# Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

```> 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
>
>
>
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