On Sun, Dec 16, 2018 at 4:14 PM Bruce Kellett <bhkellet...@gmail.com> wrote:
> On Mon, Dec 17, 2018 at 9:04 AM Jason Resch <jasonre...@gmail.com> wrote: > >> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett <bhkellet...@gmail.com> >> wrote: >> >>> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch <jasonre...@gmail.com> >>> wrote: >>> >>>> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker <meeke...@verizon.net> >>>> wrote: >>>> >>>>> >>>>> 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? >>>> >>> >>> Physical theories do not claim to prove theorems - they are not systems >>> of axioms and theorems. Attempts to recast physics in this form have always >>> failed. >>> >>> >> Physical theories claim to describe models of reality. >> > > Physical theories are models of reality -- using the word "model" in the > physicists sense. > > >> You can have a fully consistent physical theory that nevertheless fails >> to accurately describe the physical world, >> > > Like Brent's example of an axiomatic description of Trump...... > > >> or is an incomplete description of the physical world. Likewise, you can >> have an axiomatic system that is consistent, but fails to accurately >> describe the integers, or is less complete than we would like. >> > > Axiomatic system are always going to fail to capture everything we would > like to capture about any domain. That is why attempted axiomatisation of > physics have been rather unsuccessful. > > >> It is a completely analogous situation. If you hold the physical reality >> is real because we can study it objectively and refine our understanding of >> it through observations, >> > > That is not "why" I hold the physical world to be real. I take the > physical world to be real because that is the definition of reality. > There is no evidence that physics reality marks the end of our ability to explain anything deeper. > > >> then the same would hold for the mathematical reality. >> > > No, mathematical "reality" (note the scare quotes) is a derived realm, > entirely dependent on the set of axioms chosen in any instance. So it is > not in any way analogous to physics. > > Did you miss my earlier posts to Brent on this? The integers and their relations are not modeled by any axiomatic system, they transcend the axioms and therefore we must conclude have a reality independent from our attempts to model them. 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. 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.
