hellm001@umn.edu

845 Heller
612-625-8201

Professor Hellman's homepage

Over the last decade and a half, my work has been concentrated in the areas of philosophy of mathematics and philosophy of science. In the former, I have been developing a modal-structural interpretation of mathematics, a variety of structuralism quite distinct from set theoretic or other Platonistic accounts.

This also has concerned the closely related question of the scope and limits of nominalism. In a second line of research, I have been examining varieties of constructive mathematics (e.g. Bishop's constructivism, intuitionism, predicativism) and apparent limitations in connection with scientific applications, arising especially in quantum mechanics and space-time physics. Closely related is the whole question of indispensability arguments for classical mathematics.

In the philosophy of science, I have pursued work on the significance of the Bell results in the foundations of quantum mechanics, e.g., implications concerning determinism, locality, and realism (a kind of "experimental metaphysics," as Shimony has put it). Other contributions have included a critique of quantum logic, and, more recently, a volume of Minnesota Studies on recent approaches to the quantum measurement problem (co-edited with Richard Healey). I also continue to think about more general topics in philosophy of science such as Bayesian confirmation, reasonable realism, physicalism and unity of science. Finally, I continue to develop material in musical aesthetics, which I teach occasionally, informed through active work as a concert pianist.

Selected Publications

"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).

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

"Three Varieties of Mathematical Structuralism", Philosophia Mathematica 9 (2001): 184-211.

"Mathematical Constructivism in Spacetime." British Journal for the Philosophy of Science 49 (1998).

"Structuralism without Structures." Philosophia Mathematica 4 (1996).

"Predicative Foundations of Arithmetic." With Solomon Feferman. Journal of Philosophical Logic 24 (1995).

"Bell-Type Inequalities in the Non-Ideal Case: Proof of a Conjecture of Bell." Foundations of Physics 22 (1992).

"Never Say 'Never'! On the Communication Problem between Intuitionism and Classicism", Philosophical Topics 17 (1989): 47-67.

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

"Logical Truth by Linguistic Convention", in L.E. Hahn and P.A. Schilpp, eds. The Philosophy of W.V. Quine (La Salle, IL: Open Court, 1986), pp. 189-205.

"Einstein and Bell: Strengthening the Case for Microphysical Randomness." Synthese 53 (1982).