ABSTRACT
I examine two instances of the Irrelevance strategy. The first is from Bangu objecting to the assumption that randomness of a variable gives randomness of a scaling of that variable. Bangu addresses only the square paradox. I add a general premiss about the transmission of randomness to extend the objection to the chord paradox. I finish by showing that, in fact, randomness does transmit across event entailment.
I then turn to the main contender for the Irrelevance strategy: Gyenis and Rédei’s classical interpretation of probability. Supplementing their interpretation with a distinction between what they call labelling invariance and labelling irrelevance, they claim thereby to show that the paradoxes that have troubled classical probabilism are defused. In particular, they claim that their interpretation shows Bertrand’s paradox should be diagnosed as nothing more than a restatement of a fact from measure theory. As such, they contend, the paradox is irrelevant to the question of the consistency of their interpretation and consequently it can be rejected rather than solved. In short, they claim that their interpretation defuses Bertrand’s paradox. Here I refuse their defusal. I show that the Gyenis and Rédei’s use of their distinction incurs a significant philosophical cost and cannot do the job they require of it. Consequently their defusal fails completely and their classical interpretation contradicts one of its own normative commitments, making it internally inconsistent. Their attempt at the Irrelevance strategy fails and leaves Bertrand’s paradox ready to detonate.
