> On 16 May 2019, at 01:20, 'Brent Meeker' via Everything List > <everything-list@googlegroups.com> 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 >> <everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>> >> 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?
The Gödelian sentences are know to be true, because as humans we believe that PA’s axiom are true. That entails their truth, although not probably so for PA, which cannot prove its own truth/correctness. But there might be other reason, notably for other sentences, like the fact that the Goodstein sequence converge, or that Hercule wins the hydras, etc. No mathematicians doubt those theorem, because thy use stringer theory than PA all the times. We don’t use formal theory to do mathematics. Mathematics is always done informally, even by logicians. We study formal theory like biologist study DNA and brains. You would not attack a neurophysiologist theory of brain just because they use a brain to produce it OK? Bruno > > Brent > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/1f08ad00-890c-8802-175f-73235c7b4d2e%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/1f08ad00-890c-8802-175f-73235c7b4d2e%40verizon.net?utm_medium=email&utm_source=footer>. -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/B2E7E06D-E370-469F-8F0A-DCD78FA27A6C%40ulb.ac.be.
