings in the metaphysics of modality.Michael J. Loux (ed.) - 1979 - Ithaca, N.Y.: Cornell University Press.
    Preface In these days, an anthology on the topic of possible worlds hardly needs justification. No issue has given rise to as much literature in the past ...
    Download  
     
    Export citation  
     
    Bookmark   93 citations  
  • The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
    This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
    Download  
     
    Export citation  
     
    Bookmark   277 citations  
  • Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
    In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...)
    Download  
     
    Export citation  
     
    Bookmark   206 citations  
  • Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
    This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...)
    Download  
     
    Export citation  
     
    Bookmark   244 citations  
  • Frege.Michael Dummett - 1981 - Cambridge: Harvard University Press.
    In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...
    Download  
     
    Export citation  
     
    Bookmark   235 citations  
  • The reality of numbers: a physicalist's philosophy of mathematics.John Bigelow - 1988 - New York: Oxford University Press.
    Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.
    Download  
     
    Export citation  
     
    Bookmark   200 citations  
  • Quality and concept.George Bealer - 1982 - New York: Oxford University Press.
    This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.
    Download  
     
    Export citation  
     
    Bookmark   206 citations  
  • Kit Fine: First-Order Modal Theories I--Sets.First-Order Modal Theories.First-Order Modal Theories III--Facts.W. Kroon - 1988 - Journal of Symbolic Logic 53 (4):1262-1269.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • A Difficulty with the Frege-Russell Definition of Number.Robert Hambourger - 1977 - Journal of Philosophy 74 (7):409-414.
    An objection is offered to the Frege-Russell definition, which identifies the number 1 with the set of all unit sets. It is argued here that the identity conditions for sets require that if any member of a set had not existed, the set itself would not have. Therefore, had any object whatever not existed, the unit set containing it would not have either, and thus the set with which the definition identifies 1 would not have. But then, 1 either would (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Inquiry.Robert Stalnaker - 1984 - Cambridge University Press.
    The abstract structure of inquiry - the process of acquiring and changing beliefs about the world - is the focus of this book which takes the position that the "pragmatic" rather than the "linguistic" approach better solves the philosophical problems about the nature of mental representation, and better accounts for the phenomena of thought and speech. It discusses propositions and propositional attitudes (the cluster of activities that constitute inquiry) in general and takes up the way beliefs change in response to (...)
    Download  
     
    Export citation  
     
    Bookmark   391 citations  
  • Belief and the basis of meaning.Donald Davidson - 1974 - Synthese 27 (July-August):309-323.
    A theory of radical interpretation gives the meanings of all sentences of a language, and can be verified by evidence available to someone who does not understand the language. Such evidence cannot include detailed information concerning the beliefs and intentions of speakers, and therefore the theory must simultaneously interpret the utterances of speakers and specify (some of) his beliefs. Analogies and connections with decision theory suggest the kind of theory that will serve for radical interpretation, and how permissible evidence can (...)
    Download  
     
    Export citation  
     
    Bookmark   176 citations  
  • Platonism and Anti-Platonism in Mathematics. [REVIEW]Matthew McGrath - 2001 - Philosophy and Phenomenological Research 63 (1):239-242.
    Mark Balaguer has written a provocative and original book. The book is as ambitious as a work of philosophy of mathematics could be. It defends both of the dominant views concerning the ontology of mathematics, Platonism and Anti-Platonism, and then closes with an argument that there is no fact of the matter which is right.
    Download  
     
    Export citation  
     
    Bookmark   84 citations  
  • (2 other versions)Inquiry.Robert C. Stalnaker - 1984 - Linguistics and Philosophy 11 (4):515-519.
    Download  
     
    Export citation  
     
    Bookmark   543 citations  
  • (1 other version)Foundational aspects of Theories of Measurement.Dana Scott & Patrick Suppes - 1968 - Journal of Symbolic Logic 33 (2):287-288.
    Download  
     
    Export citation  
     
    Bookmark   23 citations  
  • Mathematics in Philosophy: Selected Essays.Charles Parsons - 1985 - British Journal for the Philosophy of Science 36 (4):437-457.
    Download  
     
    Export citation  
     
    Bookmark   36 citations  
  • The (Metaphysical) Foundations of Arithmetic?Thomas Donaldson - 2017 - Noûs 51 (4):775-801.
    Gideon Rosen and Robert Schwartzkopff have independently suggested (variants of) the following claim, which is a varian of Hume's Principle: -/- When the number of Fs is identical to the number of Gs, this fact is grounded by the fact that there is a one-to-one correspondence between the Fs and Gs. -/- My paper is a detailed critique of the proposal. I don't find any decisive refutation of the proposal. At the same time, it has some consequences which many will (...)
    Download  
     
    Export citation  
     
    Bookmark   38 citations  
  • (1 other version)The worlds of possibility: modal realism and the semantics of modal logic.Charles S. Chihara - 1998 - New York: Oxford University Press.
    A powerful challenge to some highly influential theories, this book offers a thorough critical exposition of modal realism, the philosophical doctrine that many possible worlds exist of which our own universe is just one. Chihara challenges this claim and offers a new argument for modality without worlds.
    Download  
     
    Export citation  
     
    Bookmark   52 citations  
  • The nature of mathematical knowledge.Philip Kitcher - 1983 - Oxford: Oxford University Press.
    This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...
    Download  
     
    Export citation  
     
    Bookmark   278 citations  
  • Mathematics in philosophy: selected essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell University Press.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
    Download  
     
    Export citation  
     
    Bookmark   52 citations  
  • Mathematics and reality.Stewart Shapiro - 1983 - Philosophy of Science 50 (4):523-548.
    The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...)
    Download  
     
    Export citation  
     
    Bookmark   54 citations  
  • (1 other version)Foundational aspects of theories of measurement.Dana Scott & Patrick Suppes - 1958 - Journal of Symbolic Logic 23 (2):113-128.
    Download  
     
    Export citation  
     
    Bookmark   68 citations  
  • Structuralism and the concept of set.Charles Parsons - 1997 - In Evandro Agazzi & György Darvas (eds.), Philosophy of Mathematics Today. Kluwer Academic Publishers. pp. 171--194.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • (1 other version)Grundgesetze Der Arithmetik Vol. (Band 2).Friedrich Ludwig Gottlob Frege - 1903 - Jena: Verlag Hermann Pohle.
    Download  
     
    Export citation  
     
    Bookmark   34 citations  
  • Constructibility and mathematical existence.Charles S. Chihara - 1990 - New York: Oxford University Press.
    This book is concerned with `the problem of existence in mathematics'. It develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. It explores the philosophical implications of such an approach through an examination of the writings of Field, Burgess, Maddy, Kitcher, and others.
    Download  
     
    Export citation  
     
    Bookmark   106 citations  
  • (1 other version)Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
    Download  
     
    Export citation  
     
    Bookmark   223 citations  
  • (1 other version)Frege: Philosophy of Mathematics. [REVIEW]William Demopoulos - 1993 - Canadian Journal of Philosophy 23 (3):477-497.
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  • (1 other version)Constructibility and Mathematical Existence.M. D. Potter - 1991 - Philosophical Quarterly 41 (164):345-348.
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  • III.—External and Internal Relations.G. E. Moore - 1920 - Proceedings of the Aristotelian Society 20 (1):40-62.
    Download  
     
    Export citation  
     
    Bookmark   48 citations  
  • Infestation or pest control: the introduction of group theory into quantum mechanics.Otávio Bueno & Steven French - 1999 - Manuscrito 22 (2):37-68.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • The Applicability of Mathematics as a Philosophical Problem.Mark Steiner - 1998 - Harvard University Press.
    This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics ...
    Download  
     
    Export citation  
     
    Bookmark   110 citations  
  • Frege's philosophy of mathematics.William Demopoulos (ed.) - 1995 - Cambridge: Harvard University Press.
    Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work on Frege's (...)
    Download  
     
    Export citation  
     
    Bookmark   43 citations  
  • (1 other version)Frege: Philosophy of Mathematics.Alex Oliver - 1994 - Inquiry: An Interdisciplinary Journal of Philosophy 37 (3):349.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic.Charles Chihara - 2001 - Philosophical Quarterly 51 (202):108-110.
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • (1 other version)Quality and Concept. [REVIEW]Joachim Buhl - 1985 - Erkenntnis 23 (2):203-212.
    Download  
     
    Export citation  
     
    Bookmark   88 citations  
  • Science without Numbers.Michael D. Resnik - 1983 - Noûs 17 (3):514-519.
    Download  
     
    Export citation  
     
    Bookmark   164 citations  
  • Grundgesetze der Arithmetik. Section 56ff.Gottlob Frege - 1952 - In Peter Geach & Max Black (eds.), Translations From the Philosophical Writings of Gottlob Frege. Philosophical Library.
    Download  
     
    Export citation  
     
    Bookmark   64 citations  
  • The Applicability of Mathematics as a Philosophical Problem.Mark Steiner - 2000 - Mind 109 (434):390-394.
    Download  
     
    Export citation  
     
    Bookmark   119 citations  
  • Properties.Chris Swoyer - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
    Download  
     
    Export citation  
     
    Bookmark   51 citations  
  • (2 other versions)First-order modal theories I--sets.Kit Fine - 1981 - Noûs 15 (2):177-205.
    Download  
     
    Export citation  
     
    Bookmark   32 citations  
  • Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Bulletin of Symbolic Logic 8 (4):516-518.
    This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism or anti-platonism is true.
    Download  
     
    Export citation  
     
    Bookmark   225 citations  
  • (1 other version)Grundgesetze Der Arithmetik Vol. (Band 1).Friedrich Ludwig Gottlob Frege - 1893 - Verlag Hermann Pohle.
    Download  
     
    Export citation  
     
    Bookmark   45 citations  
  • Properties and Predicates.D. H. Mellor - 1997 - In David Hugh Mellor & Alex Oliver (eds.), Properties. New York: Oxford University Press.
    Download  
     
    Export citation  
     
    Bookmark   57 citations  
  • The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic. [REVIEW]Dominic Gregory - 2001 - Mind 110 (439):736-740.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Mathematics in Philosophy, Selected Essays.Stewart Shapiro - 1983 - Journal of Symbolic Logic 53 (1):320.
    Download  
     
    Export citation  
     
    Bookmark   21 citations  
  • A Structuralist Approach to Applying Mathematics.Chris John Pincock - 2002 - Dissertation, University of California, Berkeley
    A long-standing problem in the philosophy of mathematics concerns the application of mathematics in reasoning about the physical world. Almost without exception philosophers considering applications of mathematics first provide an account of pure mathematics and then try to show how this is consistent with applied mathematics. But this unquestioned practice has obscured certain fundamental issues in the philosophical study of applied mathematics. In my dissertation, I develop the first classification of accounts of applied mathematics that is independent of views about (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • (2 other versions)Science Without Numbers. A Defence of Nominalism.Kenneth L. Manders - 1984 - Journal of Symbolic Logic 49 (1):303-306.
    Download  
     
    Export citation  
     
    Bookmark   21 citations