ABSTRACT
My earlier Principle of Indifference for Continua has been faulted qua principle of indifference for producing paradoxical probabilities. This critique defines the principle of indifference as a something, we yet know not what, that by its true definition, whatever that is, gives unique probabilities for possibilities of which we are equally ignorant. This amounts to the claim that uniqueness is a criterion of identity for the principle of indifference and is an instance of the Irrelevance strategy.
In the previous chapter I showed that uniqueness arises independently of the principle, being a requirement that epistemic objectivity places on a philosophical theory of probability that advances the principle of indifference. So uniqueness is a criterion of epistemic objectivity that applies to the principle of indifference but that is independent of and logically prior to the principle. Consequently determining a unique probability measure is not a matter of the principle of indifference’s identity but of its success, and of the success of a philosophical theory that uses it at being an epistemically objective theory. So in demanding that of its nature the principle picks out a unique probability measure, this solution mistakes a criterion of success for a criterion of identity.
