Geoffrey Hellman | |
---|---|

Born | August 16, 1943 |

Alma mater | Harvard University |

Era | Contemporary philosophy |

Region | Western philosophy |

School | Analytic 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.

## Books

- 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.

## Notes

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