My two favorite statisticians back in grad school, Jaynes and David Wolpert, both had declarations of independence from infinity, deeming finite sets adequate for human purposes, and extensions to infinity (and beyond!) as an exercise left to the interested reader.
I see this trend all the time. A claim that "mathematics proves" something in the real world, couple with lots of equations, but a complete dismissal of questions like "And where have you shown that your mathematics accurately models the world?" If I had more energy and talent, I'd write a poem - Sylvester's got a Slide Rule.
Today's post, Trust in Bayes was originally published on 29 January 2008. A summary (taken from the LW wiki):
There is a long history of people claiming to have found paradoxes in Bayesian Probability Theory. Typically, these proofs are fallacious, but correct seeming, just as apparent proofs that 2 = 1 are. But in probability theory, the illegal operation is usually not a hidden division by zero, but rather an infinity that is not arrived as a limit of a finite calculation. Once you are more careful with your math, these paradoxes typically go away.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was The "Intuitions" Behind "Utilitarianism", and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.