An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand's chord paradox than the principle of indifference. In this paper I show that it is not. 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.
Author’s contributions: Shackel 90%, Rowbottom 10%. In memoriam Michael Clark 1940–2019, whoshared our delight in the philosophical problems posed by paradoxes.