> On 4 Jun 2018, at 21:05, Brent Meeker <[email protected]> wrote: > > > > On 6/4/2018 6:50 AM, Bruno Marchal wrote: >> >> There is not one argument here. >> >> You seem to confuse arithmetical realism, used in all branches of science, >> and Platonism (which is part of the consequence). To define mathematically >> what a computation is, we need arithmetical realism. > > Science doesn't need arithmetical realism in the sense of numbers exist in a > Platonic realm.
Good, because I have never used the idea that “numbers exist in a Platonic realm”. I use only that facts like Ex(x+2 = 5), and that this does not assume any temporal or spatial reality assumption. > Science, and everyday life, uses arithmetic as a language to describe things. That is not true. They use the fact that the arithmetical relations are true, independently of any language to describe them. String theory would have called cheater if they would have decided that 1+2+3+4+ … = -1/12 just to make the photon massless. But it makes sense when arithmetic take into account the mathematics of the prime number (the zeta function), and that was a nontrivial discovery and surprised. You confuse the arithmetical reality that we can explore, and the linguistic tools and theories that we use to explore it. > Numbers are abstractions from instances of sets of things. You can represent them in that way, but usually, we don’t, so to see that number theory assumes much less than set theory. Then, you seem to assume some things, but the whole point is that we have to assume things at the start, and we are searching the simplest one from which we can explain the rest, including consciousness. > >> In SANE04, my definition is redundant because the Church-Turing thesis makes >> no sense at without arithmetical realism. >> If anyone would believe that arithmetical realism is false, we would have >> heard argument that Rieman hypothesis or the twin conjecture or Goldbach are >> senseless. But that does not exist. > > Descriptions don't exist in the same sense as the thing described. Yes, that is my point. The arithmetical reality is much more than any theory can ever unify. That might, or not, be the case with the physical reality. Computationalism suggest that the physical reality is like that, but it is an open problem. Bruno > > Brent > >> >> If you could avoid ad hominem remark, that would be nice. Also. >> >> 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]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
