 for some positive real number \(r\) and constant \(c\). Given Ramsey’s background assumptions (6.1)–(6.3), these two points together entail that the subject’s preferences satisfy Ramsey’s conditions on preferences only if \(\mathcal{U}\) is the function that represents her utilities on an interval scale. Or, to put the point more simply: if the subject’s preferences satisfy Ramsey’s conditions, then they contain enough information to determine her utilities exactly.