> On 16 May 2019, at 03:27, Bruce Kellett <[email protected]> wrote: > > On Thu, May 16, 2019 at 12:59 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > On 11 May 2019, at 01:02, Bruce Kellett <[email protected] > <mailto:[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, > > On Mondays, Wednesdays, and Fridays. The other days of the week they are all > nominalists.
No, only at the pause-café and during the week-end. I would say. When they stop using their brain. > > 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 > > You are just using your personal Humpty-Dumpty dictionary to define > "realism". Arithmetical realism is a bit more than just the axioms above -- > it is a metaphysical notion. “Metaphysical notion is fuzzy”, but I have given a precise definition of realism in arithmetic, the one used in the work. Realism is just the belief in the truth of the axioms above (and a bit of logic). > And if you think you can get away without acknowledging your metaphysics, > then you are dreaming. I do metaphysics with the scientific method. I give the axiom and theory. The only things which I can’t formalise is the yes doctor. Arithmetical realism issued only to make sense of the Church-Turing thesis. 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 view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLQDgjbCL2Px9VUJ%3Dm%3D9wV1paL89mcTFvo77%3DwafhwK78Q%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLQDgjbCL2Px9VUJ%3Dm%3D9wV1paL89mcTFvo77%3DwafhwK78Q%40mail.gmail.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/75D92B9C-F5BB-4DAA-BCC1-C97D25E7BD47%40ulb.ac.be.
