Non-metric Propositional Similarity

Abstract

AbstractThe idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘$$p_1$$ p 1 is closer in meaning to $$p_2$$ p 2 than $$p_3$$ p 3 is to $$p_4$$ p 4 ’ and thereby give a precise account of comparative propositional similarity facts. Notably, our definition eschews metric assumptions, which are unrealistic in most applications of interest.