Resolving the Bayesian Problem of Idealization

version of S, so that g(x) = 0 correctly characterizes S A . Then the "y → 0" idealization functions to transform one description -viz., f(x,y) = 0 -into a (more) incomplete description -viz., g(x) = 0; and the "y → 0" idealization determines which details g(x) = 0 ignores about S and the respects in which S A is an abstract version of S. Provided that there is an appropriate relationship between S A and S itself, it is possible for g(x) = 0 to be true of S because, as an abstract description of S, g(x) = 0 need not be false of S. (More on this below.) This point generalizes: an idealized description need not be false if it is an abstract description, because it only purports to characterize real systems indirectly, based upon whether the abstract system it characterizes bears an appropriate relation to real systems. The preceding discussion highlights an important point, namely, that if idealized hypotheses are abstract descriptions, then the details they leave aside are determined by the idealizations used to obtain them. For instance, if the ideal gas law is an abstract description of real gases, then (among other things) it leaves aside details about interparticle forces. And if the law of motion for simple pendulums is an abstract description of real pendulum motion, then (among other things) it leaves aside details about the damping and pivot friction on real pendulums as well as the extension of real pendulum bobs.