Non-metric Propositional Similarity

The 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) is closer in meaning to p(2) than p(3) is to 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.

Automated summary

This paper proposes a novel approach for comparing the "distance" between pairs of propositions, providing a precise account of comparative propositional similarity facts without relying on unrealistic metric assumptions.