That's an interesting point. I did wonder, after posting the above comment, whether frequentists, at least, are ipso facto committed to all probabilities being

That's an interesting point. I did wonder, after posting the above comment, whether frequentists, at least, are ipso facto committed to all probabilities being rational, on account of their insistence that they are only meaningful in the context of repeated trials? (FWIW, I lean towards the frequentist viewpoint, insofar as I have a coherent position on the issue.) But then, what are we to make of physical formulae in which complex, transcendental and other non-rational numbers appear? Are they 'just' tractable approximate models of physical reality? I guess the Maxwell-Boltzmann distribution, at least, could be fairly characterized as such.