Title：Omega

Spearker：Prof. Alan Hajek

Time：2020/11/17 (TUE) 15:00-16:30. 

Zoom Webinar ID: 831 4148 9830, Passcode: 047501 Link

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. My most recent project regarding probability is to put Ω in the spotlight; this is a progress report.

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. Along the way, I will question the notion of a ‘catch-all’ that is supposed to cover all possibilities that have not been explicitly identified. I will end with an omega dilemma: roughly, either orthodox probability theory breaks down, and must be rethought; or we need an account of how probabilities should be revised when a proposition that is not in Ω is learned.