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Stewart Shapiro

Ohio State UniversityUniversity of Connecticut
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Columbus, Ohio, United States of America
Areas of Specialization
Philosophy of Language
Logic and Philosophy of Logic
Philosophy of Mathematics
Areas of Interest
Philosophy of Language
Logic and Philosophy of Logic
Philosophy of Mathematics
  •  39
    The Limits of Logic: Higher-order Logic and the Löwenheim-Skolem Theorem
    Routledge. 1996.
    The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question what is second-order logic? and examine various interpretations of the Lowenheim-Skolem theorem.
    Logics
  •  328
    Conservativeness and incompleteness
    Journal of Philosophy 80 (9): 521-531. 1983.
    Mathematical Fictionalism
  •  211
    Mathematics and philosophy of mathematics
    Philosophia Mathematica 2 (2): 148-160. 1994.
    The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.
    Mathematical Practice
  •  3
    Thinking about Mathematics
    Oxford University Press. 2001.
    Philosophy of Mathematics, Misc
  •  283
    An “I” for an I: Singular terms, uniqueness, and reference
    Review of Symbolic Logic 5 (3): 380-415. 2012.
    There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in lingu…Read more
    Semantics
  •  247
    Logical consequence, proof theory, and model theory
    In Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press. pp. 651--670. 2005.
    This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.
    Logical Consequence and Entailment