Capturing Consequence

Alex Paseau (Oxford University)

The ability to capture implicational structure is a significant virtue in a logic. First-order formalisations are for instance often preferred to propositional ones because they are thought to underwrite the validity of more natural-language arguments than the latter.

My talk will compare and contrast the ability of some well-known logics---propositional and first-order in particular---to capture the implicational structure of natural language. Surprisingly, there is a precise and important sense in which first-order logic does not improve on propositional logic as far as respecting natural-language validity is concerned. The correct way to state the oft-cited superiority of first-order logic vis-à-vis propositional logic is more nuanced. I shall articulate this and other philosophical morals. The question, informally, is whether the implicational structure of natural language can 'fit' into a particular logic, and how 'capacious' in this regard various well-known logics are.