On Mon, Jul 3, 2017 at 6:18 AM, Bruno Marchal <[email protected]> wrote:
>>> >>> there is no proof that such larger prime number don't exist in the >>> theory RA: >> >> > >> >> Then theory RA sucks. > > > > > It is a very useful theory > Useful maybe, but " *very* *"* useful? There is no largest prime number, if RA can't prove there is no largest prime number then it is weaker than another axiomatic system that can. > > You could say that E. Coli sucks because it cannot write english. > Exactly. E. Coli is less useful at writing English literature than William Shakespeare was because The Bard of Avon had more literary power than bacteria does. As a poet E. Coli sucks. > > > RA can (and do) emulate PA, and all other Löbian machine including us. > I wish you's stop talking about that, even Google doesn't know what a "Löbian machine" is. Turing explained exactly how to build one of his machines but I've never heard the construction details on just how to manufacture one of your "Löbian machines". > > It is good to keep in mind that emulating is not the same as proving or > believing. RA can prove that PA can prove RA's consistency, but that does > NOT make RA able to prove its own consistency > Nothing powerful enough to do arithmetic can prove it's own consistency; and if it is consistent then there are true statements that it can't prove. 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 [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.
