On Mon, Dec 17, 2018 at 9:04 AM Jason Resch <[email protected]> wrote:
> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett <[email protected]> > wrote: > >> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch <[email protected]> wrote: >> >>> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker <[email protected]> >>> 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. > 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. Bruce -- 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.
