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Geoffrey Hellman

Geoffrey Hellman
Born (1943-08-16) August 16, 1943 (age 80)
Alma materHarvard University
EraContemporary philosophy
RegionWestern philosophy
SchoolAnalytic philosophy
Main interests
Philosophy of mathematics
Notable ideas
Mathematical structuralism (modal variety)[1]

Geoffrey Hellman (born August 16, 1943[2]) is an American professor and philosopher. He is Professor of Philosophy at the University of Minnesota in Minneapolis, Minnesota.[3] He obtained his B.A. (1965) and Ph.D. (1972) degrees in philosophy from Harvard University. He was elected to the American Academy of Arts and Sciences in 2007.


  • Hellman, Geoffrey (1989). Mathematics without Numbers. Towards a Modal-Structural Interpretation. The Clarendon Press, Oxford University Press, New York, 1989.[4]
  • Mathematics and Its Logics: Philosophical Essays (Cambridge University Press, 2021).
  • Mathematical Structuralism, with Stewart Shapiro (Cambridge University Press, 2019).
  • Varieties of Continua: From Regions to Points and Back, with Stewart Shapiro (Oxford University Press, 2018).
  • Hilary Putnam on Mathematics and Logic, coedited with Roy Cook (Springer Verlag, 2018).
  • Quantum Measurement: Beyond Paradox, Minnesota Studies in Philosophy of Science (University of Minnesota Press, 1998) co-edited with Richard Healey.

Selected works

  • “Extending the Iterative Conception of Set: a Height-Potentialist Perspective”, in Mathematics and Its Logics: Philosophical Essays (op. cit).
  • “On the Gödel-Friedman Program”, in Mathematics and Its Logics: Philosophical Essays (op. cit).
  • “If ‘If-Then’ Then What?”, in Mathematics and Its Logics: Philosophical Essays (op. cit).
  • ”Extendability and Paradox” (with Roy Cook), in Putnam on Mathematics and Logic, eds. Roy Cook and Geoffrey Hellman (Springer Verlag, 2018).
  • Predicativity and Regions-based Continua (with Stewart Shapiro), in a volume of essays honoring Solomon Feferman, Feferman on Logic and Foundations eds. Wilfried Sieg and Gerhard Jaeger (Springer Verlag, 2018).
  • “Reflections on Reflection in a Multiverse” in a Festschrift in honor of W.W. Tait, Erich Reck ed. (College Publications, London, 2018).
  • ”Carnap* Replies” Monist 101 (2018): 388-393.
  • Hellman, Geoffrey (1993) Constructive Mathematics and Quantum Mechanics: Unbounded Operators and the Spectral Theorem, Journal of Philosophical Logic 12, 221-248.
  • Feferman, Solomon; Hellman, Geoffrey (1995) Predicative foundations of arithmetic. J. Philos. Logic 24, no. 1, 1--17.
  • Hellman, Geoffrey (1997) Bayes and beyond. Philos. Sci. 64, no. 2, 191–221.
  • Hellman, Geoffrey (1998) Mathematical constructivism in spacetime. British J. Philos. Sci. 49, no. 3, 425–450.
  • Feferman, Solomon; Hellman, Geoffrey (2000) "Challenges to predicative foundations of arithmetic" in G. Sher and R. Tieszen, eds.Between logic and Intuition, 317–338, Cambridge Univ. Press, Cambridge.


  1. ^ Stewart Shapiro, "Mathematical Structuralism", Philosophia Mathematica, 4(2), May 1996, pp. 81–2.
  2. ^ "Curriculum Vitae, Geoffrey Hellman" (PDF). University of Minnesota. Archived from the original (PDF) on 29 October 2018. Retrieved 29 October 2018.
  3. ^ University of Minnesota department page
  4. ^ Hellman, Geoffrey (1989). Mathematics without Numbers: Towards a Modal-Structural Interpretation. Clarendon Press. ISBN 978-0-19-824034-1. Retrieved September 6, 2011.
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Geoffrey Hellman
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