Are the Laws of Quantum Logic Laws of Nature?

Abstract

The main goal of quantum logic is the bottom-up reconstruction of quantum mechanics in Hilbert space. Here we discuss the question whether quantum logic is an empirical structure or a priori valid. There are good reasons for both possibilities. First, with respect to the possibility of a rational reconstruction of quantum mechanics, quantum logic follows a priori from quantum ontology and can thus not be considered as a law of nature. Second, since quantum logic allows for a reconstruction of quantum mechanics, self-referential consistency requires that the empirical content of quantum mechanics must be compatible with the presupposed quantum ontology. Hence, quantum ontology contains empirical components that are also contained in quantum logic. Consequently, in this sense quantum logic is also a law of nature.

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Fig. 1

Notes

  1. 1.

    Armstrong (1983), Mittelstaedt and Weingartner (2004), Van Fraassen (1989).

  2. 2.

    von Neumann (1932).

  3. 3.

    Birkhoff and von Neumann (1936).

  4. 4.

    For a very detailed presentation of the history of quantum logic cf. Jammer (1974, 341–616).

  5. 5.

    Feyerabend (1965), Stegmüller (1970, 438–461).

  6. 6.

    Putnam (1969).

  7. 7.

    Stachow (1976), Mittelstaedt (1978, 2011, chapter 3).

  8. 8.

    Kant (1998, B 600).

  9. 9.

    Newton (1729).

  10. 10.

    Leibniz(1686, 433–434).

  11. 11.

    Kant (1998, B 600).

  12. 12.

    Lorenzen (1955).

  13. 13.

    Curry (1952).

  14. 14.

    Mittelstaedt (1978, 2003, 2011), Mittelstaedt and Weingartner (2004). Stachow (1980, 2003).

  15. 15.

    Mittelstaedt (2008).

  16. 16.

    A lattice of this kind is atomic and fulfils the covering law. Cf. Stachow (1984).

  17. 17.

    This remark confirms the more general point of view that quantum logic does not describe directly quantum reality but rather the way speak about this reality.

  18. 18.

    Mittelstaedt (2011, section 3.5).

  19. 19.

    Busch et al. (1995).

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Correspondence to Peter Mittelstaedt.

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Mittelstaedt, P. Are the Laws of Quantum Logic Laws of Nature?. J Gen Philos Sci 43, 215–222 (2012). https://doi.org/10.1007/s10838-012-9195-z

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Keywords

  • Bottom-up reconstruction
  • Quantum logic
  • Quantum ontology
  • Self-consistency