How good of you to read the book! I’m glad it wasn’t too unpleasant an experience.
Don’t you find that a bit harsh for the concept of “intrinsic”?
Maybe you haven’t yet reached the punch lines in the final chapter. There I lay out the view of intrinsic justifications we’ve been talking about here: they’re very valuable, but only as means toward outcomes with extrinsic support.
Yes, it is harsh!
I appreciate your AC example (if the math is better, change the concept!) but as I currently understand “intrinsic” we’re talking about the beloved MIC! Would you really trash the MIC for “good set theory”? (I guess I know your answer!)
You probably do: my answer is yes.
But a more serious worry is: What do we do if the axioms dessirable for “good set theory” conflict with those which are best for the foundations of math outside set theory? Large cardinals and determinacy are largely irrelevant to mathematics outside of set theory (so far!) so how do you know that they don’t obstruct other axioms that are good for the foundations of math outside of set theory? Are you prepared to give up on large cardinals and determinacy if that happens? (Of course when I say “you” I mean your friend, the Thin Realist.)
As I said the last time you asked this question, I don’t think we can decide this in advance of seeing the actual theories.