The weather report says that the chance of a hurricane arriving later today is 90 percent. Forewarned is forearmed: Expecting a hurricane, before leaving home I pack my hurricane lantern.

Probability enters into this scenario twice, first in the form of a physical probability, sometimes called a chance, quantifying certain aspects of the local weather that make a hurricane very likely, and second in the form of an epistemic probability capturing a certain attitude to the proposition that a hurricane will strike, in this case one of considerable confidence.

It is not immediately obvious that these two probabilities are two different kinds of thing, but a prima facie case can be made for their distinctness by observing that they can vary independently of one another: For example, if the meteorologists are mistaken, the chance of a hurricane may be very low though both they and...