Polyadic Inductive Logic and Spectrum Exchangeability

Jeff Paris, University of Manchester. Part of the logic seminar series.

Inductive Logic ´a la Carnap & Johnson was founded on the idea that the probabilities we assign in our everyday lives may be logical in the sense that they are determined by our knowledge via general rationality considerations. As a potentially applicable topic Inductive Logic is nowadays widely considered by philosophers as having failed, largely on account of Nelson Goodman’s GRUE Paradox. However as a ‘pure’ mathematical investigation into rationality it survives and has recently seen some interesting developments. In particular the serious investigation into Polyadic Inductive Logic (Carnap et al only ever considered unary properties) has uncovered some new rational principles which appear to be remarkably powerful, even when reflected down to the unary level. In my talk I shall try to give a fairly informal introduction to one such principle.

Jeff Paris, University of Manchester