Is Quantum Logic Really Logic?

Abstract

Putnam and Finkelstein have proposed the abandonment of distributivity in the logic of quantum theory. This change results from defining the connectives, not truth-functionally, but in terms of a certain empirical ordering of propositions. Putnam has argued that the use of this ordering (“implication”) to govern proofs resolves certain paradoxes. But his resolutions are faulty; and in any case, the paradoxes may be resolved with no changes in logic. There is therefore no reason to regard the partially ordered set of propositions as a logic—i.e. as embodying a criterion for soundness of proofs. Its role in quantum theory ought to be understood in an entirely different way.