# Stewart Shapiro

**Stewart Shapiro** (born 1951) is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is a 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.

## Publications

### Books

*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

### Editorships

*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.

### Papers

- "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.