According to Van Fraassen's Reflection Principle, a rational agent's
subjective probability for proposition A, on the supposition that his subjective probability for this proposition will equal r at some later time, must equal this same number r.So if you are rational and see that you will assign r to A later, you now already assign r to A.
It seems that Reflection can only be plausible if there is a uniquely rational subjective probability for every set of evidence where there is something one can rationally think (are there any where there isn't? interesting question). For suppose that given my evidence, I can be epistemically rational in assigning different probabilities r1 and r2 to some proposition A, but I have non-epistemic reasons for assigning r1 to A today and r2 tomorrow (they might actually be in a way epistemic--for instance, it could be that changing between these assignments will help me see things from different points of view). Then I am epistemically rational in assigning r1 today and planning to assign r2 tomorrow (I know I will get no new relevant evidence, let's say), and I could well be rational simpliciter. But my present subjective probability for A, on my prediction that I will assign r2 tomorrow, is still r1 and not r2.
So Reflection needs to be restricted to cases where there is a uniquely rational answer. I am wondering if this doesn't vitiate one of White's arguments against imprecise probabilities (see here for a careful discussion of that argument).
How does van Fraassen's idea of a "brute contingent fact" affect the new PSR?
ReplyDeletePresumably, the PSR is incompatible with the existence of such facts.
ReplyDeleteOK. Is there such a thing, or did van Fraassen have something else in mind than what I'm thinking?
ReplyDeleteMy philosophy professor brought up this objection, by the way. He used Avogadro's number as an example of a BCF.
Avogadro's number is presumably explained by more fundamental constants in physics.
ReplyDeleteBut the fundamental constants? Well, that's a big question. Physicists are very unhappy with thinking they're just brute contingent facts. They'd rather suppose a multiverse to explain them.