Orgulity is the opposite of humility. Not being a native speaker, I had to open a dictionary when I saw Gordon Belot’s paper “Bayesian Orgulity” (Philosophy of Science 2013).
This putative orgulity concerns two sorts of theorems about subjective probability, frequencies, and calibration. Informally put, the first sort shows that a Bayesian agent will, indeed must, be sure that his probabilities are the right ones, and that statistics would bear that out in the long run. “Sure” means here that in his self-assessment, he will give zero probability to the contrary. Equally informally put, the other sort of theorem shows that Bayesian agents will, in an overwhelming majority of possible cases, be wrong in just that respect.
All the makings of a true paradox!
Need we take it as a paradox? It could just stand as an indictment of Bayesian epistemology. The main arguments concern an orthodox Bayesian agent with a numerically precise prior probability function, whose sole updating means is conditionalization on data coming in with certainty (like the voice of an angel). So there is much to be complained about here already.
But the arguments are in some respects very general and would seem to indict much more liberal forms of probabilism as well.
I want to offer, at the end of the discussion, a resolution of the paradox, based on an idea which I already know to encounter a lot of resistance.
I’ve heard that early missionaries in Polynesia faced first of all the onerous task of convicting the natives of sin, before they could preach salvation. So, first of all, I’ll make a good effort to show that we are not dealing with narrow technical issue here, but with a paradox eminently worthy of taking seriously.
My plan for the posts to follow:
First, how is subjective probability related to actual frequencies? (How does a probabilist agent — whose opinion is represented by a subjective probability function — reply when asked about the relative frequencies of actual occurrences ‘in the world’?)
Second, what about self-assessment by such an agent? (If asked whether, or to what extent, his or her own opinions concerning the future are well-calibrated, how must s/he answer?)
Third, how does Belot present the Bayesian’s orgulity, and how badly do they fare given his results? (Spoiler: Belot takes the wind out of their sails if they seek refuge in the leeway between zero probability and impossibility.)
Fourthly, most importantly, are there different ways to read the results? (Must we take them as an indictment of probabilism, or of the idea of subjective probability, or can we, on the contrary, offer a narrative on which everything makes sense?)
Bas van Fraassen's philosophy blog 