On Thu, May 16, 2019 at 12:59 AM Bruno Marchal <[email protected]> wrote:
> 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]> wrote: > >> On Fri, May 10, 2019 at 8:16 AM Bruce Kellett <[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. > 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. And if you think you can get away without acknowledging your metaphysics, then you are dreaming. 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQDgjbCL2Px9VUJ%3Dm%3D9wV1paL89mcTFvo77%3DwafhwK78Q%40mail.gmail.com.
