Alexander Pruss's Blog

A couple of years ago I showed how to construct hyperreal finitely additive probabilities on infinite sets that satisfy certain symmetry co...

Standard Bayesianism requires regularity : it requires that I not assign prior probability zero to any contingent proposition. There are two...

It seems that the aphorism “Absence of evidence is not evidence of absence” is typically false. For if H is a hypothesis and E is the cla...

Abstract: Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the...

Suppose that a point is uniformly randomly choosen in the unit square. Then you learn that either the point lies on the diagonal y  =  x ...

In “Underdetermination of infinitesimal probabilities” , following a referee’s suggestion, I allow that qualitative (i.e., comparative) prob...

Suppose that we have some sort of (not merely real-valued) probability assignment P to the Lebesgue measurable subsets of the unit circle Ω...

Plausibly—though there are some set-theoretic worries that require some care if the language is rich enough—for a fixed language, there are...

Let G p be the law of gravitation that states that F  =  G m 1 m 2 / r p , for some real number p . There was a time when it was rational t...

It seems that every mathematical structure (there are some technicalities as to how to define it) could metaphysically be the correct descri...

For a totally ordered field K , say a hyperreal one, write x ≈ y (and say that they are approximately equal) provided that x − y is 0 ...

I spent the last week trying to get clear on the logical interconnections between a number of results about probabilities that are relev...

The brunt of a lot of my recent posts has been that there is no hope for Bayesian regularity if one requires natural invariance conditi...

Suppose that a point is uniformly chosen on the circumference of the circle T . Write A ≤ B for "the point is at least as l...

For probabilities that have values, regularity is normally defined as the claim that P ( A )>0 whenever A is non-empty. Given finit...

Normally, regularity is formulated as saying that P ( A )>0 for every non-empty A . But suppose that instead of working with numeric...

Given the Axiom of Choice, there is no translation invariant probability measure on the interval [0,1) (the relevant translation is tran...

Take regularity as the thesis that the rational agent assigns a probability of 0 only to impossible propositions and a probabilit...