Hardy-type "proofs" or paradoxes as true-implies-false gadgets

Abstract

Hardy-type arguments are presented uniformly by enumerating the orthogonality hypergraphs that underly their structure. The resulting collection of observables, if interpreted classically, induce a true-implies-false relation to the respective observable terminal points of the hypergraph. Such relations have already been used by Kochen and Specker, Stairs and Clifton, but for a single quantum in dimension three and higher, and not among entangled quanta. They can be extended to true-implies-true gadgets and even to propositional structures which are very special in that they still allow classical predictions but do no longer support any faithful classical embeddability.