Books
Mathematics and Its Logics: Philosophical Essays (Cambridge University Press, 2021).
Mathematical Structuralism, with Stewart Shapiro (Cambridge UP, 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, 2018).
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
"Quantum Logic and Meaning", PSA, 1980, Volume 2, pp. 493-511.
"Challenges to Predicative Foundations of Arithmetic," in G. Sher and R. Tieszen, eds., Logic and Intuition(Cambridge University Press, 2000): 317-338 (with Solomon Feferman).
"Predicative Foundations of Arithmetic," Journal of Philosophical Logic24 (l995): l-l7 (with Solomon Feferman).
"Structuralism without Structures", Hellman, Geoffrey, Philosophical Mathematica, 4 , 1996.
"Mathematical Constructivism in Spacetime", Hellman, Geoffrey, British Journal for the Philosophy of Science, 49 , 1998.
"Against "Absolutely Everything"
“Structuralism, Mathematical”, in The Encyclopedia of Philosophy, ed. Donald M. Borchert. Vol. 9. 2nded. Detroit: Macmillan Reference USA, 2006, pp. 270-273.
”Carnap* Replies” Monist 101(2018): 388-393.
“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 Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle:essays in honour of Abner Shimony, J. Christian and W. Myrvold, eds. (Springer: 2009).
"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, 2006,with J. L. Bell.
“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, 2005).
“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.
"Reflections on Reflection in a Multiverse in Logic", Philosophy of Mathematics and their History: Essays in Honor of W.W. Tait, Erich Reck ed. (College Publications, London, 2018).
Unpublished Works