Belief and degrees of belief

Abstract

Degrees of belief are familiar to all of us. Our con\dence in the truth of some propositions is higher than our con\dence in the truth of other propositions. We are pretty con\dent that our computers will boot when we push their power button, but we are much more con\dent that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent\textbackslashtextquoteright\s degree of belief for a particular proposition, the higher her con\dence in the truth of that proposition. For instance, Sophia\textbackslashtextquoteright\s degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief.