[FOM] 511: A Supernatural Consistency Proof for Mathematics
Harvey Friedman
hmflogic at gmail.com
Mon Jan 14 16:14:21 EST 2013
As I stated in connection with concept calculus, the idea is to
formulate principles concerning the informal notions, and then show
that these principles correspond logically to ZFC in various rigorous
senses. That's what I do with the latest stuff, and have done in some
earlier contexts.
Harvey
On Mon, Jan 14, 2013 at 4:49 AM, Vaughan Pratt <pratt at cs.stanford.edu> wrote:
> On 1/13/2013 10:12 PM, Harvey Friedman wrote:
>>
>> Con(ZFC) is not a natural principle when thinking about rainbows,
>> horizons, and beauty.
>
>
> Harvey, if the principle is to be "mutually interpretable with ZFC" as you
> required then I don't see how it could be inconsistent with the physical
> phenomena of rainbows and horizons, which as far as I know are not disputed
> on any logical grounds.
>
> For beauty however I don't know where to turn but poetry. If beauty is
> truth and vice versa then one might conclude that if Con(ZFC) is not
> beautiful then it is not true.
>
> Four decades ago I occupied an office three doors down from Professor Gerry
> Sussman at MIT. Gerry consistently claimed he never claimed to be
> consistent. I was ok with at least that much since what I was doing didn't
> seem to depend on whether Gerry was consistent. In fact my work turned out
> better when he wasn't.
>
> Meanwhile I will continue to ponder the possibility you raise that
> consistency of ZFC is unnatural. Maybe ZFC itself is unnatural, but in that
> case scientists as students of nature might be motivated to look for a logic
> of science, as distinct from a logic of mathematics which is how I've been
> taught to understand ZFC.
>
> There is the further possibility that we're not even talking at cross
> purposes, which would be the exception to the usual rule.
>
> Vaughan
>
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