
1Vagueness and ConversationIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. 2004.

1""Bertrand Russell," On Denoting"(1905) and" Mathematical Logic as Based on the Theory of Types"(1908)In Jorge J. E. Gracia, Gregory M. Reichberg & Bernard N. Schumacher (eds.), The Classics of Western Philosophy: A Reader's Guide, Blackwell. pp. 460. 2003.

1Vagueness, Metaphysics, and ObjectivityIn Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic, Oxford University Press. 2010.

1BuraliForti's revengeIn J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.

D. GABBAY and F. GUENTHNER "Handbook of philosophical logic. Volume 1: Elements of classical logic"History and Philosophy of Logic 6 (2): 215. 1985.

Mathematical StructuralismCambridge University Press. 2018.The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, settheoretic and categorytheoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as a…Read more

Mathematics as a Science of PatternsBritish Journal for the Philosophy of Science 49 (4): 652656. 1997.

Antirealism and modalityIn J. Czermak (ed.), Philosophy of Mathematics, Hölderpichlertempsky. pp. 269287. 1993.

Thinking about Mathematics: The Philosophy of MathematicsPhilosophical Quarterly 52 (207): 272274. 2002.

Philosophy of Mathematics: Structure and OntologyPhilosophy and Phenomenological Research 65 (2): 467475. 2002.

Mathematics and ObjectivityIn John Polkinghorne (ed.), Meaning in Mathematics, Oxford University Press. 2011.

Philosophy of MathematicsOxford University Press USA. 1997.Moving beyond both realist and antirealist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

Friedrich Waismann: The Open Texture of Analytic Philosophy (edited book)Palgrave Macmillan. forthcoming.

Varieties of Continua: From Regions to Points and BackOxford University Press. 2018.Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or spacetime.

Review of Kleene 1981, Davis 1982, and Kleene 1987 (review)Journal of Symbolic Logic 55 348350. 1990.

An Introduction to Nonclassical Logic (review)Review of Metaphysics 56 (3): 670671. 2003.This book is just what its title says: an introduction to nonclassical logic. And it is a very good one. Given the extensive interest in nonclassical logics, in various parts of the philosophical scene, it is a welcome addition to the corpus. Typical courses in logic, at all levels and in both philosophy departments and mathematics departments, focus exclusively on classical logic. Most instructors, and some textbooks, give some mention to some nonclassical systems, but usually few details are p…Read more
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 