On Sun, Jun 4, 2017 at 1:15 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> >> Anything that can be done a Turing Machine can do, if it can't be done >> then a Turing Machine can't do it, and neither can anything else. > > > > If "can be done" means "can compute or emulate", I am OK. That is > basically Church's Thesis. > > If by "can be done" mean solve a problem, or prove a theorem, then it is > an entirely different story. > If you were bound and determined to prove that the Halting Problem had a solution you could certainly find starting axioms that would allow you to construct that conclusion, but then you could also prove there was a one to one correspondence between the integers and the Real Numbers. Perhaps that doesn't frighten you but a proof is only as good as the axioms it starts with , so I want to be very very conservative with my choice of axioms because I'd rather there be true statements that have no proof they are true than false statements that do have a proof they are true. In the fist case you can't know everything for certain and that's a shame, but in the second case you can't know anything for certain and that's worse. 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 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.
