On the nature of continuous physicae quantities in ceassicae and quantum mechanics

Journal of Philosophical Logic

Volumn 30, Issue 1, 2001, Pages 27-50

  Halvorson, Hans ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040484450     PISSN: 00223611     EISSN: 15730433     Source Type: Journal    
DOI: 10.1023/A:1017574203443     Document Type: Article

References (26)

1. Birkhoff, G. and von Neumann, J.: 1936, The logic of quantum mechanics, Ann. of Math. 37, 823-843.
2. Bub, J.: 1997, Interpreting the Quantum World, Cambridge University Press.
3. Bub, J. and Clifton, R.: 1996, A uniqueness theorem for 'no-collapse' interpretations of quantum mechanics, Stud. Hist. Philos. Modern Phys. 27, 181-219.
4. Busch, P., Grabowski, M., and Lahti, P. J.: 1997, Operational Quantum Physics, Springer, New York.
5. Dalla Chiara, M. L.: 1994, Unsharp quantum logics, Internat. J. Theoret. Phys. 34, 1331-1336.
6. Dalla Chiara, M. L. and Giutini, R.: 1994, Partial and unsharp quantum logics, Found. Phys. 24, 1161-1177.
7. Clifton, R.: 1999, Beables in algebraic quantum theory, in J. Butterfield and C. Pagonis (eds.), From Physics to Philosophy, Cambridge University Press, pp. 12-44.
8. Fine, A.: 1971, Probability in quantum mechanics and in other statistical theories, in M. Bunge (ed.), Problems in the Foundations of Physics, Springer, New York, pp. 79-92.
9. Foulis, D. J. and Bennett, M. K.: 1994, Effect algebras and unsharp quantum logics, Found. Phys. 24, 1331-1352.
10. Garnir, H. G., DeWilde M., and Schmets, J.: 1968, Analyse Fonctionnelle: Théorie constructive des espaces linéaires à semi-normes, Birkhauser, Basel.
11. Gleason, A. M.: 1957, Measures on the closed subspaces of a Hubert space, J. Math. Mech. 6(6), 885-893.
12. Halvorson, H. and Clifton, R.: 1999, Maximal beable subalgebras of quantum mechanical observables, Internat. J. Theoret. Phys. 38, 2441-2484.
13. Hirsch, F. and Lacombe, G.: 1999, Elements of Functional Analysis, Springer, New York.
14. Just, W. and Weese, M.: 1991, Discovering Modern Set Theory, Amer. Math. Soc., Providence, RI.
15. Kadison, R. and Ringrose J.: 1997, Fundamentals of the Theory of Operator Algebras, Amer. Math. Soc., Providence, RI.
16. Mackey, G. W.: 1968, Mathematical Foundations of Quantum Mechanics, W.A. Benjamin, New York.
17. Moschovakis, Y N.: 1994, Notes on Set Theory, Springer, New York.
18. Pincus, D. and Solovay, R. M.: 1977, Definability of measures and ultrafilters, J. Symbolic Logic 42, 179-190.
19. Schechter, E.: 1997, Handbook of Analysis and its Foundations, Academic Press, New York.
20. Summers, S. J.: (forthcoming), On the Stone-von Neumann uniqueness theorem and its ramifications, in M. Redei and M. Stoelzner (eds.), John von Neumann and the Foundations of Quantum Mechanics, Kluwer Acad. Publ., Dordrecht.
21. Teller, P. : 1979, Quantum mechanics and the nature of continuous physical quantities, J. Philos. LXXVI, 345-361.
22. Varadarajan, V. S.: 1985, Geometry of Quantum Theory, Springer, New York.
23. von Neumann, J.: 1931, Die Eindeutigkeit der Schrödingerschen Operatoren, Math. Ann. 104, 570-578.
24. von Neumann, J.: 1932, Operatorenmethoden in der klassischen Mechanik, Ann. of Math. 33, 595-598.
25. von Neumann, J.: 1932, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin.
26. Wright, J. D. M.: 1977, Functional analysis for the practical man, in K.-D. Bierstedt and B. Fuchssteiner (eds.), Functional Analysis: Surveys and Recent Results, North-Holland, Amsterdam, pp. 283-290.