A Second Philosophy of Logic

Abstract

This essay begins with the commonsense view that the world contains many individual objects—with properties, standing in relations—a view confirmed by science, and defends it against those who claim that the scientific and commonsense perspectives conflict. These very general features of the world ratify a rudimentary logic as broadly applicable, short of the quantum realm, and developmental psychology reveals that our basic cognitive structures are equipped to detect them, presumably shaped by evolutionary pressures from the macro-world. This rudimentary logic is awkward, though, so two idealizations are added to generate classical first-order logic. Advocates of most deviant logics reject one or the other of these idealizations; their case depends on showing that the relevant idealization is damaging in a particular application and offering something better. Deviant logics intended for something other than the world (e.g., mathematical constructions, belief systems) can peacefully coexist.