Stewart Shapiro

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Stewart Shapiro (born 1951) is O'Donnell Professor of Philosophy at the Ohio State University. He is a leading figure in the philosophy of mathematics where he defends a version of structuralism. He studied Mathematics and Philosophy at Case Western Reserve University in 1973. Then, he got his M.A. in Mathematics at the State University of New York at Buffalo in 1975. He transferred to the UB Philosophy Department, where three years later he received a Ph.D. His doctoral supervisor was John Corcoran.



  • Philosophy of Mathematics: Structure and Ontology. Oxford University Press, 1997. ISBN 0-19-513930-5
  • Thinking about Mathematics: The Philosophy of Mathematics. Oxford University Press, 2000. ISBN 0-19-289306-8
  • Foundations without Foundationalism: A Case for Second-Order Logic. Oxford University Press, 1991. ISBN 0-19-853391-8
  • Vagueness in Context. Oxford University Press, 2006. ISBN 0-19-928039-8


  • The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press, 2005. ISBN 0-19-514877-0
  • Special issue of "Philosophia Mathematica", devoted to structuralism.

Contributors: P. Benacerraf, G. Hellman, B. Hale, C. Parsons, M. Resnik, S. Shapiro, forthcoming.

  • "The limits of logic: Second order logic and the Skolem paradox", The international research library of philosophy, Dartmouth Publishing Company, forthcoming.
  • Intensional Mathematics, Studies in Logic and the Foundations of Mathematics 113, Amsterdam, North Holland Publishing Company, 1985.

Contributors: S. Shapiro, J. Myhill, N. D. Goodman, A. Scedrov, V. Lifschitz, R. Flagg, R. Smullyan.


  • "The Work of John Corcoran: an Appreciation" Scanlan, M. and Shapiro, S. 1999., ‘‘History and Philosophy of Logic’’, 20, 149–158.
  • "Corcoran the mathematician", Current Issues in Logic / Temas Actuales de Lógica. Imprenta Universidade Santiago de Compostela, Santiago de Compostela, Spain, 2007, 271-288.
  • "Cognitive command and excluded middle" (with William Taschek), Journal of Philosophy, forthcoming.
  • "Space, number, and structure: A tale of two debates", Philosophia Mathematica, forthcoming.
  • "Introduction", Philosophia Mathematica (see above), forthcoming.
  • "The limits of logic", introduction to The limits of logic: Second order logic and the Skolem paradox, The international research library of philosophy (see above), Dartmouth Publishing Company, forthcoming.
  • "The triumph of first order logic", Festschrift for Alonzo Church, University of Chicago Press, forthcoming.
  • "Logical consequence: Models and modality", Philosophy of mathematics today: Proceedings of an international conference in Munich, The Mind Association, Oxford, Oxford University Press, forthcoming.
  • "Understanding Church's thesis, again", Acta Analytica 11 (1993), 59-77 published in August 1995.
  • "Reasoning, logic, and computation", Philosophia Mathematica (3) 3 (1995), 31-51.
  • "Mathematics and philosophy of mathematics", Philosophia Mathematica (3) 2 (1994), 148-160.
  • "Modality and ontology", Mind 102 (1993), 455-481.
  • "Antirealism and modality", Philosophy of Mathematics: Proceedings of the Fifteenth International Wittgenstein Symposium, Vienna, Verlag Holder Pichler Tempsky, 1993,269-287.
  • "Foundationalism and foundations of mathematics", in Proof and knowledge in mathematics, ed. by Michael Detlefsen, London and New York, Routledge, 1992, 171-207.
  • "Second order logic, foundations, and rules", Journal of Philosophy 87 (1990), 234-261.
  • "Expressive completeness and decidability" (with George Schumm),Notre Dame Journal of Formal Logic 31 (1990), 576-579.
  • "Structure and ontology", Philosophical Topics 17 (1989), 145-171.
  • "Logic, ontology, mathematical practice", Synthese 79 (1989), 13-50
  • "The Lindenbaum construction and decidability", Notre Dame Journal of Formal Logic 29 (1988), 208-213.
  • "Principles of reflection and second-order logic", Journal of Philosophical Logic 16 (1987), 309-333.
  • "Turing projectibility" (with Timothy McCarthy), Notre Dame Journal of Formal Logic 28 (1987), 520-535.
  • "Actuality and essence" (with William Lycan), Midwest Studies in Philosophy 11 (1986), 343-377.
  • "Second-order languages and mathematical practice", Journal of Symbolic Logic 50 (1985), 714-742.
  • "Epistemic arithmetic and intuitionistic arithmetic" in Intensional Mathematics (see above), 11-46.
  • "Introduction" in Intensional Mathematics (see above), 1-10.
  • "Arithmetic Sinn and effectiveness", Dialectica 38 (1984), 3-16.
  • "On an empiricist philosophy of mathematics", Philosophia 14 (1984), 213-223.
  • "Mathematics and reality", Philosophy of Science 50 (1983), 523-548.
  • "Remarks on the development of computability", History and Philosophy of Logic 4 (1983), 203-220.
  • "Conservativeness and incompleteness", The Journal of Philosophy 80 (1983), 521-531
  • "Acceptable notation", Notre Dame Journal of Formal Logic 23 (1982), 14-20
  • "Understanding Church's thesis", Journal of Philosophical Logic 10 (1981), 353-365
  • "Largomento con la tesi di Church" (Argument by Church's thesis), Nominazione 2 (1981), 195-199.
  • "On the notion of effectiveness", History and Philosophy of Logic 1 (1980), 209-230.
  • "Incomplete translations of complete logics", Notre Dame Journal of Formal Logic 18 (1977), 248-250.

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