BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px;
}Priscila - I find your signtree model very interesting. I wonder if
you would explain - let's say - two of the sign classes - I'll
randomly pick # 5 and 44.
I can understand your ten class diagram and I can see the nodal
sites for your 66 classes but I'm curious about the functions of
these expanded nodal sites. That is - I see Robert's point of a
'linear series of successive determinations' . Perhaps I'm not clear
about your model, but in the expanded model - for example, all the
nodal sites in, let's say, a rhematic iconic legisign- except for the
legisign in 3ns, the rest of the nodes are all in 1ns. Therefore - how
does the expansion 'develop' the full Sign? I see the same properties
in other signs...that is, does the expansion of nodes increase the
information capacity of the full Sign?
Thanks in advance
Edwina
On Wed 29/04/20 8:08 PM , Priscila Borges primbor...@gmail.com
sent:
Dear Helmut, Robert and list,
I've been following this topic on the tree-structure trying to
understand why a tree-structure would not lead to 66 sign classes.
Robert said:
"If you put a tree structure on the ten trichotomies you can say
probably goodbye to the 66 classes of signs which are coextensive
with a linear series of successive determinations."
As you have seen, I've built a model for the system of 66 sign
classes based on a tree structure. In that visual model, a tree
structure was apllied to the set of 66 sign classes and not to each
sign class. That is, to build the system, I adopted an order for the
trichotomies, as Peirce did with the 3 tricotomies of the 10 sign
classes, and with the 6 tricothomies of the 28 sign classes.
I do not undestand why should we not adopt a linear order for the
trichotomies. It seems to me that some order of determination between
trichotomies is fundamental to reach the classes of signs.
This is true for the 10 sign classes, which can only be reached if
we follow the [S] > [S-O] > [S-I] order.
When Peirce proposes the 28 sign classes he says (SS 84; EP2:481,
1908):
"It is evident that a Possible can determine nothing but a
Possible; it is equally so that a Necessitant can be determined by
nothing but a Necessitant. Hence it follows from the Definition of a
Sign that since the Dynamoid Object determines the Immediate Object,
which determines the Sign itself,
which determines the Destinate Interpretant,
which determines the Effective Interpretant,
which determines the Explicit Interpretant,
the six trichotomies, instead of determining 729 classes of signs,
as they would if they were independent, only yield 28 classes"
In the 66 sign classes, there is a letter to L. Welby from December
24, 1908 (EP2:483-488), in which Peirce analyses the relation between
two trichotomies [S] and [IO]. He says:
"Before proceeding to the third trichotomy, let [us] inquire what
relations, if any, are found between the two that have been brought
to light. What I mean precisely by between these relations is
whether or not the three members of the first trichotomy, which we
may for the moment denote as 11, 12, 13, are or are not independent
of the three members of the second, which we may denote by 21, 22,
23; so that they form nine classes, which if we use a dot to mean
"which is," will be denoted by
11-21 11-22 11-23 12-21 12-22
12-23 13-21 13-22 13-23
The inquiry ought, one would expect, to be an easy one, since both
trichotomies depend on there being three Modes of Presence to the
mind, which we may term
The Immediate,—The Direct,—The Familiar
Mode of Presence.
The difference between the two trichotomies is that the one refers
to the Presence to the Mind of the Sign and the other to that of the
Immediate Object. The Sign may have any Modality of Being, i.e. may
belong to any one of the three Universes; its Immediate Object must
be in some sense, in which the Sign need not be, Internal." (Peirce,
1908, EP2:483-488).
It is interesting that he begins the letter presenting the [S]
"I. According to the mode of presentation of the sign itself
Potisign / Actisign / Famisign"
and then he presents the [IO]
"II. According to the mode of presentation of the immediate object
Descriptive / Designative / Copulant"
but his analyses on the relationship between these two tricotomies
shows that the Immediate Object precedes the Sign and not the
contrary (Peirce, 1908, EP2:483-488).
The third trichotomy he presents in this letter is the [DO]
"III. According to the nature of the dynamic object
Abstractive / Concretive / Collective"
And just after presenting it he says:
I was of the opinion that if the Dynamical Object be a mere
Possible the Immediate Object could only be of the same nature,
while if the Immediate Object were a Tendency or Habit then the
Dynamical Object must be of the same nature. Consequently an
Abstractive must be a Mark, while a Type must be a Collective, which
shows how I conceived Abstractives and Collectives." (Peirce, 1908,
EP2:489)
If the DO is a mere possible, then the IO is a mere possible.
If the IO is a tendency, then the DO is a tendency.
And here he gives a hint at the order of the trichotomies between
the [DO] and [IO]. If the Immediate Object is a tendency and if it
preceded the Dynamical object, there would be no restriction for the
Dynamical Object to be a tendency, it could be a possible, a fact, or
a tendency.
It is the same as saying that all Qualisigns are Icons and all
Symbols are Legisigns.
And this is due to the relationship between the universal
categories:
“Firstness is the mode of being of that which is such as it is,
positively and without reference to anything else. Secondness is the
mode of being of that which is such as it is, with respect to a second
but regardless of any third. Thirdness is the mode of being of that
which is such as it is, in bringing a second and third into relation
to each other.” (CP 8.328 [1904])
It is based on that that I said, as Robert quoted:
"A relation of dependence is established between the three
categories as follows: firstness is independent of anything,
secondness depends on firstness, and thirdness depends on secondness
and firstness."
Robert, also, asked what is the parallelism that inspered the form
of a tree. Let me explain, then.
When I created the Signtree visual model, I was inspired by some
drawings, specially the following one, which appears in SANDERS,
GARY. Peirce's Sixty-six Signs , Charles S. Peirce Society,
Transactions, 6:1 (1970:Winter):
(Sanders, 1970)
Also, by Peirce's scheme for the degenerated categories (EP2: 162,
1903):
EP2:162, 1903
And some other drawings I found on Peirce's manuscripts such as:
(MS 74, p. 02)
(MS 137, p. 95, 1904)
(MS 137, p. 117, 1904)
(MS 278D4, p. 1086)
(MS 278C, p. 501)
All these structures seem to derive from the tripod being repeated
recursively, which results in a tree-structure. The affinity between
the growth of the tree and the sign processes is quite obvious,
since each bifurcation of a branch results in a triadic structure.
(EP2:364)
That's why I adopted the form of a tree to my visual model and
called it Signtree. Because I believe the tree-structure applied to
the set of sign classes evinces that they constitute an integrated
system. The sign classes should not be understood as pidgeon-holes
to qualify signs. Peirce defines semiotics as “the science of the
necessary laws of thought” (Peirce c.1896: CP 1.444). Peirce’s
classes are not simply a set of categories to qualify signs. They
express a logical process for inquiry that makes clear the growth of
signs. And that is why I don't represent the classes of signs in
boxes separeted one from the other. Instead, I represent them as
bifurcating one from the other. This may not be evident on
Peirce’s threefold classification system, because in that case the
process has only three steps. It begins to appear in Peirce’s
tenfold classification, which brings up a process in ten steps.
However, the growing process of the sign only becomes explicit in
Peirce’s extended system of sixty-six classes.
(Signtree, 66 sign classes)
(Signtree, 66 sign classes)
The Signtree model can be used to express any type of class system
emphasizing characteristics that are not exclusive of the 66
classes’ system, but are essential to Peirce’s semiotics. I've
built visual models as this one for all the systems of sign classes
and even proposed one with 21 classes.
(Signtree, 3 and 10 sign classes)
(Signtree, 28 sign classes)
(Signtree, 21 sign classes)
These I published in The American Journal of Semiotics 31.3–4
(2015), 245–276. The paper is called "A System of 21 Classes of
Signs as an Instrument of Inquiry", its aim is not only to deduce
the system of 21 classes, but also to allow the reader to understand
how each class represents a step in a semiotic inquiry. With that in
mind, I also provided an example of how to proceed with a semiotic
analysis using the system of 21 classes.
I have also published other papers where I apply the 66 sign
classes shown in the Signtree as an instrument of inquiry:
*Borges, Priscila (2014). Experience and Cognition in Peirce’s
Semiotics. The American Journal of Semiotics 30.1–2, 1–26.
*Borges, Priscila (2019). Confidence through the semiotic
process. Semiotica Journal 228. https://doi.org/10.1515/sem-2018-0083
*Borges, Priscila (2020). A Complex System of Sign Classes for
complex Sign Systems. In JAPPY, Tony (ed.). Bloomsbury Companion to
Contemporary Peircean Semiotics. Bloomsbury Publishing.
Best,Priscila
Em qua., 29 de abr. de 2020 às 20:51, robert marty escreveu:
Helmut, John,Jon, List
You have made a wise decision ... Stopping would be better ...😊
Ok... In terms of "dependency," "determinations" or "involutions,"
or "objects of thought" and even "categories, I made too many
concessions to Cerberus ... Indeed I do not even need to call
"objects of thought" the objects Ai and "determinations" the
successive arrows, nor do I need to name the relationships between
categories that I could just note Xà YàZ, or even as a result call
protosigns these formal constructions. In doing so I wanted to
anticipate their ability to give form to Peirce's empirical proposals
on the functioning of signs in human minds and even in other fields. I
thought about improving the acceptability of my approach and
apparently I did not succeed. I understood that this made me enter
prematurely in the battlefield of the choices of trichotomies, the
correct definition of the sign (in this respect I must recall that I
published 76 from CP, NEM, MS and LW still available on peirce.org
[2]), etc ... Etc...
So I should point out that if we consider two abstract categories
X àYàZ on the one hand
A1 àA2 àA3 …… àAn on the other hand (with all axioms checked
for the composition of the arrows)
It is found that there are exactly (n + 2)*(n +1)/2 covariant
functors from the first to the second and that, moreover, this set of
functors is naturally organized in a lattice structure by the natural
transformations of functors that we know how to define on this set. A
computer tool can do that very well
(patrick-benazet.chez-alice.fr/treillis_en_ligne/lattices)
This lattices are compounds mathematical objects, not very complex
if n not too large ... Indeed for n = 3 there are 10 functors, 28 for
n = 10, 66 for n = 10 ...
If I take up the Peirce's classification of sciences that John Sowa
has emphasized above:
JS > "This quotation is important for understanding his 1903
classification. It shows that the empirical aspects of science
require mathematics to interpret experiences in the phaneron."
these objects are part of the "ideal constructions without reference
to their real existence," of the mathematics …"
Now, as soon as we see that Peirce is proposing after years of
studying the functioning of:
- phenomena (phanerons) in human minds that he reduces to 3
major categories (corroborated by a reduction theorem: Herzberger,
Burch, Marty), between which he recognizes relationships of
involution
- and also signs in social life,starting with three-item signs
that he calls Object, Sign and Interpretant, of which a very large
number includes the term "determines" (it appears 76 times - it is
a coincidence - in the 76 definitions of the sign) and that he
classifies them into ten classes, and then when the sign expands to
six elements with 28 classes, ...
- and even that it highlights affinities between the signs
that direct attention to relationships between classes of signs by
triplets between these elements
then, and only then are you justified in saying that these forms you
have built are the ones to which he refers in the second part of his
classification:
"Empirics, the study of phenomena with the purpose of identifying
their forms with those *mathematics* has studied,"
From then on you can have an instrument of knowledge to study the
practices of communication and meaning:
"Pragmatics, the study of how we ought to behave in the light of the
truths of empirics." ((NEM, vol.IV, p. 1122)
Le mer. 29 avr. 2020 à 22:56, robert marty <
robert.mart...@gmail.com [3]> a écrit :
Thank you John for this information. I believe that a reassessment
of the importance of mathematics in Peirce's work must be obtained
from the community of Peirceans.
As for Hegel's mathematical competence, Peirce was not very
charitable :
"He has usually overlooked external Secondness, altogether. In
other words, he has committed the trifling oversight of forgetting
that there is a real world with real actions and reactions. Rather a
serious oversight that. Then Hegel had the misfortune to be unusually
deficient in mathematics. He shows this in the very elementary
character of his reasoning. " (CP 1.368)
Robert
Le mer. 29 avr. 2020 à 20:48, John F. Sowa a écrit :
Jon and Robert,
This issue illustrates an important point about Peirce's
development. His ideas were constantly "growing" (Peirce's own
word), and he kept revising his terminology as he continued to find
new ways of relating his ideas to one another and to the common
vocabulary of his day (much of which he defined for the Century
Dictionary).
JAS> That passage is from R 1345, dated c. 1896, and thus was
written several years prior to Peirce's much more comprehensive
classification of 1903. It seems to me that empirics became
phenomenology
Yes, but it does not contradict what he wrote in 1896. Unless
Peirce explicitly rejects something he wrote earlier, we must
consider it a valid aspect of his thought. And we should try to
understand what differences, if any, there may be in the different
choices of words.
Instead of saying that empirics became phenomenology, it's better to
say that empirics, phenomenology, and phaneroscopy are three related,
but slightly different ways of talking about closely related issues.
RM> I always thought that the most peircean of the classifications
of sciences was this one :
CSP> *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
light of the truths of empirics." (NEM, vol.IV, p. 1122)
This quotation is important for understanding his 1903
classification. It shows that the empirical aspects of science
require mathematics to interpret experiences in the phaneron.
And the passage from 1896 should be compared with R602, which Peirce
wrote a few years after 1903. In R602, Peirce goes back to the issues
about the role of mathematics. (See
http://jfsowa.com/peirce/r602.htm [5] )
A comparison of the 1896 version with the later two shows the
differences and the similarities between Peirce's views and Hegel's.
Husserl, by the way, earned his PhD in mathematics. In his book on
diagrammatology, Frederik Stjernfelt showed many of the similarities
between Peirce's phaneroscopy and Husserl's version of phenomenology.
I strongly recommend Stjernfelt's book for its insights into the ways
that two mathematicians addressed closely related issues.
John
Links:
------
[1]
http://webmail.primus.ca/javascript:top.opencompose(\'robert.mart...@gmail.com\',\'\',\'\',\'\')
[2] http://peirce.org
[3]
http://webmail.primus.ca/javascript:top.opencompose(\'robert.mart...@gmail.com\',\'\',\'\',\'\')
[4]
http://webmail.primus.ca/javascript:top.opencompose(\'s...@bestweb.net\',\'\',\'\',\'\')
[5] http://jfsowa.com/peirce/r602.htm
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