## LESSWRONGLW

Eliezer Yudkowsky wrote this article a while ago, which basically states that all knowledge boils down to 2 premises: That "induction works" has a sufficiently large prior probability, and that there exists some single large ordinal that is well-ordered.

# 1

Notes :

• "Epistemy" refers to the second meaning of epistemology : "A particular theory of knowledge".
• I'm more interested in ideas to further the thoughts exposed here than exposing them.

## Good Experiments

The point of "Priors are useless" is that if you update after enough experiments, you tend to the truth distribution regardless of your initial prior distribution (assuming its codomain doesn't include 0 and 1, or at least that it doesn't assign 1 to a non-truth and 0 to a truth). However, "enough experiments" is magic :

1. The pure quantitative aspect : you might not have time to do these experiments in your lifetime.
2. Having independent experiments is not defined. Knowing which experiments are pairwise independent embeds higher-level knowledge that could easily be used to derive truths directly. If we try to prove a mathematical theorem, comparing the pairwise success probability correlations of different approaches would give much more insights and results than trying to prove it as usual.
3. We don't need pairwise independence. For instance, assuming we assume P=/=NP because we couldn't prove it, we assume so because we expect all used techniques not to be all correlated together. However, this expectation is ether wrong (Small list of fairly accepted conjectures that were later disproved), or stems from higher-order knowledge (knowledge about knowledge). Infinite regress.

## Good Priors

However, conversely, having a good prior distribution is magic too. You can have a prior distribution affecting 1 to truths, and 0 to non-truths. So you might want the additional requirement that the prior distribution has to be computable. But there are two problems :

1. There aren't many known computable prior distribution. Occam's razor (in term of Kolmogorov complexity in a given language) is one. But fails miserably in most interesting situations. Think of poker, or a simplified version thereof : A+K+Q. If someone bets, the simplest explanation is that he has good cards. Most interesting situations where we want to apply bayesianism are from human interactions (we managed to do hard sciences before bayesianism, and we still have troubles with social sciences). As such, failing to take into account bluff is a big epistemic fault for a prior distribution.
2. Evaluating the efficiency of a given prior distribution will be done over the course of several experiments, and hence requires a higher order prior distribution (a prior distribution over prior distributions). Infinite regress.

## Epistemies

In real-life, we don't encounter these infinite regresses. We use epistemies. An epistemy is usually a set of axioms, and a methodology to derive truths with these axioms. They form a trusted core, that we can use if we understood the limits of the underlying meta-assumptions and methodology.

Epistemies are good, because instead of thinking about the infinite chain of higher priors every time we want to prove a simple statement, we can rely on an epistemy. But they are regularly not defined, not properly followed or not even understood. Leading to epistemic faults.

## Questions

As such, I'm interested in the following :

• When and how do we define new epistemies ? Eg, "Should we define an epistemy for evaluating the Utility of actions for EA ?",  "How should we define an epistemy to build new models of human psychology ?", etc.
• How to account for epistemic changes in Bayesianism ? (This requires self-reference, which Bayesianism lacks.)
• How to make sense of of Scott Alexander's yearly predictions ? Is it only a blackbox telling us to bet more on future predictions, or do we have a better analysis ?
• What prior distributions are interesting to study human behavior ? (For a given restricted class of situations, of course.)
• Are answers to the previous questions useful ? Are the previous questions meaningful ?

I'm looking for ideas and pointers/links.

Even if your thought seems obvious, if I didn't explicitly mention it, it's worth commenting it. I'll add it to this post.

Even if you only have idea for one of the question, or a particular criticism of a point made in the post, go on.

Thank you for reading this far.