Geoffrey Hellman Explained

Region:	Western philosophy
Era:	Contemporary philosophy
Geoffrey Hellman
Birth Date:	16 August 1943
Alma Mater:	Harvard University
School Tradition:	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.

External links

• Academic profile: University of Minnesota

Notes and References

1. [Stewart Shapiro]
2. Web site: Curriculum Vitae, Geoffrey Hellman. University of Minnesota. 29 October 2018 . 29 October 2018 . https://web.archive.org/web/20181029232417/http://hellman.umn.edu/sites/g/files/pua2166/f/media/geoffrey_hellman_cv_12-17.pdf.
3. http://philosophy.umn.edu/people/ University of Minnesota department page
4. Book: Hellman, Geoffrey . Mathematics without Numbers: Towards a Modal-Structural Interpretation . 1989 . Clarendon Press . 978-0-19-824034-1 . September 6, 2011.