The Principle of Indifference for Sets

We take an excursion into the elements of measure theory that I will need and define namings and renamings of events in terms of functions to mathematical objects, showing the relation of renamings to Paris’s renaming principle. With this material in hand I am able to define the subordinate Principle of Indifference for Sets that applies to sets of events, including continuum-sized sets. This definition brings into view the two distinct roles played by measures in the principle of indifference, one a logically prior role that I call the normative measure role and the other a logically posterior role defining probabilities. I discuss briefly the context and relevance of alternative axiomatizations of quantitative probability.