Séminaire Philmath

« When Rules Define Logical Operators: Rules as Second-Order Definitions »

 

Résumé : Logical inferentialists hold that the meaning of logical operators is given by their rules of inference. Arthur Prior cast doubt on this by introducing rules for his tonk operator that would allow for the derivation of any sentence whatsoever from any sentence whatsoever. The obvious inferentialist reply was to require some constraints on the defining rules, such as conservativeness (Belnap) or harmony (Dummett). In this talk, I will defend and investigate a different constraint: rules define a classical logical operator just in case they translate into an explicit definition in pure classical second-order logic.