BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Robert, list
And here is the scientific method as outlined by Robert - and, in my
view, Peirce. It seems different from that outlined by De Tienne.
And I have several questions about these differences.
Robert's Outline of the Scientific Method:
1] the abstract observation of phenomena [this is mere physical and
mental observation of 'facts']
2]the search in the mathematical repository for an object in strict
correspondence (i.e. isomorphism) with these observations (otherwise
mathematicians can create new ad-hoc objects). --> a Poset
3]the inductive phase: by going back to the phenomena provided with
this abstract form, [and testing its validity]
4]In the purely mathematical field, we can now generate new forms
with all guarantees of universality
Notice how embedded this method is in BOTH matter-and-mind; how the
two continuously work together to understand the real world. Notice
how abduction generates an hypothesis and model [poset], which is
then tested within induction, which is then set up as a deductive
premise.
And notice the difference between this and the outline by De Tienne,
where we are told that 'pure mathematics plays freely with forms,
unconcerned with whether they play any part in experience' but then,
he also says that 'phaneroscopy may help mathematicians through
corrective suggestions, observational clues, theoretical validation'.
[Question: When does this interaction happen?]
Because he also tells us that we have: 'The Urge to transition out
of mathematics', for 'we cannot count on mathematicians to help
figure out what goes on in experience"....and insists on this
irrelevance, despite mathematics being 'the first' stage of research
'.He writes: ".How do we transition out of it into a concern no longer
detached from but attached to the conditions sustaining the cosmos,
the world, nature, life in general, our life?"
A. My first question- is, so what is the point of mathematics if you
have to transition out of it?
B My second question is: What is the definition of Mathematics? De
Tienne seems to redefine mathematics - moving it from what I
understand as an Argument - i.e., an intellectual process in
Thirdness, capable of offering rhematic symbols [those Posets]…..
into a purely detached abstract 'feeling' in a mode of Firstness!
That is, are 'Posets' or Forms really similar to what I understand as
Qualia? Or are they Rhematic Symbols?
As Rhematic Symbols, I can see Posets as explaining the Real World.
I don't see how a 'possible' - which to me is Qualia - can explain
the Real World.
That's where I have trouble with the differences between Marty and
De Tienne's outlines.
Edwina
On Sun 15/08/21 5:50 AM , robert marty robert.mart...@gmail.com
sent:
List,
My initial comment was to salute Jon Alan's message (Peirce-l - Re:
[PEIRCE-L] AndrÃ(c) De Tienne: Slow Read slide 23 - arc (iupui.edu),
with a single quote from Peirce that I thought particularly adapted to
introduce the objectivity necessary to understand the current debate
started with André de Tienne's slow read bellicose towards
mathematics and mathematicians... I wanted to exploit the general
scope, but this finally led me to a too-long text, the basis of a
future article and/or book chapter. So I propose it to the debate in
several parts ... a quick read, so to speak ... Here is the quote
from JAS and then the part (A):
"The only end of science, as such, is to learn the lesson that the
universe has to teach it. In Induction it simply surrenders itself to
the force of facts. But it finds, at once--I am partially inverting
the historical order, in order to state the process in its logical
order--it finds I say that this is not enough. It is driven in
desperation to call upon its inward sympathy with nature, its
instinct for aid, just as we find Galileo at the dawn of modern
science making his appeal to il lume naturale. But in so far as it
does this, the solid ground of fact fails it. It feels from that
moment that its position is only provisional. It must then find
confirmations or else shift its footing. Even if it does find
confirmations, they are only partial. It still is not standing upon
the bedrock of fact. It is walking upon a bog, and can only say, this
ground seems to hold for the present. Here I will stay till it begins
to give way. (CP 5.589, EP 2:54-55, 1898)[emphasize mine]
Modeling in Humanities: the case of Peirce's Semiotics.
Chronological, logical and sociological aspects.
A - the chronological order of discovery is:
1- the abstract observation of phenomena; it suggests that three
categories in relation of "involvement" are candidates for a complete
description of phenomena (this is the work of the "phaneroscopists"
with Peirce at the forefront, of course)
2- the search in the mathematical repository for an object in strict
correspondence (i.e. isomorphism) with these observations (otherwise
mathematicians can create new ad-hoc objects). We find a very simple
object which fulfils these conditions. It is a candidate to be the
"skeleton-set" of phenomenology. It is a very simple structure of
order called (Poset).
3 - the inductive phase: by going back to the phenomena provided
with this abstract form, one verifies in each particular field [such
as Experience (see Houser), relative predicates, psychology, etc],
the relevance and the correctness of the abstract observation made in
point 1. It is an implementation phase which verifies that the formal
structure is well inscribed in each field of knowledge. This
verification is possible thanks to the mathematical language provided
in point 2, which is stripped of substance from the specificities of
each of the fields in which the abstractions have been made. It is a
common language that allows us to verify the universality of the
first extraction (realized more than a century ago by Peirce).
4 - In the purely mathematical field, we can now generate new forms
with all guarantees of universality since they are independent of any
real existence. As we have a Poset, we can in this (algebraic)
category of Posets, not only generate new Posets, but also benefit
from all the possibilities of linking them to other mathematical
structures (graphs for example). One can then proceed to"natural"
(formal) extensions and then return to the abstract observations of
the "phaneroscopists", starting with those of Peirce, in order to
"see" (sometimes literally by observing various mathematical
diagrams: Veen or representations with points and arrows) if there is
the possibility of finding other skeleton-sets which would be endowed
with the same utility and the same universality. This is notably the
case for the 10 classes of signs, which are not only generated but
are also naturally classified in a particular structure of Poset
called Lattice. Peirce did not have this structure at his disposal,
since it only really became established in the mathematical field in
1940 (Birkhoff). However, he had the intuition of it by identifying
"affinities" (CP 2.264) between classes, thanks to which he traced
diagrams which it is easy to show that they are inscriptions of the
mathematical lattice in Peirce's semiotic theory.One can easily spend
time on the hexadic signs and discover that this is not possible for
the decadic sign as long as new observations have not shown how to
classify the four new trichotomies with relations of determination.
Everyone will realize that this chronological order is the one I
have personally followed. But I used the "on" and not the "I",
because I claim without fear of being contradicted, that any other
mathematician, connoisseur of Peirce's writings or any connoisseur of
Peirce who would make the effort to go towards this mathematics,
certainly abstract, but not very technical, would come to the same
conclusions as I did. I am the inventor (1977) in the sense that this
term is used in archaeology; in fact, in archaeology, an invention is
the discovery of an archaeological site or object. The term
"inventor" is used to qualify the person responsible for this
discovery.
What I have just described is the chronology of a mathematical model
of phaneroscopy and Peirce's semiotics. The "phaneroscopists", the
"bricoleurs" in Lévi-Strauss' non-pejorative sense, the "informed"
mathematicians, are the actors. By necessity, mathematicians have a
particular role that Peirce has described with precision:
"… Thus, the mathematician does two very different things:
namely, he first frames a pure hypothesis stripped of all features
which do not concern the drawing of consequences from it, and this he
does without inquiring or caring whether it agrees with the actual
facts or not; and, secondly, he proceeds to draw necessary
consequences from that hypothesis" (CP 3.559).
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty [1]
https://martyrobert.academia.edu/ [2]
Links:
------
[1] https://fr.wikipedia.org/wiki/Robert_Marty
[2] https://martyrobert.academia.edu/
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