In the infinite case there is still the problem of how to get an infinite number of equally-weighted hypotheses to sum to probability 1. But this is what Measure Theory does, I believe. (I’m not a mathematician, but this is what I’ve read and been told.) So it isn’t a problem, any more than math is a problem.
I am a mathematician, and yes measure theory can do this, but it will require you to make many (in fact infinitely many) arbitrary choices along the way.
Huh. Okay, thanks for the info. This is troubling, because I have long held out hope that SI would not turn out to be arbitrary. Could you direct me to where I can learn more about this arbitrariness in measure theory?
I am a mathematician, and yes measure theory can do this, but it will require you to make many (in fact infinitely many) arbitrary choices along the way.
Huh. Okay, thanks for the info. This is troubling, because I have long held out hope that SI would not turn out to be arbitrary. Could you direct me to where I can learn more about this arbitrariness in measure theory?