On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker <[email protected]> wrote:
> > > On 12/16/2018 1:56 PM, Jason Resch wrote: > > > > 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? > > > The difference is that mathematicians can't test their theories. > Sure they can: A set of axioms predicts a Diophantine equation has no solutions. We happen to find it does have a solution. We can reject that set of axioms. 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.
