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

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On Friday, November 16, 2018 at 11:05:51 AM UTC-6, Bruno Marchal wrote:
>
>
> On 15 Nov 2018, at 18:13, Philip Thrift <cloud...@gmail.com <javascript:>>
> wrote:
>
>
>
> On Thursday, November 15, 2018 at 5:15:39 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 13 Nov 2018, at 11:06, Philip Thrift <cloud...@gmail.com> wrote:
>>
>>
>>
>> On Monday, November 12, 2018 at 8:35:23 PM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> 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
>>>
>>>
>>>
>> This is why some have mathematical theories (alternatives to ZF) that
>> have finite (i.e. Only a finite number of numbers needed!) models (e.g. *Jan
>> Mycielski,* "Locally Finite Theories" [
>> https://www.jstor.org/stable/2273942 ]). In this approach quantifiers
>> are effectively replaced by typed quantifiers, where the type says "this
>> quantifier ranges over some finite set".
>>
>> Another approach is to nominalize physical theories theories (*Hartry
>> Field*, *Science Without Numbers,* summary [
>> http://www.nyu.edu/projects/dorr/teaching/objectivity/Handout.5.10.pdf
>> ]). In this approach the model of the theory is a finite set of (references
>> to) physical objects.
>>
>> This is the best point-of-view to have: *The set of natural numbers
>> simply doesn't exist!*
>>
>>
>>
>> I agree. It is actually a consequence of mechanism. The set of natural
>> numbers does not exist, nor any infinite set. But that does not make a
>> physical universe into something existing. Analysis, physics, sets, …
>> belongs to the numbers “dreams” (a highly structured set, which has no
>> ontology, but a rich and complex phenomenological accounts).
>>
>> I gave my axioms (Arithmetic, or Kxy = x, Sxyz = xz(yz)). As you can see,
>> there is no axiom of infinity.
>>
>> Bruno
>>
>> PS Sorry for the delay.
>>
>>
>
>
> The "highest" programming may be higher-type (or higher-order) programming:
>
>
> http://www.cs.bham.ac.uk/~mhe/papers/introduction-to-higher-order-computation-NLS-2017.pdf
> examples @ http://www.cs.bham.ac.uk/~mhe/
>
>
> "Higher-order [programming involves] infinite objects, such as infinite
> strings, real numbers, and even functions themselves, etc. [which
> themselves] are computable. And, more importantly, how to compute them. In
> practice, computation with infinite objects often takes place in languages
> such as ML, Haskell, Agda etc. In theory, some canonical systems are
> Godel’s system T, Platek-Scott-Plotkin PCF, Martin-Lof’s dependent type
> theory, among many others. But how can we (or a computer) compute with
> infinite objects, given that we have a finite amount of time and a finite
> amount of memory and a finite amount of any resource? *Topology comes to
> the rescue* [revolving] around the [finite vs. infinite dichotomy],
> mediated by topology. *We can say that topology is precisely about the
> relation between finiteness and infiniteness that is relevant to
> computation.*"
>
>
>
> But there is a new biochemical programming language:
>
> *CRN++: Molecular Programming Language*
> (Submitted on 19 Sep 2018)
> https://arxiv.org/abs/1809.07430
> "We present its syntax and semantics, and build a compiler translating
> CRN++ programs into chemical reactions...laying the foundation of a
> comprehensive framework for molecular programming."
>
> A programming language whose purpose is to create bugs!
>
> So the question becomes: Is bioprogramming > programming? (if biomatter
> has experiential qualities in addition to informational quantities)
>
>
> Assuming some primary matter, and some non mechanist theory, why not. That
> seems to quite speculative, though, and adding difficulties to a subject
> which is already difficult when assuming the “simplifying” assumption of
> Mechanism. With mechanism, the mind-body problem reduced into justifying
> the existence of a canonical measure on all computations “seen from inside”
> (which admits a number of modes, imposed by incompleteness). In case the
> physics in the head of the universal machine/number departs from
> observation, we get the mean to make sense of some non-mechanism, and this
> might show you right. So let us continue the testing/comparison.
>
> What do you think your biomatter do which would be non Turing emulable,
> nor “first person measurable(*) and in what sense would that be relevant
> with respect of consciousness?
>
> I have no doubt chemical computation is a wonderful subject, but with
> “Indexical Digital Mechanism”, the theology and the physics is independent
> of the language and the basic theories as far as they are Turing
> complete(*), the physical appearance, needs to be justified in term of a
> relative measure state/computations "seen from inside” (Incompleteness
> makes the usual standard definition getting sense in those “enough rich”
> Turing complete(**) theories.
>
> Bruno
>
>
> (*) This provides some “free oracle”, like the random oracle and the
> halting oracle, due to the limiting behaviour of the first person
> indeterminacy).
>
> (**) Turing complete means that for all p sigma_1 (shape ExA(x, y), A
> decidable) we have, with “[]” Gödel’s arithmetical provability predicate,
>
>                    p -> []p
>
> is true.
>
> Löbian (sufficiently rich) means that for all such p,"p -> []p" is not
> only true, but provable. Put it in another way, this means that
>
>                    [](p -> []p)
>
> is true. (This makes the machine obeying to G and G* and their intensional
> variants).
>
> (See all definitions in the second part of sane04, I recall them in most
> of my papers).
>
>
>
*What do you think your biomatter do which would be non Turing emulable,
nor “first person measurable(*) and in what sense would that be relevant
with respect of consciousness?*```
```
One analogy I came up with (will see how this goes): Think of a Turing
computing that doesn't manipulate (only) symbols (information, or numbers),
but manipulates (also) emojis [ https://emojipedia.org/ ]! Now emojis
themselves are symbols of course, but suppose that they "embody" real
elements of *experience* that are ontologically separate from *information*
(or numbers).

(One could call this *e-Turing* computing non-Turing or not, depending on
whether how one defines unconventional computing.)

- pt

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