Fri Feb 21, 2020
Rohan French (UC Davis)
First Steps in a Theory of Metainferences
According to the nonreflexive approach to the semantic paradoxes presented in French (2016), no inference is, strictly speaking, valid. Nonetheless, there are a number of inference, such as that from a pair of sentences to their conjunction, which strike many of us as being valid. In order to account for this, it is argued in French (2016) that what we are really judging to be valid are metainferences—relations between sets of inferences and inferences. In this talk I’ll introduce the notion of a metainference, providing a partial taxonomy of the kinds of formal objects we might take them to be, and how we might reason about them semantically, before going on to provide a proof-system which treats metainferences as first-class citizens, showing it to be sound and complete with respect to a particular notion of validity for metainferences.