Chris_Leong comments on Probability as Minimal Map

• I hope that I’m not becoming that annoying person who redirects every conversation towards their own pet theory even when its of minimal relevance, but I think there are some very strong links here with my theory of logical counterfactuals as forgetting or erasing information (https://​​www.lesswrong.com/​​posts/​​BRuWm4GxcTNPn4XDX/​​deconfusing-logical-counterfactuals).

In fact, I wasn’t quite aware of how strong these similarities were before I read this post. Both probabilities* and logical counterfactuals don’t intrinsically exist in the universe; instead they seem to draw their existence from our epistemic situation. Zoom into the universe enough everything is deterministic and there is only one thing that an agent ever could have chosen; zoom out and there are multiple possibilities.

I’m currently writing a post where I’ll argue that logical counterfactuals are an answer and not a question and I think this applies to probability too. Both exist in the map and not in the territory; this means that they are human created terms that exist for human purposes. Arguing what they are or aren’t in the abstract indicates confusion; instead, we need to choose a purpose (or question) and then we can choose to notion appropriate to that. This is part of why these notions come apart with questions like Sleeping Beauty and Counterfactual Mugging.

*Okay, it kind of does under some theories of quantum mechanics, but lots of the discussion of probability uses probability to deal with a lack of complete knowledge as opposed to intrinsically existing uncertainty, which is of a different kind and can’t be explained by quantum mechanics

• That is highly relevant, and is basically where I was planning to go with my next post. In particular, see the dice problem in this comment—sometimes throwing away information requires randomizing our probability distribution. I suspect that this idea can be used to rederive Nash equilibria in a somewhat-more-embedded-looking scenario, e.g. our opponent making its decision by running a copy of us to see what we do.

Thanks for pointing out the relevance of your work, I’ll probably use some of it.