> On 11 May 2019, at 01:02, Bruce Kellett <[email protected]> wrote: > > On Fri, May 10, 2019 at 11:42 PM Jason Resch <[email protected] > <mailto:[email protected]>> wrote: > On Fri, May 10, 2019 at 8:16 AM Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: > > Then with mechanism, we get the many-histories from a simple fact to prove: > all computations are realised in all models of arithmetic. > > But arithmetic does not exist independently of the human mind, and mechanism > is manifestly a pipe dream. > > > You sound certain. What is your evidence? > > Jason > > The is no evidence for mathematical realism, and mechanism is a failed idea > because it cannot account for our experience.
99,9 % of the mathematician are realist, without even thinking about this. But I would say that 100% of all scientists are arithmetical realist, which is more than what we need to study Mechanism (which eventually requires only sigma_1 arithmetical realism, just to understand that the Universal Dovetailer is a non stopping program. The first order theory of the real numbers does not require arithmetical realism, but the same theory + the trigonometrical functions reintroduce the need of being realist on the integers. Sin(2Pix) = 0 defines the integers in that theory. If you reject arithmetical realism, you need to tell us which axioms you reject among, 1) 0 ≠ s(x) 2) x ≠ y -> s(x) ≠ s(y) 3) x ≠ 0 -> Ey(x = s(y)) 4) x+0 = x 5) x+s(y) = s(x+y) 6) x*0=0 7) x*s(y)=(x*y)+x Some people add some metaphysical baggage in “realism” which is not there., “Arithmetical realism” is just the doctrine according to which the axioms above make sense. Usually, they are implicitly taught in primary school. It is used only for the Church-Turing thesis and the (mathematical) definition of “digital machine”. Bruno > > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLRON3vdt4GwUdvbCFnhp98Ges2OyXFAD7dgoThNomJv3w%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLRON3vdt4GwUdvbCFnhp98Ges2OyXFAD7dgoThNomJv3w%40mail.gmail.com?utm_medium=email&utm_source=footer>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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/1917E2A0-3E26-402B-8B21-2CAC19FAB4FF%40ulb.ac.be.
