We shall need to talk about decision making so we shall introduce a simple model of decisions in terms of gambles. We can view bounded real valued functions \(f\) as “gambles” that are functions from some set \(\Omega\) to real numbers. A gamble \(f\) pays out \(f(\omega)\) if \(\omega\) is the true state. We assume that you value each further unit of this good the same (the gambles’ pay outs are linear in utility) and you are indifferent to concerns of risk. Your attitude to these gambles reflects your attitudes about how likely the various contingencies in \(\Omega\) are. That is, gambles that win big if \(\omega\) look more attractive the more likely you consider \(\omega\) to be. In particular, consider the indicator function \(I_X\) on a proposition \(X\) which outputs \(1\) if \(X\) is true at the actual world and \(0\) otherwise. These are a particular kind of gamble, and your attitude towards them straightforwardly reflects your degree of belief in the proposition. The more valuable you consider \(I_X\), the more likely you consider \(X\) to be. Call these indicator gambles.