Chapter 12 - Vagueness, Uncertainty, and Degrees of Belief

Abstract

This chapter looks at objective probabilities, subjective probabilities, vague predicates, and degrees of belief. This separation of concerns allows to better determine appropriate representational mechanisms for less-than-categorical statements. Objective probabilities are about frequency. The kind of probability that deals with factual frequencies is called objective because it does not depend on who is assessing the probability and because this is a statistical view, it does not directly support the assignment of a belief about a random event that is not part of any obvious repeatable sequence. A key idea in probability theory is conditioning. The probability of one event may depend on its interaction with others. Because degrees of belief often derive from statistical considerations, and are referred to as subjective probabilities. Subjective probabilities and their computations work mechanically like objective ones, but are used in a different way. In the world of subjective probability two types of probability are defined relative to drawing a conclusion.