[FOM] Fwd: 546: New Pi01/solving CH

[Harvey Friedman]

Mitchell Spector wrote:

"There's something appealing about an Occam's razor approach, as
Harvey Friedman recently proposed (each time you're faced with two
alternative possibilities, pick the simpler of the two).

However... Maybe I'm missing something, but wouldn't "ZFC is
inconsistent" be preferred over "ZFC is consistent" (over ZFC, of
course)?  "Preferred" here is to be taken in Harvey's technical sense.

[Needless to say, I'm assuming that ZFC actually is consistent.]"

Two comments.

1. I said that the Sigma sides are lower than Pi sides, all things
being equal. That was an error. The Pi sides are lower than the Sigma
sides. That takes care of the particular kind of example that you
raised.

2. Even beyond that, I was careful to say that you get to list your
favorite MATHEMATICAL
set theoretic questions, in order, and even experiment with that
order.

Is Con(ZFC) your favorite mathematical question? It's not a
mathematical question at all, or if it is one, it's probably not your
favorite one. I also mentioned that one can list these mathematical set
theoretic questions in order of, say, Google Scholar hits.

Harvey