Thank you, Robert. This indeed is how the game should be played.
Mike
On 5/16/2020 11:18 AM, robert marty wrote:
The general clash over the role of mathematics in knowledge creation
was preceded by a debate between Jon Alan and myself. It was a false
debate because Jon Alan only paraphrased Peirce, I'll show it.
I begin with a short history that will show that the state of the
relationship between proponents of methods described as empirical and
those of mathematical methods is not good. In most likely the
embodiement of the former by the latter often experienced as a
domination while it is an obligatory passage for the increase of
knowledge. We will check it in a particular case, without excessive
passion even if there will be no charity ...
JAS > (07/05)
"Unfortunately I am not adept enough with mathematical category theory
to make heads or tails of Robert's exposition below. It still seems
to me that "category" means something quite different in that context
than it does for Peirce when he is writing about 1ns, 2ns, and 3ns.
Am I wrong? If so, I would appreciate some further explanation of how
they relate to each other."
RM > (07/05)
I create for him a short post that I finally posted on the
web:https://www.academia.edu/42974040/Build_the_lattice_of_the_10_classes_of_signs_in_one_lesson
Here's his polite answer... and treacherous ...
JAS > (08/05)
"I sincerely appreciate the additional attempt to explain below, but I
am afraid that I still cannot detect an answer despite reading it
several times, because it remains couched entirely in the unfamiliar
vocabulary of mathematical category theory--"morphism," "composition,"
"functor," "natural transformation," etc. I do not have the requisite
acquaintance with that *particular system* *of signs* to interpret it
successfully".
RM > It is clear: for JAS a vocabulary that is not familiar to him
can only produce *a particular system of signs* that he cannot
decipher (a bit like hieroglyphics before Champollion). Yet I was
exhausted to say that the axiomatized objects I used benefited of the
usual universality of mathematics in the sense that Peirce means
precisely:
CSP > (classifications of sciences)
- mathematics, the study *of ideal constructions* without reference to
their real existence,
-empirics, the study of phenomena with the purpose of identifying
their forms with those mathematics has studied,
- Pragmatics, the study of how we ought to behave in the ligth of the
truths of empirics." [C.S. Peirce, 1976: NEM , vol.III.2 , 1122]
What he notes again in another text:
1.Mathematics, which frames and studies the consequences of hypotheses
without concerning itself about whether there is anything in nature
analogous to its hypotheses or not. [C.S. Peirce, 1976: NEM , vol. IV,
228]
Moreover, the rest is eloquent on Peirce's opinion about the
relationship of philosophers with mathematics ... I can provide it on
request ...
Everyone will understand that I did not appreciate that the work I
have been doing for 45 years is relegated to the particular systems
... I find it *treacherous * to use one's incapacity (and de facto any
supposed individual or collective incapacity outside) to marginalize a
scientific practice. This debate is also open and I have spoken ... In
my opinion what I am trying to do now is to bring it down in the field
of semiotics. It is long and difficult but it must be conducted with
all the necessary critical sense and restraint, i.e. with "generosity
and no charity" ...
I'm going to put it all back in place since I now have the information
to analyze Jon Allan's system which opens a singular fight between
this S → Od-S → S-Ifchain dated 1903 and the mathematical object
"functor" that formalizes the chain of determinations OàSàI dated 1905
and sqq...
Indeed he writes in an answer:
JAS > (12/05)
"Hence the logical order of determination is S → Od-S → S-If, which we
use to obtain the familiar ten classes of signs.
Note that this has nothing whatsoever to do with which classes of
signs can be determined *(in a different sense)* by other signs. In
fact, only a symbolic sign can determine a further sign as its
dynamical interpretant. An indexical sign can only produce an
exertion or a feeling, and an iconic sign can only produce a feeling.
It also has nothing whatsoever to do with which classes of signs
are involved in other signs. Every actual replica of a legisign is a
sinsign that possesses qualisigns. Every symbolic sign involves
indexical and iconic signs, and every indexical sign involves iconic
signs. Every argument involves dicisigns and rhemes, and every
dicisign involves rhemes."
RM > I noted immediately that he wrote that the sign determined his
own determination, a strange thing difficult to attribute to Peirce
but he gives us incomprehensible details about what some others do in
a different sense ... and it states some truisms in reinforcement ...
We can forget this because fortunately comes this post the next day:
.JAS > 13/05
Part 1 :" In my post
<https://list.iupui.edu/sympa/arc/peirce-l/2020-05/msg00117.html> yesterday,
I was not referring to any particular /definition /of a sign, but
rather Peirce's 1903 /taxonomy /of ten classes of signs (CP 2.243-265,
EP 2:291-297). It should not be controversial at all to say that it is
based on three trichotomies--for the sign itself (S) as
qualisign/sinsign/legisign, for its dyadic relation with the object
(Od-S) as iconic/indexical/symbolic, and for its dyadic relation with
the interpretant (S-If) as rheme/dicisign/argument--arranged in
logical order as S → Od-S → S-If.
Part 2 : "This is not my personal opinion, it is what Peirce himself
presents in the referenced passage "
Part 3 : Please note, the arrows here do not have anything to do with
involution or presupposition, only determination as the /logical
/relation between the different trichotomies for sign classification,
such that "a Possible can determine nothing but a Possible" and "a
Necessitant can be determined by nothing but a Necessitant" (EP 2:481,
1908)."
RM > These texts CP 2.243-265, EP 2:291-297 are also references that
I have been cultivating for decades. There is everything it takes to
open (and close) an exemplary debate, far from the anathemas to those
who block or not the way of inquiry.
I cut it into three parts for convenience reasons.
I immediately notice that in Part 1 the term determination has
disappeared when compared with the post of the previous day and that
in Part 3 Jon Alan brings details on his arrows saying what they are
not (presupposition or involution) which is also the case of the
arrows of O àSàI which are true determinations. Also in Part3 he adds
again says that these are determinations that act as relationships
between different trichotomies. I develop them in betraying it as follows:
First Trichotomy [ Qualisigne ; Sinsign ; Legisign ] *S *
↓
Second Trichotomy [ Icon ; Index
; Symbol ] *Od-S*
↓
Third Trichotomy [ Rhème ; Dicisign ;
Argument ] *S-If*
He goes on to say how he intends to combine these trichotomies and
cites Peirce's well-known conditions that ""a Possible can determine
nothing but a Possible" and "a Necessitant can be determined by
nothing but a Necessitant, dated 1908. (which I have shown are
equivalent to the presupposition relationships between the
coenopythagorean categories he now uses).
But what he does was already done a long time ago by Peirce himself
(see attachment)
Une image contenant dessin Description générée automatiquement
Jon Alan was absolutely right in his Part 2: "is what Peirce himself
presents in the referenced passage"
But no more.
*Conclusion *: His whole speech is therefore merely a *paraphrase* and
the famous logical arrangement
S → Od-S → S-If is a mystification, just a label on a handyman box
that contains CP 2.243-265, EP 2:291-297. To use it you have to do
what almost all beginners have done and that I have also done, that is
to reinvent the wheel. But when you do this with simple functors as I
did, you then have the natural transformations of the functors and the
organization of all the classes of signs in a lattice. It helps to
understand why Peirce is legitimate when he writes in the class
description from 2,254 to 2.2.263 for each sign that embody other
signs. I have shown it extensively for a long time. And of course we
can do tests like the one I did on nicotine and much more.
https://www.academia.edu/42930701/Nicotine_a_semiotic_confrontation_between_life_and_death
END OF GAME
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