On Monday, November 19, 2018 at 4:54:47 AM UTC-6, Bruno Marchal wrote:
>
>
> On 16 Nov 2018, at 19:55, Philip Thrift <[email protected] <javascript:>>
> wrote:
>
>
>
> On Friday, November 16, 2018 at 11:05:51 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 15 Nov 2018, at 18:13, Philip Thrift <[email protected]> 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 <[email protected]> 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.)
>
>
> Hmm… The emojis would be pointer to expérience. That would be just a
> coding, if we assume computationalism, or an oracle, perhaps, or something
> unknown … just to claim that the brain is not digitalis able?
> This seems to me only to make things more complex, and if the things
> invoked through the emoji needs to be material, it looks like an artificial
> trick “just” to save a metaphysical option. Personally, I could do that the
> day I have more empirical evidence for matter or for non-mechanism.
>
> Bruno
>
>
I wrote this short Note:
*EMP: Effective Matter Programming*
https://codicalist.wordpress.com/2018/11/19/emp-effective-matter-programming/
"Matter compilers receive their raw materials from the Feed, a system
analogous to the electrical grid of modern society. The Feed carries
streams of both energy and basic molecules
<https://en.wikipedia.org/wiki/Molecules>, which are rapidly assembled into
usable goods by matter compilers."
- https://en.wikipedia.org/wiki/The_Diamond_Age
>From usable goods to sensitive robots?
- pt
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