Douglas, if your interlocutor is a really consistent Bayesian and has a probability estimate of exactly zero for whatever-it-is then I advise you to talk to someone else instead. If (as is more commonly the case) their prior is merely very small, then what you need to do is to present them with evidence that brings their posterior probability high enough for them to think it worthy of further discussion.
This is in fact exactly the problem you face when discussing anything with anyone (Bayesian or not) who finds your position or some part of it wildly improbable. At least a Bayesian is (in principle) committed to taking appropriate note of evidence.
Constant, I think even the strictest subjective Bayesian should be happy to agree that in the presence of suitable symmetries the only sensible prior may be determined by those symmetries, and that in such cases you can save some mental effort by just talking about the symmetries. Just as you can talk about the axioms of number theory or logic or whatever even if you think they’re really empirical generalizations rather than descriptions of Platonic Mathematical Reality, and usually when doing mathematics it’s appropriate to do so.
Douglas, if your interlocutor is a really consistent Bayesian and has a probability estimate of exactly zero for whatever-it-is then I advise you to talk to someone else instead. If (as is more commonly the case) their prior is merely very small, then what you need to do is to present them with evidence that brings their posterior probability high enough for them to think it worthy of further discussion.
This is in fact exactly the problem you face when discussing anything with anyone (Bayesian or not) who finds your position or some part of it wildly improbable. At least a Bayesian is (in principle) committed to taking appropriate note of evidence.
Constant, I think even the strictest subjective Bayesian should be happy to agree that in the presence of suitable symmetries the only sensible prior may be determined by those symmetries, and that in such cases you can save some mental effort by just talking about the symmetries. Just as you can talk about the axioms of number theory or logic or whatever even if you think they’re really empirical generalizations rather than descriptions of Platonic Mathematical Reality, and usually when doing mathematics it’s appropriate to do so.