2012/12/17 meekerdb <[email protected]> > 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 >
ISTM that consistency is the fact that you can't have contradiction. Incompletness that you can't prove every proposition. Quentin > > > True entails consistency, but consistency does not entail truth. > > Bruno > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- All those moments will be lost in time, like tears in rain. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
