On the Adequacy of a Substructural Logic for Mathematics and Science

Abstract Williamson argues for the contention that substructural logics are ‘ill-suited to acting as background logics for science’. That contention, if true, would be very important, but it is refutable, given what is already known about certain substructural logics. Classical Core Logic is a substructural logic, for it eschews the structural rules of Thinning and Cut and has Reflexivity as its only structural rule. Yet it suffices for classical mathematics, and it furnishes all the proofs and disproofs one needs for the hypothetico-deductive method in science. We explain exactly what Classical Core Logic is, why it is a substructural logic par excellence, and what the basic requirements would be for a logic to be ‘suited to acting as [a] background logic for science’. We also explain how Classical Core Logic meets all these requirements. We end by examining Williamson’s argument in order to expose where its error lies.