ESRogs comments on You only need faith in two things - Less Wrong

22 Post author: Eliezer_Yudkowsky 10 March 2013 11:45PM

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Comment author: ESRogs 12 March 2013 12:42:21AM 2 points [-]

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.

Comment author: [deleted] 13 March 2013 08:47:10PM 1 point [-]

Can you elaborate on the first step?

Comment author: ESRogs 14 March 2013 01:11:53AM 0 points [-]

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.

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