Non-metric Propositional Similarity
Alexander Paseau
Abstract
Abstract 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 ‘ $$p_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> is closer in meaning to $$p_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> than $$p_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> is to $$p_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> ’ 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.