On Fri, Jul 12, 2002 at 06:47:46PM +0200, Bruno Marchal wrote: > Those I have encapsulated in the label "comp". Precisely it consists in > 1)accepting a minimal amount of arithmetical realism, i.e. the truth of > elementary statements of arithmetic does not depend of me or us ... > 2) the Church Thesis (also called the Church Turing Thesis, or the > Post Law, etc.) > i.e. all universal machine are equivalent with respect to their simulation > abilities (making abstraction of the duration of those simulation). > 3) [skipped]
Couple of questions that arise from reading Hartley Rogers's book. Why stop at arithmetical realism? Why not analytical realism (truth of statements of analysis does not depend on us) or set theoretic realism (truth of statements of set theory does not depend on us), both of which are stronger than arithmetical realism? Isn't (even) arithmetical realism incompatible with the Church-Turing Thesis, because no Turing machine can enumerate all true statements of elementary number theory? (BTW, according to http://plato.stanford.edu/entries/church-turing/, there is quite a bit of confusion about what people mean by the Church-Turing Thesis. Could you take a look at that article and tell me which version of the Thesis you have in mind? For now I'll assume that you mean what the article refers to as Thesis M.) So why do you restict your Universal Dovetailer to be a Turing machine? Why not one of the more powerful machines surveyed in http://www.phil.canterbury.ac.nz/jack_copeland/pub/broad.pdf?