Measuring Meaning

In proof-theoretic semantics, the logical connectives derive their meaning from their proof rules, ‘meaning as use’. However, we argue that this view underdetermines when different rules confer the same meaning. To address this underdetermination, we propose measuring the use of a connective via its inference behaviour in a minimal derivability relation, ‘use as behaviour’. This allows us to analyse what parameters of the proof rules affect connective meaning. We use this methodology to build a novel proof-theoretic approach to meaning, called inference-behaviour semantics. To do so, we combine inferentialism with a novel form of methodological anti-exceptionalism, building on ideas from Gilbert Harman and Bogdan Dicher’s work on meaning-invariant logical pluralism. As a proof-of-concept, we apply this theory to measure connective meaning for a range of logics, including classical, intuitionistic, dual-intuitionistic, lattice logic and their relevant logic counterparts. This results in comprehensive connective semantics for the LK-family of logics