This article is about formal models of belief and as such, there needs to be a certain amount of formal machinery introduced. There is a set of states \(\Omega\) which represents the ways the world could be. Sometimes \(\Omega\) is described as the set of “possible worlds”. The objects of belief—the things you have beliefs about—can be represented by subsets of the set of ways the world could be \(\Omega\). We can identify a proposition \(X\) with the set of states which make it true, or, with the set of possible worlds where it is true. If you have beliefs about \(X\) and \(Y\) then you also have beliefs about “\(X\cap Y\)”, “\(X \cup Y\)” and “\(\neg X\)”; “\(X\) and \(Y\)”, “\(X\) or \(Y\)” and “it is not the case that \(X\)” respectively. The set of objects of belief is the power set of \(\Omega\), or if \(\Omega\) is infinite, some measurable algebra of the subsets of \(\Omega\).