= 27d567bc2d48d9f40e9ccc20ea370b15)
Eliezer_Yudkowsky comments on You only need faith in two things - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (86)
Consider the following toy model. Suppose you are trying to predict a sequence of zeroes and ones. The stand-in for "induction works" here will be Solomonoff induction (the sequence is generated by an algorithm and you use the Solomonoff prior). The stand-in for "induction doesn't work" here will be the "binomial monkey" prior (the sequence is an i.i.d. sequence of Bernoulli random variables with p = 1/2, so it is not possible to learn anything about future values of the sequence from past observations). Suppose you initially assign some nonzero probability to Solomonoff induction working and the rest of your probability to the binomial monkey prior. If the sequence of zeroes and ones isn't completely random (in the sense of having high Kolmogorov complexity), Solomonoff induction will quickly be promoted as a hypothesis.
Not all Bayesian inference is inductive reasoning in the sense that not all priors allow induction.
To amplify on Qiaochu's answer, the part where you promote the Solomonoff prior is Bayesian deduction, a matter of logic - Bayes's Theorem follows from the axioms of probability theory. It doesn't proceed by saying "induction worked, and my priors say that if induction worked it should go on working" - that part is actually implicit in the Solomonoff prior itself, and the rest is pure Bayesian deduction.
Doesn't this add "the axioms of probability theory" ie "logic works" ie "the universe runs on math" to our list of articles of faith?
Edit: After further reading, it seems like this is entailed by the "Large ordinal" thing. I googled well orderedness, encountered the wikipedia article, and promptly shat a brick.
What sequence of maths do I need to study to get from Calculus I to set theory and what the hell well orderedness means?