Skip to main content
SpringerLink
Log in

Philosophical remarks

  • Chapter
  • First Online:
Quantum Probability — Quantum Logic

Part of the book series: Lecture Notes in Physics ((LNP,volume 321))

  • 1307 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Aspect, A., Grangier, P. and Roger, G. (1981), Experimental tests of realistic local theories via Bell's theorem, Phys. Rev. Lett. 47, 460, reprinted in Wheeler and Zurek (1983).

    Google Scholar 

  • Bellfante, F.J. (1973), A Survey of Hidden-Variable Theories, Pergamon, Oxford.

    Google Scholar 

  • Bell, E.T. (1973), Men of Mathematics, Simon and Schuster, New York.

    Google Scholar 

  • Bell, J.S. (1964), On the Einstein-Podolsky-Rosen paradox, Physics 1, 195.

    Google Scholar 

  • Beltrametti, E.G. and van Fraassen, B.C. (1981) eds., Current Issues in Quantum Logic, Plenum, New York.

    Google Scholar 

  • Birkhoff, G. and von Neumann, J. (1936), The logic of quantum mechanics, Ann. Math. 37, 823.

    Google Scholar 

  • Black, M. (1967), Probability, Encyclopedia of Philosophy, Macmillan, New York.

    Google Scholar 

  • Bohm, D. (1951), Quantum Theory, Prentic-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Bohm, D. (1952), A suggested interpretation of quantum theory in terms of “hidden variables”, Phys. Rev. 85, 180, reprinted in Wheeler and Zurek (1983).

    Google Scholar 

  • Bohm, D. (1981), Wholeness and the Implicate Order, Rutledge and Kegan, London.

    Google Scholar 

  • Bohr, N. (1949), Discussions with Einstein on epistemological problems in atomic physics, in P.A. Schlipp ed., Albert Einstein Philosopher—Scientist, The Library of Living Philosphers, Evanston, reprinted in Wheeler and Zurek (1983).

    Google Scholar 

  • Bonferroni, C.E. (1936a), Teorie statistica delle classi e calcolo delle probabilita, Public Inst. Sup. Sc. Ec. e Comm. di Firenze 8, 1.

    Google Scholar 

  • Bonferroni, C.E. (1936b), II calcolo delle assicurazioni su grappi di teste, Studi in Onore del Prof. S.O. Carboni, Roma.

    Google Scholar 

  • Bub, J. (1977), The Interpretation of Quantum Mechanics, Reidel, Dordrecht

    Google Scholar 

  • Bub, J. and Pitowsky, I. (1985), Critical notice on K.R. Popper's postscript to the logic of scientific discovery, Can. J. of Phil. 15, 539.

    Google Scholar 

  • Capra, F. (1975), The Tau of Physics, Shambahala, Berkeley, CA.

    Google Scholar 

  • Carnap, R. (1950), Logical Foundations of Probability, U. of Chicago Press, Chicago, IL.

    Google Scholar 

  • Clauser, J.F. and Horne, M.A. (1974), Experimental consequences of objective local theories, Phys. Rev. D. 10, 526.

    Google Scholar 

  • Clauser, J.F. and Shimony, A. (1978), Bell's theorem. Experimental tests and implications, Rep. Prog. Phys. 41, 1881.

    Google Scholar 

  • Clauser, J.F., Horne, M.A., Shimony, A. and Holt, R.A. (1969), Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 83, 880, reprinted in Wheeler and Zurek (1983).

    Google Scholar 

  • Cohen, P. (1966), Set Theory and the Continuum Hypothesis, Benjamin, New York.

    Google Scholar 

  • Cooke, R., Keane, M. and Moran, W. (1985), An elementary proof of Gleason's theorem, Math. Proc. Comb. Phil. Soc. 98, 117.

    Google Scholar 

  • d'Espangant, B. (1971), Conceptual Foundations of Quantum Mechanics, W.A. Benjamin, Menlo Park, CA.

    Google Scholar 

  • De Finnetti, B. (1972), Proabability Induction and Statistics, Wiley.

    Google Scholar 

  • Dummett, M. (1978), Is logic empirical?, in Truth and Other Enigmas, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Einstein, A., Podolsky, B. and Rosen, W. (1935), Can quantum mechanical description of physical reality be considered complete?, Phys. Rev. 47 777, reprinted in Wheeler and Zurek (1983).

    Google Scholar 

  • Fine, A. (1982a), Hidden variables, joint probability and Bell inequalities, Phys. Rev. Lett. 48, 291.

    Google Scholar 

  • Fine, A. (1982b), Reply to Garg A. and Mermin N.D., Phys. Rev. Lett. 49, 243.

    Google Scholar 

  • Finkelstein, D. (1962), The logic of quantum physics, Trans. New York Acad. of Sci. 25, 621.

    Google Scholar 

  • Finkelstein, D. (1968), Matter, space and logic, in R. Cohen and M. Wartofsky, eds., Boston Studies in the Philosophy of Science 5, 199, Reidel, Dordrecht.

    Google Scholar 

  • Fréchet, M. (1940), Les Probabilités Associées a un Systéme D'Événtments Compatibles et Dépandants, Hermann, Paris.

    Google Scholar 

  • Garey, M.R. and Johnson, D.S. (1979), Computers and Intractability, A Guide to the Theory of NP-Completeness, W.H. Freeman, New York.

    Google Scholar 

  • Garg, A. and Mermin, N.D. (1982a), Bell inequalities with range of violation that does not diminish as the spin becomes arbitrarily large, Phys. Rev. Lett. 49, 901.

    Google Scholar 

  • Garg, A. and Mermin, N.D. (1982b), Comment on “Hidden variables, joint probability and Bell inequalities”, Phys. Rev. Lett. 49, 242.

    Google Scholar 

  • Garg, A. and Mermin, N.D. (1983), Local realism and measured correlations in the spin s Einstein-Podolsky-Rosen experiment, Phys. Rev. D. 27, 339.

    Google Scholar 

  • Garg, A. and Mermin, N.D. (1984), Farkas's lemma and the nature of reality: Statistical implications of quntum correlations, Found. of Phys. 14, 1.

    Google Scholar 

  • Gauss, K.F. (1831), Letters to Olbers, Collected Works vol. II, 177.

    Google Scholar 

  • Gleason, A.M. (1957), Measures on the closed subspaces of a Hilbert space, J. Math. and Mech. 6, 885.

    Google Scholar 

  • Gödel, K. (1940), The consistency of the axiom of choice and the generalized continuum hypothesis, Annals of Math 3, Princeton U. Press, Princeton, NJ.

    Google Scholar 

  • Gudder, S.P. (1970), On hidden variable theories, J. Math. Phys. 11, 481.

    Google Scholar 

  • Gudder, S.P. (1984a), Probability manifolds, J. Math. Phys. 25, 2397.

    Google Scholar 

  • Gudder, S.P. (1984b), Reality, locality and probability, Found. of Phys. 14, 997.

    Google Scholar 

  • Gudder, S. P. (1985), Amplitude phase space model for quantum mechanics, Int. J. of Theor. Phys. 24, 343.

    Google Scholar 

  • Gudder, S.P. (1988), Quantum Probability, Academic Press, Orlando, FL.

    Google Scholar 

  • Hewitt, E. and Ross, K.A. (1979), Abstract Harmonic Analysis, Springer, Berlin.

    Google Scholar 

  • Hume, D. (1739), A Treatise of Human Nature, modern edition: D.G.L. Macnabb ed., Fontana/Collins, Glasgow.

    Google Scholar 

  • Jech, T.J. (1973), The Axiom of Choice, North Holland, Amsterdam.

    Google Scholar 

  • Jauch, J.M. (1968), Foundations of Quantum Mechanics, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Karp, R.M. and Papadimitriou, C.H. (1980), On linear characterizations of combinatiorial optimization problems, Proc. of the 21 Symp. Found. Comput. Sci., 1.

    Google Scholar 

  • Keynes, J.M. (1943), A Treatise on Probability, McMillan, London (originally published in 1923).

    Google Scholar 

  • Kochen, S. and Specker, E.P. (1967), The problem of hidden variables in quantum mechanics, J. Math. and Mech. 17, 59.

    Google Scholar 

  • Macdonald, A.L. (1982), Comment on “Resolution of the Einstein-Podolsky-Rosen and Bell paradoxes”, Phys. Rev. Lett. 49, 1214.

    Google Scholar 

  • Mandelbrot, B. (1977), Fractals — Form, Chance and Dimension, W.H. Freeman, San Francisco.

    Google Scholar 

  • Mermin, N.D. (1982), Comment on “Resoultion of the Einstein-Podolsky-Rosen and Bell paradoxes”, Phys. Rev. Lett. 49, 1215.

    Google Scholar 

  • Mermin, N.D. and Schwarz, G. (1982), Joint distributions and local realism in the higher spin Einstein-Podolsky-Rosen experiment, Found. of Phys. 12, 101.

    Google Scholar 

  • Messiah, A. (1963), Quantum Mechanics, North Holland, Amsterdam.

    Google Scholar 

  • Mott, N.F. and Massey, H.S.W. (1965), The Theory of Atomic Collisions, Claredon Press, Oxford.

    Google Scholar 

  • Pitowsky, I. (1982a), Substitution and truth in quantum logic, Philos. of Sci. 49, 380.

    Google Scholar 

  • Pitowsky, I. (1982b), Resolution of the Einstein-Podolsky-Rosen and Bell paradoxes, Phys. Rev. Lett. 48, 1299.

    Google Scholar 

  • Pitowsky, I. (1983), Deterministic model of spin and statistics, Phys. Rev. D. 27, 2316.

    Google Scholar 

  • Pitowsky, I. (1985a), On the status of statistical inferences, Synthese 63, 233.

    Google Scholar 

  • Pitowsky, I. (1985b), Discussion: Quantum mechanics and value definiteness, Philos. of Sci. 52, 154.

    Google Scholar 

  • Pitowsky, I. (1985c), A phase space model of quantum mechanics in which all operators commute, in L.M. Roth and A. Inomata, eds., Foundamental Questions in Quantum Mechanics, Gordon and Breach, New York.

    Google Scholar 

  • Pitowsky, I. (1986), The range of quantum probability, J. Math of Phys. 27, 1556.

    Google Scholar 

  • Pitowsky, I. (1988), Correlation polytopes, their geometry and complexity, forthcoming.

    Google Scholar 

  • Popper, K.R. (1959), The Logic of Scientific Discovery, Basic Books, New York (German original 1934).

    Google Scholar 

  • Putnam, H. (1968), Is logic empirical? in R. Cohen and M. Wartofsky, eds., Boston Studies in the Philosophy of Science, Vol. 5, Reidel, Dordrecht.

    Google Scholar 

  • Putnam, H. (1976), How to think quantum logically, in P. Suppes, ed., Logic and Probability in Quantum Mechanics, Reidel, Dordrecht.

    Google Scholar 

  • Putnam, H. (1983), Models and reality, in Realism and Reason, Cambridge U. Press, Cambridge.

    Google Scholar 

  • Quine, W.V.O. (1953), Two dogmas of empiricism, in From a Logical Point of View, Harper and Row, New York.

    Google Scholar 

  • Quine, W.V.O. (1975), On empirically equivalent systems of the world, Erkenntnis IX, 313.

    Google Scholar 

  • Ramsey, F.P. (1926), Truth and probability, in R.B. Brathwaite, ed., The Foundations of Mathematics, Routledge and Kegan, London.

    Google Scholar 

  • Reichenbach, H. (1944), Philosophical Foundations of Quantum Mechanics, University of California Press, Berkeley.

    Google Scholar 

  • Rockafeller, R.T. (1970), Convex Analysis, Princeton University Press, Princeton.

    Google Scholar 

  • Shaeffer, T.J. (1978), The complexity of satistiability problem, Proc. 10th. Ann. Syp. on Theory of Computing, 216, Association for Computing Machinary, New York.

    Google Scholar 

  • Shelah, S. (1984), Can you take Solovay's inaccessible away? Israel J. of Math. 48, 1.

    Google Scholar 

  • Shimony, A. (1984), Contextual hidden variable theories and Bell inequalities, Brit. J. Phil. Sci. 35, 25.

    Google Scholar 

  • Solovay, R.M. (1970), A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 92, 1.

    Google Scholar 

  • Stairs, A. (1983), Quantum logic, realism and value definiteness, Phil. of Sc. 50, 578.

    Google Scholar 

  • van Fraasen, B.C. (1980), The Scientific Image, Oxford U. Press, oxford.

    Google Scholar 

  • van Fraassen, B.C. (1982), The Charidbis or realism: Epistemological implications of Bell's inequality, Synthese 52, 885.

    Google Scholar 

  • Varadarajan, V. (1962), Geometry of Quantum Theory, Vol. I, II, van Nostrand, Princeton, NJ.

    Google Scholar 

  • von Mises, R. (1957), Probability Statistics and Truth, Dover, New York (original German edition, 1928).

    Google Scholar 

  • von Neumann, J. (1955), Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton (original German edition, 1933).

    Google Scholar 

  • Wheeler, J.A. and Zurek, W.H. (1983), eds., Quantum Theory and Measurement, Princeton University Press, Princeton.

    Google Scholar 

  • Wigner, E.P. (1961), Remarks on the mind-body question in Symmetries and Reflections, Indiana University Press, Bloomington, reprinted in Wheeler and Zurek, 1983.

    Google Scholar 

  • Wigner, E.P. (1970), On hidden variables and quantum mechanical probabilities, Amer. Jour. Phys. 38, 1005.

    Google Scholar 

  • Wigner, E.P. (1976), Interpretation of quantum mechanics, mimeographed note, reprinted in Wheeler and Zurek, 1983.

    Google Scholar 

  • Wittgenstein, L. (1939), On Certainty, eds.: E.M. Enscomb and G.H. von Wright, Blackwell, Oxford.

    Google Scholar 

  • Yemlichev, A.V., Kovalev, M.M. and Kravtsov, M.K. (1984), Polytopes, Graphs and Optimizations, Cambridge University Press, Cambridge (Russian original, 1981).

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this chapter

Cite this chapter

(1989). Philosophical remarks. In: Quantum Probability — Quantum Logic. Lecture Notes in Physics, vol 321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021192

Download citation

  • DOI: https://doi.org/10.1007/BFb0021192

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50679-9

  • Online ISBN: 978-3-540-46070-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation