BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Robert - thank you for this clarity -of-the-game.
I have one question. You use both O-S-I and Od-S-If in your outline.
I think that the more intricate use of Od and If really belong to
another discussion. For example, JAS has been introducing the idea
that If functions BEFORE the II and DI - a concept which I reject.
I'm not sure if you share the same opinion on this as JAS - but- I
would appreciate clarification.
Again - thank you for your posts.
Edwina
On Sat 16/05/20 12:18 PM , robert marty robert.mart...@gmail.com
sent:
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-If chain dated 1903 and the
mathematical object "functor" that formalizes the chain of
determinations O à S à I 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 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 à S à I 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)
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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