Counterfactuals and non-locality of quantum mechanics: The bedford–stapp version of the GHZ theorem

Foundations of Science 12 (1):85-108 (2007)
In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it appeals to the unwarranted principle of “elimination of eliminated conditions” (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Finally, a general argument is produced to the effect that the locality condition in the form accepted by Stapp and Bedford is consistent with the quantum-mechanical predictions for the GHZ case under the assumption of indeterminism. This result undermines any future attempts of proving the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence in the GHZ case, quite independently of the negative assessment of the particular derivation proposed by Stapp and Bedford.
Keywords counterfactuals  non-locality  quantum mechanics  Bell’s theorem
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DOI 10.1007/s10699-006-0006-z
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Tomasz Bigaj (2010). How to (Properly) Strengthen Bell's Theorem Using Counterfactuals. Studies in History and Philosophy of Science Part B 41 (1):58-66.
Tomasz Bigaj (2010). How to Strengthen Bell's Theorem Using Counterfactuals. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):58-66.

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