Bangu (2010) claims that Bertrand’s paradox rests on a hitherto unrecognized assumption, which assumption is sufficiently dubious to throw the burden of proof back onto ‘objectors to [the principle of indifference]’ (2010: 31). We show that Bangu’s objection to the assumption is ill-founded and that the assumption is provably true.

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Bangu discerns a ‘common structure’ in some of Bertrand’s paradoxes:

One begins with a variable x… and then one considers a scaling transformation θ such that x′=θ(x). (Bangu 2010: 31)

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Speaking in these terms on Bertrand’s behalf, we construe his objection to the principle of indifference thus: The second premiss might be rejected: we might have an empirical situation in which the transformed variable is a causally dependent variable, in...

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