> On 10 Nov 2018, at 17:09, John Clark <[email protected]> wrote: > > On Sat, Nov 10, 2018 at 1:09 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> 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 [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [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.
