Alexander Pruss's Blog

Assume Molinism. Suppose T is a set of character traits that makes one be equipoised between freely taking and refusing a $5000 bribe for ...

Suppose infinitely many people independently roll a fair die. Before they get to see the result, they will need to guess whether the die sho...

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

Suppose that I uniformly randomly choose a number x between 0, inclusive, and 1, exclusive. I then look at the bits b 1 ,  b 2 , ... after...

Suppose you do two independent experiments, A and B , each of which uniformly generates a number in the interval I  = [0, 1). Here are som...

Say that a “spinner” is a process whose output is an angle from 0 ∘ (inclusive) to 360 ∘ (exclusive). Take as primitive a notion of unifor...

Here’s another problem with independence for friends of infinitesimal probabilities. Let ...,  X −2 ,  X −1 ,  X 0 ,  X 1 ,  X 2 , ... be a...

Suppose that a random variable X is uniformly distributed (in some intuitive sense) over some space. Then : P ( X  =  y )= P ( X  =  z ) ...

Consider the concept of a complete probabilistic characterization (CPC) of an experiment. It’s a bit of a fuzzy concept, but we can get som...

Suppose I independently randomly and uniformly choose X and Y between 0 and 1, not including 1 but possibly including 0. Now in the dia...

Thesis : If we stick to real-numbered probabilities, genuine independence of events A and B cannot be defined in terms of any condition o...

Here’s a quick argument that classical probability cannot capture all probabilistic phenomena even if we restrict our attention to phenomena...

It is often assumed that one couldn’t finitely specify a nonmeasurable set. In this post I will argue for two theses: It is possible that ...

Suppose that I am throwing a perfectly sharp dart uniformly randomly at a continuous target. The chance that I will hit the center is zero. ...

Here's a standard theistic argument against Platonism: If Platonism is true, then God is dependent on properties like divinity, goodness...

This is really very obvious, and no doubt in the literature, but somehow hasn't occurred to me until now. Suppose that a fair coin is to...

Suppose we have an infinite sequence of independent and fair coins. A betting portfolio is a finite list of subsets of the space of outcome...

Suppose infinitely many thin arrows are independently shot at a continuous target, with hitting points uniformly distributed over...

Williamson gave a lovely argument that infinitesimals can't capture the probability of an infinite sequence of heads in fair indepe...

This is an argument for the Axiom of Choice where the sets we're choosing from are all subsets of the real numbers. The argument ne...