On Wed, May 15, 2019 at 7:20 PM 'Brent Meeker' via Everything List < [email protected]> wrote:
> > > On 5/15/2019 7:39 AM, Jason Resch wrote: > > > > On Tue, May 14, 2019 at 7:29 PM 'Brent Meeker' via Everything List < > [email protected]> wrote: > >> >> >> On 5/14/2019 9:49 AM, Jason Resch wrote: >> >> What is truth? (Pontus Pilate). Arithmetical statements are true if they >>> are theorems derived from the axioms. >>> >> >> This is false. In every consistent system of axioms there are statements >> that are true but cannot be derived from the axioms. >> >> >> That's not true. There are axiomatic systems that are complete. >> > > > You are right, but in the above context we were speaking of arithmetical > statements, for which my statement is correct. > > >> >> In other words truth =/= proof, truth is always greater that what can be >> proved. >> >> >> That's because you have recourse to an idea of "true" that is outside of >> logical inference...such as "empirically true". >> > > Even entirely within the system there's such statements that you know are > true but not provable. > > > HOW do you know they are true? Because they say they are not provable? > > Brent > That's the trick Godel used to constructively build such statements, yes. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUi6jbm4Q2WuqKabQw%3D6W4Hs%2Bj12swm66GFVLLtzePbgBg%40mail.gmail.com.
