Douglas writes: Suppose I want to discuss a particular phenomena or idea with a Bayesian. Suppose this Bayesian has set the prior probability of this phenomena or idea at zero.
What would be the proper gradient to approach the subject in such a case?
I would ask them for their records or proof. If one is a consistent Bayesian who expects to model reality with any accuracy, the only probabilities it makes sense to set as zero or one are empirical facts specificied at a particular point in space-time (such as: “I made X observation of Y on Z equipment at W time”) or statements within a formal logical system (which are dependent on assumptions and can be proved from those assumptions).
Even those kinds of statements are probably not legitimate candidates for zero/one probability, since there is always some probability, however minuscule that we have misremembered, misconstrued the evidence or missed a flaw in our proof. But I believe these are the only kinds of statements which can, even in principle have probabilities of zero or 1.
All other statements run up against possibilities for error that seem (at least to my understanding) to be embedded in the very nature of reality.
Douglas writes: Suppose I want to discuss a particular phenomena or idea with a Bayesian. Suppose this Bayesian has set the prior probability of this phenomena or idea at zero. What would be the proper gradient to approach the subject in such a case?
I would ask them for their records or proof. If one is a consistent Bayesian who expects to model reality with any accuracy, the only probabilities it makes sense to set as zero or one are empirical facts specificied at a particular point in space-time (such as: “I made X observation of Y on Z equipment at W time”) or statements within a formal logical system (which are dependent on assumptions and can be proved from those assumptions).
Even those kinds of statements are probably not legitimate candidates for zero/one probability, since there is always some probability, however minuscule that we have misremembered, misconstrued the evidence or missed a flaw in our proof. But I believe these are the only kinds of statements which can, even in principle have probabilities of zero or 1.
All other statements run up against possibilities for error that seem (at least to my understanding) to be embedded in the very nature of reality.