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Kawoomba comments on You only need faith in two things - Less Wrong
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Again, promoted how? All you know is "induction is very, very unlikely to work" (low prior, non 0), and "some single large ordinal is well-ordered". That's it. How can you deduce an inference system from that that would allow you to promote a hypothesis based on it being consistent with past observations?
It seems like putting the hoversled before the bantha (= assuming the explanandum).
Promoted by Bayesian inference. Again, not all Bayesian inference is inductive reasoning. Are you familiar with Cox's theorem?
Only in passing. However, why would you assume those postulates that Cox's theorem builds on?
You'd have to construct and argue for those postulates out of (sorry for repeating) "induction is very, very unlikely to work" (low prior, non 0), and "some single large ordinal is well-ordered". How?
Wouldn't it be: large ordinal -> ZFC consistent -> Cox's theorem?
Maybe you then doubt that consequences follow from valid arguments (like Carroll's Tortoise in his dialogue with Achilles). We could add a third premise that logic works, but I'm not sure it would help.
Can you elaborate on the first step?
I'm no expert in this -- my comment is based just on reading the post, but I take the above to mean that there's some large ordinal for ZFC whose existence implies that ZFC has a model. And if ZFC has a model, it's consistent.