Oxford Handbooks Online : The Oxford Handbook of Philosophy of Mathematics and Logic

Subject: Philosophy Book Title: The Oxford Handbook of Philosophy of Mathematics and Logic

The Oxford Handbook of Philosophy of Mathematics and Logic Shapiro, Stewart (Editor), Professor of Philosophy, Ohio State University More about the Editors Print publication date: 2005 Print ISBN-13: 978-0-19-532592-8 Published to Oxford Handbooks Online: September 2009 doi:10.1093/oxfordhb/9780195325928.001.0001	This Book in Print In the OUP catalogue
Abstract: Philosophy of Mathematics and Its Logic: Introduction - A Priority and Application: Philosophy of Mathematics in the Modern Period - Later Empiricism and Logical Positivism - Wittgenstein on Philosophy of Logic and Mathematics - The Logicism of Frege, Dedekind, and Russell - Logicism in the Twenty-first Century - Logicism Reconsidered - Formalism - Intuitionism and Philosophy - Intuitionism in Mathematics - Intuitionism Reconsidered - Quine and the Web of Belief - Three Forms of NaturalismNaturalism Reconsidered - Nominalism - Nominalism Reconsidered - Structuralism - Structuralism Reconsidered - Predicativity - Mathematics—Application and Applicability - Logical Consequence, Proof Theory, and Model Theory - Logical Consequence From a Constructivist View - Relevance in Reasoning - No Requirement of Relevance - Higher-order Logic - Higher-order Logic Reconsidered Keywords: mathematics, logic, Immanuel Kant, empiricism, John Stuart Mill, logical positivism, Wittgenstein, logicism, formalism, intuitionism, Quine, indispensability, naturalism, nominalism, structuralism, predicativity, logical consequence, paradoxes of relevance, second-order logic, higher-order logic Full Book Contents Preface The Oxford Handbook of Philosophy of Mathematics and Logic 1. Philosophy of Mathematics and Its Logic: Introduction Shapiro, Stewart 2. A Priority and Application: Philosophy of Mathematics in the Modern Period Shabel, Lisa 3. Later Empiricism and Logical Positivism Skorupski, John 4. Wittgenstein on Philosophy of Logic and Mathematics Floyd, Juliet 5. The Logicism of Frege, Dedekind, and Russell Demopoulos, William Clark, Peter 6. Logicism in the Twenty-first Century Hale, Bob Wright, Crispin 7. Logicism Reconsidered Rayo, Agustín 8. Formalism Detlefsen, Michael 9. Intuitionism and Philosophy Posy, Carl 10. Intuitionism in Mathematics McCarty, D. C. 11. Intuitionism Reconsidered Cook, Roy 12. Quine and the Web of Belief Resnik, Michael D. 13. Three Forms of Naturalism Maddy, Penelope 14. Naturalism Reconsidered Weir, Alan 15. Nominalism Chihara, Charles 16. Nominalism Reconsidered Rosen, Gideon Burgess, John P. 17. Structuralism Hellman, Geoffrey 18. Structuralism Reconsidered* MacBride, Fraser 19. Predicativity Feferman, Solomon 20. Mathematics—Application and Applicability Steiner, Mark 21. Logical Consequence, Proof Theory, and Model Theory Shapiro, Stewart 22. Logical Consequence From a Constructivist View Prawitz, Dag 23. Relevance in Reasoning Tennant, Neil 24. No Requirement of Relevance Burgess, John P. 25. Higher-order Logic Shapiro, Stewart 26. Higher-order Logic Reconsidered Jané, Ignacio Index	Related Content in OHO 'Logic and the Foundations of Mathematics' in The Oxford Handbook of American Philosophy Related Content from OUP Logic/Philosophy of Mathematics in Oxford Scholarship Online Philosophy of Science in Oxford Scholarship Online
Stewart Shapiro is the O'Donnell Professor of Philosophy at The Ohio State University and Professorial Fellow in the Research Centre Arché, at the University of St. Andrews. His publications include Foundations Without Foundationalism: A Case for Second-order Logic (Oxford University Press, 1991) and Philosophy of Mathematics: Structure and Ontology (Oxford University Press, 1997).	Stewart Shapiro Foundations without Foundationalism in OSO Philosophy of Mathematics in OSO Vagueness in Context in OSO Find in OUP journals External web page

doi:10.1093/oxfordhb/9780195325928.001.0001