> On 13 Nov 2018, at 15:38, John Clark <johnkcl...@gmail.com> wrote:
> 
> On Mon, Nov 12, 2018 at 9:35 PM Bruno Marchal <marc...@ulb.ac.be 
> <mailto:marc...@ulb.ac.be>> wrote:
> 
> >> 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. 
> 
> So you say, but I see precisely ZERO evidence that "phi_u(x, y)" can emulate 
> a machine or emulate anything a or in fact do anything at all because 
> "phi_u(x, y)" never changes, not in time and not in space. You wrote 
> "phi_u(x, y)"  in the above about 11 hours ago thousands of miles from me, 
> but here I am looking at "phi_u(x, y)"  and "phi_u(x, y)" is still just 
> "phi_u(x, y)” .


Your confusion here is equivalent with confusing a far away galaxy with the 
telescope, or confusing a physical universe with a book on the physical 
universe. The emulation is in the meaning of “phi_u(x,y)”, not in the string of 
symbols referring to that meaning.




>  
> >>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  [...]
> 
> Then logicians are talking about something that is self contradictory because 
> nothing mathematical or logical can be both complete and consistent. 

No mathematical and effective (sigma_1, checkable) theory can be complete. A 
model is complete by definition: it is what we intend to talk about.




> 
>  > [...] by definition.
> 
> You have a tendency to use those 2 words as if they were the final mark of 
> authority, but the words "by definition" does not cause things to suddenly 
> spring into existence, that utterance is no more magical than "abracadabra".  
> Hogwarts Castle is a school for wizards BY DEFINITION, there is absolutely no 
> doubt about it, but do you think it would be worth your time to go looking 
> for it?

But some existence can follow from definition, even, imprecise one. To prove 
that a computable function exist, just one example is enough, using a simple 
example. To prove that something is NOT computable, needs a precise 
mathematical definition. That is why we need Church, Turing, …
Then, if you are OK that 2+2=4 and similar are true independently of you and 
me, computations and their many realisation all exists, in a provable way, in 
the arithmetical reality/model.




>  
> > It is usually infinite,
> 
> Yet another reason to suspect it does not exist.

Indeed. Infinity exist only in the phenomenology. Just look ate the TOE I gave. 
None assumes infinity. I assume 0, s(0), s(s(0)), … only. 



> 
> > A model is a model of a theory.
> 
> So I guess a model of a theory is a model of a model of a theory, and a model 
> of a model of a theory is a model of a model of a model of a theory, and a 
> model of….

You might decide one day to study a bit of mathematical logic. The notion of 
model applies to a theory, only, or to a machine, in a related sense. (In 
infinitary logic, where we allow alphabet with arbitrary cardinality, some 
models can be see as theory, but that has no uses in our context.

Bruno



> 
>  John K Clark
> 
> 
> 
> 
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