Congrats to the perfect definition.
Add to it (my) agnostic position that we know only part of everything and
nobody will talk "truth".
To Brent: about "FACTS"? the facts we see(?) are similarly only model
related (partially understood).
JM

On Mon, Dec 17, 2012 at 4:02 PM, meekerdb <meeke...@verizon.net> wrote:

>  On 12/17/2012 11:47 AM, Bruno Marchal wrote:
>
>
>  On 16 Dec 2012, at 20:28, meekerdb wrote:
>
>  On 12/16/2012 2:31 AM, Bruno Marchal wrote:
>
> No. With the CTM the ultimate truth is arithmetical truth, and we cannot
> really define it (with the CTM). We can approximate it in less obvious
> ontologies, like second order logic, set theory, etc. But with CTM this
> does not really define it.
> Don't confuse truth, and the words pointing to it. Truth is always beyond
> words, even the ultimate 3p truth.
>
>
> What would it mean to 'define truth'?  We can define 'true' as a property
> of sentence that indicates a fact.
>
>
> That's the best definition of some useful local truth. But when doing
> metaphysics, you have to replace facts by "facts in some model/reality".
>
>
> OK. But then it's "True relative to the model." and it's not necessarily
> The Truth.
>
>
>
>
>  But I'm not sure how to conceive of defining mathematical 'true'.
>
>
> It is the object of model theory. You always need to add more axiom in a
> theory to handle its model. You cannot define the notion of truth-about-set
> in ZF, but you can define truth-about-set in ZF in the theory ZF +kappa
> (existence of inaccessible cardinals).
>
> PA can define all the notion of truth for the formula with a bounded
> restriction of the quantification.
>
>
>
> So what is that definition?
>
>
>
>
>
>
>  Does it just mean consistent with a set of axioms,
>
>
> No. That means only having a model. true in some reality. But for
> arithmetic "true" means satisfied by the usual structure (N, +, *).
>
>
>
>  i.e. not provably false?
>
>
> How is not provably false different from 'satisfied by the usual
> structure'? Can you give an example?
>
>
> That just consistent.
>
>
> I would think it was incompleteness.  Consistency means not being able to
> prove every proposition.  But in a consistent system there can be
> propositions that are neither provable nor disprovable.  Are those true?
>
> Brent
>
>
>  True entails consistency, but consistency does not entail truth.
>
> Bruno
>
>
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