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 wecannot really define it (with the CTM). We can approximate it inless 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 alwaysbeyond words, even the ultimate 3p truth.What would it mean to 'define truth'? We can define 'true' as aproperty 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".`

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.`

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?

`That just consistent. True entails consistency, but consistency does`

`not entail truth.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.