[FOM] Why not NF?

Ben Crowell fomcrowell06 at lightandmatter.com
Mon Feb 20 07:49:07 EST 2006

Martin Davis wrote:
> NF suffers from at least two grave faults:
>1. It's inconsistent with AC

It seems as though half the results that depend on AC are ones we want
to be true, and the other half are pathological results that we wish
were false. If AC isn't true in NF, then to me, the relevant question
is which results from ZFC are no longer true in NF, and whether those are
the ones that we'd be just as happy not to believe in.

Also, NFU is consistent with choice.

>2. Cantor's theorem 2^x > x fails.
That seems natural in a set theory that includes a universal set. If
the whole point of NF/NFU/... is to allow proper classes, it seems
backwards to criticize it for something that's an inevitable consequence
of achieving its goal.

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