David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Philosophical Logic 7 (1):181 - 208 (1978)
The principle of excluded middle is the logical interpretation of the law V ≤ A v ヿA in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on the very conditions under which propositions can be confirmed by measurements. From the fact that the principle of. excluded middle can be confirmed for elementary propositions which are proved by quantum mechanical measurements, we conclude that this principle is inherited by all finite compound propositions. For this proof it is essential that, in the dialog-game about a connective, a finite confirmation strategy for the mutual commensurability of the subpropositions is used
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Ernst-Walther Stachow (1977). How Does Quantum Logic Correspond to Physical Reality? Journal of Philosophical Logic 6 (1):485 - 496.
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