Alan Hájek

Australian National University

###### Ω

**11 May 2018, 16:00**

**Faculdade de Letras de Lisboa**

**Sala Mattos Romão **(Departamento de Filosofia)

**Abstract:** Probability theory is the dominant approach to modeling uncertainty. We begin with a set of possibilities or outcomes, usually designated ‘Ω’. We then assign probabilities—real numbers between 0 and 1 inclusive—to subsets of Ω. Nearly all of the action in the mathematics and philosophy of probability for over three and a half centuries has concerned the probabilities: their axiomatization, their associated theorems, and their interpretation. I want instead to put Ω in the spotlight. Ω is a set of possibilities, but *which *possibilities? While the probability calculus constrains our numerical assignments, and its interpretation guides us further regarding them, we are entirely left to our own devices regarding Ω. What makes one Ω better than another? Its members are typically not exhaustive—but which possibilities should be excluded? Its members are typically not maximally fine-grained—but how refined should they be? I will discuss both philosophical and practical problems with the construction of a good Ω. I will offer some desirable features that a given Ω might have, and some heuristics for coming up with an Ω that has them, and for improving an Ω that we already have.