30th May 2013 at 2pm
Faculty of Philosophy
ON THE LOGICAL STRUCTURE OF DE FINETTI'S NOTION OF EVENT
Hykel Hosni (Scuola Normale Superiore di Pisa / London School of Economics)
The investigation reported in this talk aims at clarifying an important yet subtle distinction between (i) the logical objects on which measure theoretic probability can be defined, and (ii) the interpretation of the resulting values as rational degrees of belief.Our central result can be stated informally as follows. Whilst all subjective degrees of belief can be expressed in terms of a probability measure, the converse doesn't hold: probability measures can be defined over linguistic objects which do not admit of a meaningful interpretation as rational degrees of belief. The logical framework capable of expressing this will allow us to put forward a precise formalisation of de Finetti's notion of event which lies at the heart of the Bayesian approach to uncertain reasoning. This, in turn, will provide grounds for more general considerations on the relation between (subjective) probability and logic. (Based on joint work with Tommaso Flaminio and Lluis Godo).