Scott Garrabrant

This post will just be a concrete math question. I am interested in this question because I have recently come tor reject the independence axiom of VNM, and am thus playing with some weaker versions. Let Ω be a finite set of deterministic outcomes. Let L be the space of...

This post will assume an understanding of the finite factored set ontology. It will be more speculative that the main FFS sequence, and I will leave out some proofs. It seems likely that I will later regret some of the definitions laid out here. I will be particularly sloppy in...

This post is partially in response to Critch's boundaries sequence. My best guess is that he would agree with most of it in theory, but disagree with some of it in practice due to tradeoffs with other considerations in defining the concepts. Boundaries and Frames Imagine a world consisting of...

Papers on Cartesian frames and factored sets are now on arXiv. Cartesian Frames: https://arxiv.org/abs/2109.10996 Factored Sets: https://arxiv.org/abs/2109.11513 The factored set paper is approximately identical to the sequence here, while the Cartesian frame paper is rewritten by Daniel Hermann and Josiah Lopez-Wild, optimized for an audience of philosophers.

We will now discuss several different applications and directions for future work on finite factored sets. We will divide these research directions into three categories: 'Inference,' 'Infinity,' and 'Embedded Agency.' This post will be much more speculative than the previous posts. It is very likely that some of these avenues...

The fundamental theorem of finite factored sets tells us that (conditional) orthogonality data can be inferred from probabilistic data. Thus, if we can infer temporal data from orthogonality data, we will be able to combine these to infer temporal data purely from probabilistic data. In this section, we will discuss...

In this post, given a finite factored set F=(S,B), we will show how to associate each E⊆S with a characteristic polynomial, QFE. We will discuss how to factor these characteristic polynomials, and use these characteristic polynomials to build up to the fundamental theorem of finite factored sets, which associates conditional...