# Stewart Shapiro

Professor

350 E University Hall

230 N Oval Mall

Columbus, OH

43210

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## Areas of Expertise

- Philosophical Logic
- Vagueness
- Philosophy of Mathematics
- Philosophy of Language

## Education

- B.A. Case Western Reserve University (Mathematics and Philosophy), 1973; Magna cum laude
- Ph.D. SUNY at Buffalo, 1978; with distinction
- M.A. SUNY at Buffalo (Mathematics), 1975

Prof. Shapiro's PhilPapers page

Stewart Shapiro's complete publication list

**Selected Publications:**

*Vagueness in context*, Oxford, Oxford University Press, 2006; reissued in paperback, March, 2008.*Thinking about mathematics: The philosophy of mathematics*, Oxford, Oxford University Press, 2000.*Philosophy of mathematics: Structure and ontology*, Oxford, Oxford University Press, 1997; reissued in paperback, Autumn 2000.*Foundations without foundationalism: A case for second-order logic*, Oxford Logic Guides 17, Oxford, Oxford University Press, 1991, reissued in paperback, Summer 2000.- “Towards a point-free account of the continuous” (with Geoffrey Hellman),
*Iyyun*61, 2012, 263-287. - “Revising logic in light of paradox”, in
*Insolubles and consequences: essays in honor of Stephen Read, Tributes 18*, edited by Catarina Dutilh and Ole Hjortland, College Publications, 2012, 213-237. - “An
*‘i’*for an*i*: singular terms, uniqueness, and reference,*Review of Symbolic Logic 5*(2012), 380-415. - “Higher-order logic and set theory: a false dilemma”,
*Philosophia Mathematica*(3) 20 (2012), 305-323. - “Objectivity, explanation, and cognitive shortfall”, in
*Mind, meaning, and knowledge: themes from the philosophy of Crispin Wright,*edited by Annalisa Coliva, Oxford, Oxford University Press, 2012, 211-237. - “The company kept by cut abstraction (and its relatives)”,
*Philosophia Mathematica (3) 19*, (2011), 107-138. - “Mathematics and objectivity”, in
*Meaning in mathematics*, edited by John Polkinghorne, Oxford, Oxford University Press, 2011, 97-108. - “Theology and the actual infinite: Burley and Cantor”,
*Theology and Science 9*(2011), 101-108. - “Foundations: structures, sets, and categories”, in
*Foundational theories of classical and constructive mathematics”, Western Ontario Series in the Philosophy of Science*, edited by Giovanni Soimmaruga, Dordrecht, Springer, 2011, 97-110. - “Varieties of pluralism and relativism for logic”, in
*A companion to relativism*, edited by Steven D. Hales, Oxford, Wiley-Blackwell, 2011, 526-555. - “Epistemology of mathematics: What are the questions? What count as answers?”,
*Philosophical Quarterly 61*(2011), 130-150 - “So truth is safe from paradox: now what?”,
*Philosophical Studies 147*(2010), 445-455. - “The good, the bad, and the ugly” (with Philip Ebert),
*Synthese 170*(2009), 415-441. - “We hold these truths to be self evident: But what do we mean by that?”,
*Review of Symbolic Logic 2*(2009), 175-207. - “Reasoning with slippery predicates”,
*Studia Logica 90*(2008), 313-336. - “Identity, indiscernibility, and ante rem structuralism: the tale of i and -i”,
*Philosophia Mathematica (*3) 16 (2008), 285-309. - “Frege meets Zermelo: a perspective on ineffability and reflection” (with Gabriel Uzquiano),
*Review of Symbolic Logic 1*(2008), 241-266. - “The objectivity of mathematics”,
*Synthese 156*(2007), 337-381. - “Where in the (world wide) web of belief is the law of non-contradiction?” (with Jack Arnold),
*Nous 41*(2007) , 276–297. - “Burali-Forti’s revenge, Revenge of the liar, edited by J. C. Beall, Oxford, Oxford University Press, 2007, 320-344.
- “Faith and reason: the perpetual war”, in
*Philosophers without gods*, 2007, edited by Louise Antony, Oxford, Oxford University Press, 3-16. - “All things indefinitely extensible” (with Crispin Wright), in
*Absolute generality*, edited by Agustín Rayo, Oxford, Oxford University Press, 2006, 255-304. - “Structure and identity” in
*Modality and identity*, edited by Fraser MacBride, Oxford University Press, 2006, 109-145. - “Computability, proof, and open-texture”, in
*Church’s thesis after 70 years*, edited by Adam Olszewski, Jan Woleński, and Robert Janusz, Frankfurt, Ontos Verlag, 2006, 420-455. - “Context, conversation, and so-called ‘higher-order vagueness’”,
*Proceedings of the Aristotelian Society, Supplemental Volume 79*(2005), 147-165. - “Sets and abstracts”,
*Philosophical Studies 122*(2005), 315-332. - “Gurus, logical consequence, and truth-bearers: What is it that is true?”, in
*Deflationary truth*, edited by Bradley Armour-Garb and J.C. Beall, Open Court Publishers, 2005, 153-170. - “Categories, structures, and the Frege-Hilbert controversy: the status of meta-metamathematics”,
*Philosophia Mathematica (3) 13*(2005), 61-77; reprinted in*Logicism, intuitionism, and formalism*, edited by Sten Lindström et al., Synthese Library 341, Springer, 2009, 435-448. - “Logical consequence, proof theory, and model theory”,
*Oxford handbook for the philosophy of mathematics and logic*, edited by Stewart Shapiro, Oxford, Oxford University Press, 2005, 651-670. - “Higher-order logic”,
*Oxford handbook for the philosophy of mathematics and logic*, edited by Stewart Shapiro, Oxford, Oxford University Press, 2005, 751-780. - “Simple truth, contradiction, and consistency”,
*The law of non-contradiction*, edited by Graham Priest and J. C. Beall, Oxford, Oxford University Press, 2004, 336-354. - “The nature and limits of abstraction”,
*Philosophical Quarterly 54*(2004), 166-174. - “Foundations of mathematics: metaphysics, epistemology, structure”,
*Philosophical Quarterly 54*(2004), 16-37. - “All sets great and small: and I do mean ALL”,
*Philosophical Perspectives 1*7 (2003), 467-490. - “Vagueness and Conversation”, in
*Liars and Heaps*, edited by J. C. Beall and Michael Glanzberg, Oxford, Oxford University Press, 2003, 39-72. - “Mechanism, truth, and Penrose’s new argument”,
*Journal of Philosophical Logic 32*(2003), 19-42. - “Prolegomenon to any future neo-logicist set theory: extensionality and indefinite extensibility”,
*British Journal for the Philosophy of Science 54*(2003), 59-91 , 160-189; reprinted in*The Arché papers on the mathematics of abstraction*, edited by Roy T. Cook, Dordrecht, The Netherlands, Springer, 353-382. - “The guru, the logician, and the deflationist”,
*Noûs 37*(2003), 113-132. - “Incompleteness and inconsistency”,
*Mind 111*(2002), 817-832. - “The ‘triumph’ of first-order logic”,
*Logic, meaning and computation: memorial volume for Alonzo Church*, edited by C. Anthony Anderson and M. Zeleny, Kluwer Academic Publishers, 2002, 219-259. - “Frege meets Dedekind: a neo-logicist treatment of real analysis”,
*Notre Dame Journal of Formal Logic 41*(2000), 335-364 , 160-189; reprinted in*The Arché papers on the mathematics of abstraction*, edited by Roy T. Cook, Dordrecht, The Netherlands, Springer, 219-252. - “The status of logic”,
*New essays on the a priori*, edited by Paul Boghossian and Christopher Peacocke, Oxford University Press, 2000, 333-366; reprinted in part as “Quine on Logic”,*Logica Yearbook 1999*, edited by Timothy Childers, Prague, Czech Academy Publishing House, 11-21. - “Do not claim too much: Second-order logic and first-order logic”,
*Philosophia Mathematica (3) 7*(1999), 42-64. - “Incompleteness, mechanism, and optimism”,
*Bulletin of Symbolic Logic 4*(1998), 273-302. - “Proof and truth: Through thick and thin”,
*Journal of Philosophy 95*(1998), 493-521. - “Logical consequence: Models and modality”,
*Philosophy of mathematics today: Proceedings of an international conference in Munich*, ed. by Mathias Schirn, The Mind Association, Oxford, Oxford University Press, 1998, 131-156.