Comparison of Medieval Logic with Contemporary Logic

Abstract

AbstractIt appears that the logic developed so far is weak without anaphoric pronouns, but with those pronouns it is as rich as ordinary first-order symbolic logic. It is easy to represent propositions of medieval logic, one at a time, within predicate logic with identity. One problem with representing modern logic within medieval logic concerns existential import; for example, a natural statement to the effect that less-than is transitive entails that something is less than zero. This can be avoided by some technical rephrases involving infinitizing negation. Representing modern logic within medieval logic raises problems because of the latter’s grammatical structure; these problems may be overcome. An algorithm is given for representing sentences of modern logic within medieval logic. In the last section an illustration is given of how first-order arithmetic would look if formulated within medieval logic.