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ThrustVectoring comments on You only need faith in two things - Less Wrong Discussion
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I don't think this got mentioned, but I assume that it's really difficult (as in, nobody has done it yet) to go from "induction works" to "a large ordinal is well-ordered". That would reduce the number of things you have faith in from two to one.
I was staring at this thinking "Didn't I just say that in the next-to-last paragraph?" and then I realized that to a general audience it is not transparent that adducing the consistency of ZFC by induction corresponds to inducing the well-ordering of some large ordinal by induction.
Not transparent? This general audience has no idea what all this even means.
I was at least familiar with the concepts involved and conflated mathematical induction and evidential inductive reasoning anyways.
I can't even understand if the post is about pure math or about the applicability of certain mathematical models to the physical world.
From what I understand it's along the same lines as Bertrand Russel's search for the smallest set of axioms to form mathematics, except for everything and not just math.
If so, it makes little sense to me. Math is one tool for modeling and accurately predicting the physical world, and it is surely nice to minimize the number of axioms required to construct an accurate model, but it is still about the model, there is no well-ordering and no ordinals in the physical world, these are all logical constructs. It seems that there is something in EY's epistemology I missed.
...unless you are dealing with phenomena where it doesn't, like stock markets? Or is this a statement about the general predictability of the world, i.e. that models are useful? Then it is pretty vacuous, since otherwise what point would be there in trying to model the world?
"Believe" in what sense? That it is self-consistent? That it enables accurate modeling of physical systems?
I figured it out from context. But, sure, that could probably be clearer.