ABSTRACT
No strategy for solving Bertrand’s paradox has worked. In this chapter, for completeness I briefly explain two responses to Bertrand’s paradox that are available if one gives up certain views of probability: Bertrand’s original aim, finitism, and the position of ontologically objective theories of probability. I discuss whether our ultimate understanding should be that the paradox proves the principle false and I defend the continuing paradoxicality of the paradox.
I then propose my own an instance of the Entirely Unanswerable strategy. The negation of the principle of indifference means that events between which we have no epistemic reason to discriminate can have distinct epistemic probabilities, but that is impossible. And yet the paradox still stands, and the firmness with which it stands is shown both by the failures of the other strategies and by the unearthed root. Consequently, there is only one answer left: that the paradox is a proof that not all events have probabilities. I show that the proposal does not vindicate a renewed Distinction strategy and look at some literature compatible with it. We need to know where my proposal leaves the principle of indifference and in particular how it fits with its central commitment to epistemic reason. The rest of the chapter sketches this in. From our proportioning ground I derive a principle more general than the principle of indifference, the Principle of Rational Strength. Making some further assumptions about the nature of epistemic reasons proves the Principle of Rational Strength true and gives a principled restriction of the domain of the principle of indifference. I finish by articulating the general shape of my Entirely Unanswerable solution to Bertrand’s paradox and the chapter concludes with a brief summary of the book.
