On Mon, Feb 19, 2018 at 3:55 PM, Brent Meeker <meeke...@verizon.net> wrote:
> > Is there a non-constructive way to determine whether an axiomatic system > (axioms+inference rules) must be Goedel incomplete? Must one show that > arithmetic is a model or is there some simpler method? Any axiomatic system powerful enough to do arithmetic (and its not much use if it isn't) can't be both self consistent (that is to say there is not a proof in the system that something is true and also a proof that the same thing is false) and complete (there are true statements that have no proof). And if the system is self consistent there is no way to prove it is so while remaining in the system. John K Clark -- 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 email@example.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.