> On 16 Dec 2018, at 03:07, Jason Resch <jasonre...@gmail.com> wrote: > > > > On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker <meeke...@verizon.net > <mailto:meeke...@verizon.net>> 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. However we can never > prove that the system doesn't prove anything false (within the theory itself).
Which implies some need of faith, intuition, etc. With mechanism we need only to agree on some axioms. We can only hope they are true, but for arithmetic, only Sunday philosopher fake to doubt them. Bruno > > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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 post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
