[FOM] Tolerance Principle

Harvey Friedman friedman at math.ohio-state.edu
Wed Feb 8 02:44:23 EST 2006

On 2/7/06 10:40 PM, "Bill Taylor" <W.Taylor at math.canterbury.ac.nz> wrote:

> Harvey Friedman <friedman at math.ohio-state.edu> writes:
> ->As I have mentioned many times before on the FOM, it appears from experience
> ->that any for any two natural formal systems, each of which interprets a
> ->small amount of arithmetic (or set theory), one of them is interpretable in
> ->the other. The two systems are based on first order predicate calculus, but
> ->may have entirely different languages.
> Does this also apply between Quine's NF and ZFC?

For almost all pairs of such natural formal systems that have been presented
in the literature, we know that one is interpretable in the other.

NF and ZFC is an exception. I don't know if one of them is interpretable in
the other. I'm nearly certain that nobody else knows, either.

My best guess is that NF is interpretable in ZFC but not vice versa.

Harvey Friedman

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