On Mon, Jun 04, 2018 at 03:50:33PM +0200, Bruno Marchal wrote: > > 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. In SANE04, my definition > is redundant because the Church-Turing thesis makes no sense at without > arithmetical realism.
Hi Bruno, I think you need to be aware that your writings do not help here, and that perhaps you need to clarify the point. For a long time I understood Arithmetic Realism <=> Platonism of the integers, but now I understand you make a more subtle distinction. One way of moving forward is that when you talk about the "Robust" universe case, you are effectively postulating Platonism of computations. So you can then move on to discussing the non-robust case, which I take to be some kind of ultrafinitism in fact. A more detailed discussion of the distinction between arithmetic realism and platonism would help here. For instance, why did you feel the need to include arithmetic realism as a distinct axiom from the CT thesis in the first place? -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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.
