Beginning with a finite population of units and the judgment of exchangeability for units with respect to lifetime, we argue that measures of similarity lead to the appropriate probabilistic models for aging. This in turn implies that Schur-concavity of the joint probability function (or, more generally, the joint survival distribution) provides the correct probabilistic description of aging. Following this argument and using the principle of indifference, we argue that the appropriate probability models for life distributions conditional onaverage lifeare in a family of distributions that we call thegeneralized gamma distributions. If, on the other hand, we are interested in probabilistic models for aging conditional on averagelifetime maintenance cost, it follows from our development thatgeneralized Weibulldistributions are appropriate.