Dear Sy,

We already know why CH doesn’t have a determinate truth value, it is because there are and always will be axioms which generate good set theory which imply CH and others which imply not-CH. Isn’t this clear when one looks at what’s been going on in set theory?

Well, I’m not sure it *is* clear that there will never be a theory whose virtues swamp the rest.

is CH one of the leading open questions of set theory?

No! The main reason is that, as Sol has pointed out, it is not a mathematical problem but a logical one. The leading open questions of set theory are mathematical.

I didn’t realize that you’d been convinced by Sol’s arguments here. My impression was that you thought it might be possible to resolve CH mathematically:

I started by telling Sol that the HP might give a definitive refutation of CH! You told me that it’s OK to change my mind as long as I admit it, and I admit it now!

That’s why I posed the question to you as I did.

All best,

Pen