> On 10 Feb 2021, at 04:26, Alan Grayson <[email protected]> wrote: > > https://www.sciencealert.com/scientists-invented-a-machine-that-generates-mathematics-we-ve-never-seen-before
Interesting. It illustrates that machine can learn to ask “interesting” questions, and amusingly, let the hard work of answering them to human mathematicians. Some day, a machine will come with a new cardinal, closer to the Kunen bound, bigger than the Laver cardinal (at the edge of the set theoretical universe). But even such a machine can only justify an infinitesimal portion of the arithmetical reality, or even of the PI_1 arithmetical reality, because if such machine is inconsistent, even Q (RA) will know it. Q has no idea what a large cardinal is, but it has a precise idea of what is a machine which believes in ZFC + a cardinal of Laver exists. Emulating is not interpreting. Anyone can emulate Einstein brain, but that does not mean anyone can understand what Einstein says. Q believe that PA can prove Q’s consistency, but that does not help Q, really. I remind Q is just first order predicate calculus + the axioms: 0 ≠ s(x) s(x) = s(y) -> x = y x = 0 v Ey(x = s(y)) x+0 = x x+s(y) = s(x+y) x*0=0 x*s(y)=(x*y)+x Bruno > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/f213f56e-0bbf-451e-876a-38f99416d738n%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/f213f56e-0bbf-451e-876a-38f99416d738n%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/62F6FAB8-88E2-444F-9834-880546F21314%40ulb.ac.be.
