On Friday, September 14, 2018 at 11:22:34 AM UTC-5, Bruno Marchal wrote: > > > On 14 Sep 2018, at 16:09, John Clark <[email protected] <javascript:>> > wrote: > > > > *>Still the same confusion between a computation (a purely mathematical >> notion) and a physical computation, * >> > > I'm not confused at all, I'm very clear on the fact that a "purely > mathematical notion of computation" can't compute a damn thing > > > A notion of computation does not compute. > > A Turing machine or a number, or a combinator compute, with respect to > some universal number. That follows from the definition of Turing, Post, > Kleene, Davis, etc. > > You are not criticising me. You are criticising the whole field of > mathematical logic. > > > > > anymore than the blueprints for a 747 airliner can fly me to London. > > > The analogy does not work. A machine is more than a blueprint. The > proposition phi_i(j) converge is a (sigma_1) proposition of arithmetic, and > it is true or false, independently of your or me. > > > > > Bruno > > > > John K Clark > > I come back to that this sort of dispute is basically about what "school" of *philosophy of mathematics* does one come from.
(One may be from a school and not be aware of it, or don't see the need to state it; they sort of think everyone went there.) A reference commonly cited: *Platonism and Anti-Platonism in Mathematics* https://books.google.com/books/about/Platonism_and_Anti_Platonism_in_Mathemat.html?id=hbGhsAJIdEQC An interesting reference worth checking out: *The Meaning of Pure Mathematics* Jan Mycielski https://www.jstor.org/stable/30227216 If one is from a Platonist school, one is going to have a different spin on what mathematics actually is and does than one from one of the anti-Platonist schools. So knowing what school someone is from indicates how they will view these issues. - pt -- 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.
