Abstract
In this paper I wish to show that we can give a statement of a restricted form of Gleason's Theorem that is classically equivalent to the standard formulation, but that avoids the counterexample that Hellman gives in “Gleason's Theorem is not Constructively Provable”.
Similar content being viewed by others
REFERENCES
Troelstra, A. S. and van Dalen, D. (1988): Constructivism in Mathematics. North-Holland, Amsterdam.
Hellman, G. (1993): Gleason's theorem is not constructively provable. Journal of Philosophical Logic 22: 193–203.
Redhead, M. (1987): Incompleteness, Nonlocality and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics.Clarendon Press, Oxford.
Keane, R., Cooke, M. and Moran, W. (1989): An elementary proof of Gleason's theorem. In [5] Appendix A.
Hughes, R. I. G. (1989): The Structure and Interpretation of Quantum Mechanics. Harvard University Press, Cambridge, MA.
Lang, S. (1983): Undergraduate Analysis. Springer, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Billinge, H. A Constructive Formulation of Gleason's Theorem. Journal of Philosophical Logic 26, 661–670 (1997). https://doi.org/10.1023/A:1004275113665
Issue Date:
DOI: https://doi.org/10.1023/A:1004275113665