ARGUMENTS FOR PROBABILISM - OR NON-PROBABILISM?

Professor Alan Hájek (Research School of Social Sciences, ANU)

DATE: 2006-05-05
TIME: 11:00:00 - 12:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU

ABSTRACT:
I critically examine four well-known justifications of probabilism, the thesis that rational belief comes in degrees that must conform to the probability calculus. Each justification proceeds in two parts: 1) A mathematical theorem that is beyond dispute. 2) A philosophical argument that takes the theorem as a premise, and concludes with a statement of probabilism.

My criticisms have the following common core: the theorem in 1) is too weak to bear the burden placed on it by the philosophical argument in 2). In each case, the theorem has the form of a conditional with an existentially quantified consequent, which is in a certain sense a 'weak' claim:

Dutch Book Theorem IF your degrees of belief violate the probability calculus, then THERE EXISTS a set of bets, each of which you regard as fair, but which collectively guarantee your loss.

Representation theorem IF your preferences obey certain rationality axioms, then THERE EXISTS a utility/probability representation < U, P > according to which you maximize expected utilities as calculated by < U, P >.

Calibration theorem IF your degrees of belief violate the probability calculus, then THERE EXISTS a set of probabilities that are better 'calibrated' - that better track (in a certain sense) the corresponding frequencies.

Predictive accuracy theorem IF your degrees of belief violate the probability calculus, then THERE EXISTS a set of probabilities that are more predictively accurate.

From these 'weak' premises, a strong conclusion is derived: probabilism. Yet with equal justification, one could could derive the opposite conclusion: rational degrees of belief must VIOLATE the probability calculus. After all, 'mirror-images' of these theorems, which equally strongly support that conclusion, are also true. For example:

Mirror image of the Dutch Book Theorem IF your degrees of belief violate the probability calculus, then THERE EXISTS a set of bets, each of which you regard as fair, but which collectively guarantee your GAIN.

(and likewise for the other three theorems).

Why, then, is probabilism the right conclusion to draw, rather than its denial?

BIO:
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 history and philosophy of science at the University of Melbourne (1990) and philosophy at Caltech (1992-2004), receiving the ASCIT Teaching Award. He has also spent time as a visiting professor at MIT (1995) and Auckland (2000).

Hájek's research interests include the philosophical foundations of probability and decision theory, epistemology, the philosophy of science, metaphysics, and the philosophy of religion. A complete list of his publications can be found here (in PDF format). These include 'What Conditional Probability Could Not Be', Synthese 2003, for which he was awarded the American Philosophical Association's 2004 Article Prize, and "Waging War on Pascal's Wager", Philosophical Review 2003, which was selected by The Philosopher's Annual as one of the ten best articles in philosophy in 2003.

Hájek joined the Philosophy Program at RSSS, ANU, as Professor of Philosophy in February 2005.

http://philrsss.anu.edu.au/people-defaults/alanh/index.php3

MEDIA:
060505_hajek.pdf
060505_hajek_redirect.html

	Skip Navigation CECS Home \| ANU Home \| Search ANU \| HORUS \| Staff Home
	Seminars @ CECS ANU College of Engineering and Computer Science