Probabilities are not the right concept

Introduction. This sequence is an attempt to sketch a unified framework for several interconnected questions: Where do Bayesian priors come from? What even are probabilities? How should we deal with infinite ethics? What's going on with anthropics? I hope to lay out both some of the existing answers and my own preferred synthesis.[1]I understand that many people have already thought about these questions, and I have only read portions of the existing literature. I think most of what I will write here, even in the section about my preferred synthesis, is not novel. People whose writing I'm building on include Wei Dai, Paul Christiano, Joe Carlsmith, Scott Garrabrant and Richard Ngo. I've also listened to some people like Lukas Finnveden, Vivek Hebbar and Ryan Greenblatt talk about related topics, which was also influential on me.[2]However, most of the prior work is scattered across many, often very confusingly written blog posts, and I can't easily tell where I first came across various ideas I'm exploring here. Therefore, I will not try to do a full exegesis of where each idea came from, and will instead present the arguments as a unified flow, with only occasional direct references to the work of prior authors. It's also very possible that there are important insights that I missed that people have already written on these topics - in that case, feel encouraged to link to them in the comments.This first post will look at some possible definitions of probabilities and why I think they don't really work. Later posts will examine what we can best replace probabilities with.What even are probabilities?What do I mean when I say that I give a 10% probability that it's going to rain in my town tomorrow? This 10% probability doesn't refer to any tangible fact about the real world. Sure, there is some amount of objective randomness in whether it will rain or not tomorrow, due to quantum randomness. But I have no idea how big the quantum effects are on the weather tomorrow, a