Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: Daryl McCullough (daryl_at_atc-nycorp.com)
Date: 01/12/05 

Date: 12 Jan 2005 03:53:01 -0800

Torkel Franzen says...
>
>"LordBeotian" <pokipsy76@CANCELLAMIyahoo.it> writes:
>
>
>> There is not a recursive procedure to assign names to costructive Ordinals.
>> We could obtain a NON-r.e. set of "possible recognizable truths" by
>> collecting the sentances "A is an ordinal" for any costructive
>> ordinal...
>
> What I was wondering was on what grounds Daryl took the notion of
>"possible truth recognizable to mathematicians" to be well-defined.
>What does it mean to "recognize" a mathematical truth, say of the
>form "for every natural number n, P(n)", where P is a mechanically
>decidable property.

I think you're making it more mysterious than it actually is. There
really are only a handful of tricks that mathematicians use to
try to determine the truth of a mathematical statement, and they
seem to be pretty much captured by ZFC, together with reflection-type
principles ("I believe ZFC, so Con(ZFC) is not much of a stretch".

Is there any reason to think that ZFC (or reflection-inspired
extensions) *doesn't* cover what mathematicians believe to be
solid mathematics? 

--
Daryl McCullough
Ithaca, NY

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