[Fis] Fw: Five Momenta. Five Itineraries

[Bruno Marchal]

Dear Loet,

Sorry for bumping this old post, but I cannot resist (I tried!) to add  
my grain of salt.


On 21 Oct 2015, at 08:37, Loet Leydesdorff wrote:

> Self-reference is a key principle in art and humor and it may also  
> be a key component of the structured coherence in science Pedro and  
> we are seeking.
>
> Dear Joseph:
>
> Do not count me in to the “we”, please. In my opinion, these “unity  
> of science” principles are outdated. At issue is to specify how the  
> sciences and specialties are different; in which respects and why?  
> Obviously, the boundaries are fuzzy, since what may seem far  
> distanced from one perspective can be nearby from another (e.g. in  
> terms of the metrics used for the measurement such as in the case of  
> biometrics and econometrics).
>
> These distinctions are not to be identified into a single “self” of  
> the self-reference, but to be dissolved (differentiated) in  
> discourse. They are carried by the communication in science &  
> technology studies or more broadly (since including the science/ 
> society interface) in the information sciences. The “self” is not  
> transcendental to these discourses, but reflexive insofar as one has  
> the communicative competencies to listen and – if so wished -- to  
> participate.
>
> The distinctions (such as the ones between your five schemes) may be  
> useful heuristics. The puzzles have then to be specified.


I think that I might agree with Pedro and Joseph. The unity of science  
should be preserved, despite this is hard to do when specialities lost  
themselves in gigantic territories.
This eventually made the search of unity in science into a "new'  
science, or perhaps, if we assume the conceptually strong hypothesis  
of Mechanism (Descartes/Turing) into the oldest of all sciences:  
theology.

In that case we can define a straitforward notion of self: the  
representation of the body of the machine in its brain. Descartes  
sought fort his without finding it, and Hanz Driesch, with embryology  
in mind, pretended this could not exist, due to the apparent infinite  
looping most naïve attempts seem to lead to. But von Neuman, and more  
conceptually Stephen Kleene solved that problem. John Case solved the  
more complex embryological problem. The basic idea is contained in the  
Dx =>T(xx) trick: DD will give (=>) T(DD), that is the transformation  
T on itself.

And I agree that there is nothing transcendental in that notion of self.

But that notion is third person descriptible, which is not the case  
for the first person "I", which is the one who know, notably when it  
has some headache, plain or some pleasure.

To get this one, Theatetus suggested to attach the "believer" ([]p)  
with "truth" (p), and we know today that such notion of truth, and  
thus of knowledge ([]p & p) is transcendental.

It is transcendental in two sense: truth (even just the arithmetical  
truth) is not exhaustible.
- It escape *all* semi-effective (proof-checkable) theories.
- it is not nameable or definable by the machine (as Gödel and Tarski  
saw).

But that transcendental aspect, which is forced by logic, is available  
by the machine. So a universal machine can know that she is universal,  
and that makes her know that there is an unavoidable gap between its  
beliefs and truth, and that it can be used to explain why  
consciousness and knowledge seem so hard/impossible to define. In fact  
the theology of the machine introduces many nuance about that self:  
which correspond at different fields of research (p, the truth, []p,  
provability/believability, []p & p (knowledge, epistemology), []p &  
<>p (observability, as explained earlier or in my papers), and []p &  
<>t & p (sensibility, qualia).

The unity here is given by a belief in Truth, the original main God of  
Plato/Parmenides/Plotinus. It is the truth we can search, and perhaps  
knows aspects on it, but never as such: doubt must remain for reason  
of self-consistency.
With Mechanism, we can limit Truth to first order arithmetical truth,  
and all other notion (second order truth, analysis) can be put in the  
epistemology of the machine. Infinities only makes proof shorter.

So, the unity of science is not a problem, if we come back to modesty  
in theology. The main formula from which all this can be derived is  
sometimes called the formula of modesty: []([]p -> p) -> []p (Löb  
formula), which is both akin to the view of the scientific attitude as  
essentially the doubting view (from Descartes to Popper) and to the  
religious attitude of staying humble in front of the Unknown. In that  
setting, the original sin is when we separate theology from science,  
and that is what threat the unity of science.

I like to say that only bad faith fear reason, and only bad reasons  
fear faith. Faith is always faith in some form of unity or unification  
of knowledge.

Best,

Bruno

PS I don't find the five scheme you mentioned. It would be nice to see  
if they are related to the five platonic hypostases, or the five first  
affirmative hypothesis of Parmenides, as those are related to the five  
nuances mentioned above of self-reference.

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http://iridia.ulb.ac.be/~marchal/



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