I don't like these types of truth predicates since they are Platonic in
their assumptions, as if statements do not even involve or relate to finite
entities like ourselves or, more relevant to my own work, real world
computers. Consider a paper by Lou Kauffman that considers a local notion
of truth values that can oscillate:
On Sat, Dec 21, 2013 at 5:28 PM, meekerdb <meeke...@verizon.net> wrote:
> On 12/21/2013 1:26 AM, Jason Resch wrote:
> If there exists a mathematical theorem that requires
>> a countable infinity of integers to represent, no finite version can exist
>> of it, in other words, can its proof be found?
> If its shortest proof is infinitely long, or if the required axioms
> needed to develop a finite proof are infinite, (or instead of infinite, so
> large we could not represent them in this universe), then its proof can't
> be found (by us), but there is a definite answer to the question.
> The other possibility is that there are mutually inconsistent axioms that
> can be added. As I understand it, that was the point of
> A truth predicate can be defined for arithmetic, but not all models or
> arithmetic are the same as the standard model.
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Stephen Paul King
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