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.
Believing that a mathematical system has a model usually corresponds to believing that a certain computable ordinal is well-ordered (the proof-theoretic ordinal of that system), and large ordinals imply the well-orderedness of all smaller ordinals.
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.
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.