A Puzzle About Partial Belief, by Alan Hajek (4 August 2011)

Philosophy Seminar Series: 4 August 2011, 2-4pm, Philosophy Resource Room; Speaker: Alan Hájek, Professor of Philosophy, Research School of Social Sciences, Australian National University; Moderator: Dr. Ben Blumson


Fill in the blank:

Truth is to belief, as ___ is to partial belief.

Orthodox Bayesianism requires exactly this much of you: your credences should be coherent—conform to the probability calculus—and they should change under the impact of new evidence by conditionalizing on that evidence. The scandal of orthodox Bayesianism is its extreme permissiveness, sanctioning as it does credences that are radically out of step with the world. We are hardly so tolerant when it comes to all-or-nothing beliefs: it is generally acknowledged that truth is a virtue (perhaps the most important one) that a belief may or may not have. What is the analogous virtue for a degree of belief?

Van Fraassen, Lange and others would fill in the blank by appeal to the notion of calibration, a measure of the extent to which degrees of belief track corresponding relative frequencies. I marshal several arguments against this answer. My own answer is:

agreement with objective chance.

Some will complain that the notion of chance is mysterious, or even nonsense. I reply by pointing out several things that we know about chance. The centerpiece of my argument is a ‘magic trick’: Give me any object, any number between 0 and 1 inclusive, and a specified accuracy, and I will use the object to generate an event whose chance is the number given to the accuracy specified.

hajekAbout the Speaker: Alan Hájek studied statistics and mathematics at the University of Melbourne (B.Sc. (Hons). 1982), where he won the Dwight Prize in Statistics. He took an M.A. in philosophy at the University of Western Ontario (1986) and a Ph.D. in philosophy at Princeton University (1993), winning the Porter Ogden Jacobus fellowship. He has taught at the University of Melbourne (1990) and at Caltech (1992-2004), where he received the Associated Students of California Institute of Technology Teaching Award (2004). He has also spent time as a visiting professor at MIT (1995), Auckland University (2000), and Singapore Management University (2005). Hájek joined the Philosophy Program at RSSS, ANU, as Professor of Philosophy in February 2005.

More information on the Philosophy Seminar Series can be found here. A list of past talks in the series can be found here.

Comments are closed.