Publications

Books

Perspectives on Mathematical Structure, with Stewart Shapiro (Cambridge University Press,  Elements series, forthcoming 2018).

Varieties of Continua: From Regions to Points and Back, with Stewart Shapiro, Oxford University Press, 2018.

 Putnam on Mathematics and Logic, coedited with Roy Cook (Springer Verlag, forthcoming).

Mathematics without Numbers: Towards a Modal-Structural Interpretation. Hellman, Geoffrey, Oxford University Press, 1989.

Quantum Measurement: Beyond Paradox. Hellman, Geoffrey, Richard Healey, University of Minnesota Press, 1998.

Selected Publications

PDF icon "Quantum Logic and Meaning", PSA, 1980, Volume 2, pp. 493-511.

PDF icon "Challenges to Predicative Foundations of Arithmetic"

"Predicative Foundations of Arithmetic",  Hellman, Geoffrey, Solomon Feferman, 1995.

"Structuralism without Structures",  Hellman, Geoffrey, Philosophical Mathematica, 4 , 1996.

"Mathematical Constructivism in Spacetime", Hellman, Geoffrey, British Journal for the Philosophy of Science, 49 , 1998.

"Foundational Frameworks"

"Against "Absolutely Everything"

"Structuralism, Mathematical", (forthcoming in The Encyclopedia of Philosophy 2d Ed. (MacMillan)).

Mereology in Philosophy of Mathematics”, Handbook of Mereology, Hans Burkhardt , Johanna Seibt and Guido Imaguire, eds. (Philosophia Verlag, 2009).

"Interpretations of Probability in Quantum Mechanics: A Case of "Experimental Metaphysics"" in W. Myrvold and J. Christian, eds., Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle (Springer: 2009), pp. 211-227.

"Pluralism and the Foundations of Mathematics", in C.K. Waters, H. Longino, and S. Kellert, eds. Scientific Pluralism, Minnesota Studies in Philosophy of Science, XIX, with J. L. Bell (forthcoming).

Predicativism as a Philosophical Position”, Revue Internationale de Philosophie (special issue ed. by P. Rouilhan) 58, 3 (2004): 295-312.

Does Category Theory Provide a Framework for Mathematical Structuralism?”, Philosophia Mathematica 11 (2003) : 129-157.

Structuralism”, S. Shapiro, ed. Handbook for Philosophy of Mathematics (Oxford University Press, forthcoming).

Russell’s Absolutism vs. (?) Structuralism”, in G. Link, ed. One Hundred Years of Russell’s Paradox (Berlin: de Gruyter, 2004), pp. 561-575.

"Maximality vs. Extendability: Reflections on Structuralism and Set Theory", in D. B. Malament, ed. Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, (La Salle, IL: Open Court, 2002): 335-361.

"On Nominalism", Philosophy and Phenomenological Research, LXII, 3 (2001): 691-705.

"Bell-Type Inequalities in the Non-Ideal Case: Proof of a Conjecture of Bell", Foundations of Physics, 22, 6 (1992): 807-l7 (special issue in honor of Henry Margenau).

"Never say 'never'! On the communication problem between intuitionism and classicism", Philosophical Topics 17, 2 (1989): 47-67.

"Review of recent work (c. late '70's) on theories of truth and semantic paradoxes", The Journal of Symbolic Logic, Vol . 50, No. 4, (1985): 1068-1071.

"Against Bad Method," Review article of Paul K. Feyerabend, Against Method (London, N.L.B., 1975), with a reply by Feyerabend and my rebuttal, "From Bad to Worse," in Metaphilosophy, 10, 2, (1979): 190-207.

A Not-So Recent Non-Publication

"Carnap* Replies"

Work in Progress

Reflections on Replacement and Reflection: The Axioms in a Structuralist Setting

Reduction, Determination, Explanation