The Underlying Logic is Mandatory also in Discussing the Philosophy of Quantum Physics

Abstract

Any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not totally made explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory’s principles, mainly when described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory’s mathematical and logical concepts. We argue that no physical theory and no philosophical discussion based on the theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just ‘relational’ and that they cannot be absolutely identified by a monadic property, are fallacious once one remains within a ‘standard’ logico-mathematical framework, grounded on classical logic. We also discuss the (to us) unjustifiable claim that some properties (such as those that came from logic) would be ‘illegitimate’ for discerning these entities. Thus, this paper may interest logicians, physicists, and philosophers.