On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker <[email protected]> wrote:
> > > On 12/15/2018 10:24 PM, Jason Resch wrote: > > > > On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker <[email protected]> > wrote: > >> >> >> On 12/15/2018 6:07 PM, Jason Resch wrote: >> >> >> >> On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker <[email protected]> >> wrote: >> >>> >>> >>> On 12/15/2018 5:42 PM, Jason Resch wrote: >>> >>> hh, but diophantine equations only need integers, addition, and >>>> multiplication, and can define any computable function. Therefore the >>>> question of whether or not some diophantine equation has a solution can be >>>> made equivalent to the question of whether some Turing machine halts. So >>>> you face this problem of getting at all the truth once you can define >>>> integers, addition and multiplication. >>>> >>>> >>>> There's no surprise that you can't get at all true statements about a >>>> system that is defined to be infinite. >>>> >>> >>> But you can always prove more true statements with a better system of >>> axioms. So clearly the axioms are not the driving force behind truth. >>> >>> >>> And you can prove more false statements with a "better" system of >>> axioms...which was my original point. So axioms are not a "force behind >>> truth"; they are a force behind what is provable. >>> >>> >> There are objectively better systems which prove nothing false, but allow >> you to prove more things than weaker systems of axioms. >> >> >> By that criterion an inconsistent system is the objectively best of all. >> >> > The problem with an inconsistent system is that it does prove things that > are false i.e. "not true". > > >> However we can never prove that the system doesn't prove anything false >> (within the theory itself). >> >> >> You're confusing mathematically consistency with not proving something >> false. >> > > They're related. A system that is inconsistent can prove a statement as > well as its converse. Therefore it is proving things that are false. > > > But a system that is consistent can also prove a statement that is false: > > axiom 1: Trump is a genius. > axiom 2: Trump is stable. > > theorem: Trump is a stable genius. > So how is this different from flawed physical theories? 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
