ABSTRACT
The Maximum Entropy Principle can be considered as a refinement and generalization of the principle of indifference: they agree on cases to which the latter principle applies whilst the former can yet be used where the latter has no purchase. Its application to the paradox is an instance of the Well-posing strategy. Since it constitutes a way of evaluating all possible probability measures for how well they respect our equal ignorance of the chords and then choosing one that does so maximally, it counts as an instance of the Well-posing strategy pursued by use of meta-indifference.
Apart from the paper upon which this chapter draws, there is no literature examining whether the Maximum Entropy principle is able to resolve Bertrand’s paradox. Indeed, there is no literature even showing how the Maximum Entropy principle can get a purchase on the paradox. In this chapter, I show that even under the most favourable assumptions allowing for that purchase, Bertrand’s chord paradox undermines the Maximum Entropy principle. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique to the Maximum Entropy principle.
