Branching Space-Time, Modal Logic and the Counterfactual Conditional

Thomas Müller, Nuel Belnap, Kohei Kishida

J. Finkelstein

Henry Pierce Stapp

Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption.

Nuel Belnap

Henry Pierce Stapp

The paper develops a version of modal logic that stays completely within the framework provided by quantum principles, and then proves, within the framework of quantum thinking, and in particular without invoking "hidden variables", a Bell-type nonlocality result.

Rodolfo Gambini, Jorge A. Pullin