'Staying Regular,' HPS Seminar

Arts West North Wing 553 (Discursive Space)

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Fiona Fidler

fidlerfm@unimelb.edu.au

Professor Alan Hajek, Philosophy, ANU

‘Regularity’ conditions provide bridges between possibility and probability. They have the form:

If X is possible, then the probability of X is positive

(or equivalents). Especially interesting are the conditions we get when we understand ‘possible’ doxastically, and ‘probability’ subjectively. I review several arguments for regularity as a rationality norm. An agent could violate this norm in two ways: by  assigning probability zero to some doxastic possibility, and by failing to assign probability altogether to some doxastic possibility. I argue for the rationality of each kind of violation.

Both kinds of violations of regularity have serious consequences for traditional Bayesian epistemology. I consider their ramifications for:

  • conditional probability
  • conditionalization
  • probabilistic independence
  • decision theory