> On 10 Nov 2018, at 17:09, John Clark <johnkcl...@gmail.com> wrote: > > On Sat, Nov 10, 2018 at 1:09 AM Bruno Marchal <marc...@ulb.ac.be > <mailto:marc...@ulb.ac.be>> wrote: > > > Any Turing machine can emulate any Turing complete subset of physics. > > You've got it backwards, physics can simulate a Turing Machine but a Turing > Machine can't simulate anything or do anything at all without the help of > matter that obeys the laws of physics.
That is plainly false. If u is a universal machine/number, phi_u(x, y) emulate the number/machine x on the input y. > >> >>> mathematical models and realities are quite different from the language >> >>> used to describe them. >> >> >> That is equivalent to saying "The English word "cat" is quite different >> >> from the English word "cat" “. >> >> > ? > > ! > A mathematical model is a description of something written in the language of > mathematics, like most descriptions it is not complete, You are using “model” in the sense of the physicist, and logicians call that a theory, which can be seen indeed as a (incomplete) theory. But a model, in the logician sense is complete by definition. It is usually infinite, and if that is the case there are models for each infinite cardinals. > some details have been left out and that's why a toy model of a battleship is > simpler than a real physical battleship. A mathematical model of another > mathematical model A model is a model of a theory. The notion of model of a model can make sense, by considering non axiomatisable theory, but that can lead to confusion, so it is better to avoid this. When a model is seen as a theory, if it contains arithmetic, the theory cannot be axiomatised, proofs cannot be checked, the set of theorems is not recursively enumerable, etc. Bruno > can be complete but not of something physical. > > John K Clark > > > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to firstname.lastname@example.org > <mailto:email@example.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to firstname.lastname@example.org. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.