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}Robert, list
Thanks for this post - which is delightful. First - a few comments:
I very much agree that Peircean semiosis is relational and feel that
this requirement for interactional networking tends to be overlooked
in many studies of Peirce - which reduce Peirce to a static and
single triangle.
I also agree with your outline of the Sign - which you refer to as
'3 item sign that he call Object, Sign and Interpretant'. I think
that this irreducible triad tends to be frequently reduced to a kind
of linear Saussurian framework and this leads to ….
…..., I think that some tend to privilege the median node, the
Representamen/sign and give it almost a separate existentiality - and
with primary agential powers . I don't see the Representamen in this
way - and feel it doesn't 'exist' or function except as embedded
within the triad. I also disagree with others who see the triad with
each node in a specific categorical function, ie, with the
Representamen/sign as 1ns, the Object as 2ns, the Interpretant as
3ns. I don't 'get' this analysis -
As for your nicotine example [and I'd bet that you are a smoker] -
it's delightful to see the rapid movement of data from presenting
itself in the most basic and firmly-set morphology [as a dicent
Symbol] and then, rapidly moving, due to interactions with other
input data - through dissolving this singular meaning and
transforming itself into other meanings - even those that contradict
the original one. . And - how quite a few of these results are
unscientific and yet, will be firmly held beliefs.
The scenario would be best viewed as an animated cartoon [ in vivid
colour of course] - to explain these flexible and dynamic
transformations!
Edwina
On Wed 06/05/20 7:09 AM , robert marty [email protected]
sent:
Gary, Jon Alan, Jon Awbrey, List
1 -First I note that the formulation "3ns involves 2ns, which
involves 1ns" is very dangerous car it forgets that 2ns has its
autonomy and 1ns too. If you look at the podium on remains in the
inner cylinder. It seems to me that Peirce's reproach to Hegel is:
"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".
It is therefore important to prefer"3ns involves 2ns and 1ns, while
2ns involves 1ns" which preserves the autonomy of the Peircian
categories so as not to encourage the idea of a possible peircean
hegelianism. "
2 – On the specific question "about the conceptual relationship
between Peirce's trichotomic category theory and contemporary
mathematical category theory if any", I will mainly have a limited
response to the field at hand, that is, the classification of signs .
Then I can give some personal reflections on the general scope of
mathematical category theory in the humanities.
I was just preparing a text on the comparison of the ways in which
classes of signs are generated by different authors and I chose the
most interesting and successful in my eyes, i.e. Gary's trikônics,
the triangles of Priscila Farias and Joao Queiroz and the signtree
of Priscila Borges . It can be said at first glance that they are
equivalent since they generate the same classes of signs that can be
characterized by sequences of numbers of length n = 3, 6 or 10 taken
in the set {1,2,3} and verifying that each number must be less or
equal to the previous number. But the question is, since these are
classes based on different graphic metaphors, what is the common
formal structure - if there is one - of which they are the graphic
inscriptions. For this it is necessary to go in the field of posets
and more precisely totally ordered sets the simplest that are the
chains:
" A set with a partial order is called a partially ordered set
(also called a poset). The term ordered set is sometimes also used,
as long as it is clear from the context that no other kind of order
is meant. In particular, totally ordered sets can also be referred to
as "ordered sets", especially in areas where these structures are more
common than posets.
For a, b, elements of a partially ordered set P, if a ≤ b or b
≤ a, then a and b are comparable. A partial order under which
every pair of elements is comparable is called a total order or
linear order; a totally ordered set is also called a chain (e.g., the
natural numbers with their standard order)".
( https://en.wikipedia.org/wiki/Partially_ordered_set)
Clearly the abstract diagram 3ns à2nsà1ns (let's call the P) is a
chain which is common to all three approaches.
We have also the maps between partially ordered sets
" Definition 6: A function f : P → Q between partially ordered
sets is order-preserving if x ≤P y ⇒ f(x) ≤Q f(y).
Definition 7: Two partially ordered sets P and Q are isomorphic if
there exists a bijective, order-preserving map between them whose
inverse is also order-preserving"
( http://www-math.mit.edu/~levine/18.312/alg-comb-lecture-7.pdf )
To use this notion of the preservation of order, it is necessary to
identify in each graphic metaphor a Q chain .
I claim that these Q chains are materialized at the moment when
everyone chooses the convention that consists of locating the sign,
the object of the sign and its interpretant on the graphic icon he
has chosen.
As for Gary: starting from the object at the lower corner of his
trikône he goes up to the sign at the top corner following the
"vertical" side and then from there he should go to interpretant it
from the top side but if his graph indicates a direct relationship
between the object and the interpretant, which is the same because it
is the concatenation of the first two paths. What is thus traced is an
OàS àI chain.
As for Priscila Farias et Joao Queiroz :
(https://www.researchgate.net/publication/249933979_On_diagrams_for_Peirces_10_28_and_66_classes_of_signs
)
it is the same ; the way is taken from Peirce for which the
categories are assigned thereby : the object to the upper left corner
to go to the sign at the bottom corner and from there to interpretant
it in the upper right corner. They create what they call "triangular
coordinates" but it's the same OàS àI chain and it's do the same
it when they process graphically n = 6 and n = 10 which has the
effect of multiplying the triangles.
Priscila Borges uses the graphic metaphor of the developing tree:
https://www.researchgate.net/publication/263463845_THE_SIGNTREE_FROM_SIGN_STRUCTURE_TO_PEIRCE'S_PHILOSOPHY_THROUGH_READING_A_VISUAL_MODEL_OF_THE_66_CLASSES_OF_SIGNS
"So, the diagram construction begins by the idea of tree rings. They
are used in dendrocronology to count the age of trees. As years go by
rings grow in trees, but they are also affected by climate factors.
More than sign of time, tree rings show interaction between systems.
All these concepts are welcome in semiotic process. Each ring
corresponds to one trichotomy: the first trichotomy comes in the
centre, the second trichotomy in the second ring and so on. "
In this text she does it for n =10:
"Consequently, since the object determines the sign, and not the
sign determines the object, it was necessary to put the dynamical
object in the central ring, followed by the immediate object and the
ground of sign. Given the first three correlates, comes the first
relation: between sign and dynamical object. This relation determines
the possible interpretants, called immediate interpretants that when
are existent become dynamical interpretants. So, the elements that
compose the second relation are given: between sign and dynamical
interpretant."
Moving from a growth ring of its tree to the next it builds the de
facto chain for n = 6:
Od àOià SàIià IdàIf
And for n =1 0 she obtient very beautiful diagrams intelligently
colored.
My conclusion is that all these iconographic constructions are
isomorphic; they are produced in the same way using the applications
of the immutable suite of the three 3nsà2ns à 1ns and the f
application in n-length chains similar to the protosigns I defined in
the article on the trichotomic machine. They all lead - we just saw -
to sets (in the sense of set theory). The results: classes of signs
without explicit relations between them.
Now here's the jump in the category theory :
"Every poset (and every preordered set) may be considered as a
category where, for objects x and y, there is at most one morphism
from x to y. More explicitly, let hom(x, y) = {(x, y)} if x ≤
y(and otherwise the empty set) and (y, z)∘(x, y) = (x, z). Such
categories are sometimes called posetal."
"Posets are equivalent to one another if and only if they are
isomorphic. In a poset, the smallest element, if it exists, is an
initial object, and the largest element, if it exists, is a terminal
object. Also, every preordered set is equivalent to a poset. Finally,
every subcategory of a poset is isomorphism-closed." (
https://en.wikipedia.org/wiki/Partially_ordered_set#Mappings_between_partially_ordered_sets)
so the same mathematical objects that are involved in the ensemblist
mathematical models that I have just listed can be looked at
differently; they are now algebraic categories. On can use all the
conceptual apparatus of the categories and first the functors and
especially the bonus of natural transformations of functors which
brings us back to the trichotomic machine. This machine naturally
produces the same classes of signs of course but with the order of a
lattice revealed by the natural transformations of functors that we
will be able to exploit to increase our knowledge of the signs and
especially to create a methodology as an example I did in the case of
nicotine.
The general idea that has guided me for a long time is that Peirce's
thought is "functorial" and that his universe of thought is above all
relational. This is the reason for the fact that I continued work
started in my book "The Algebra of Signs". I try to express all its
semiotics by starting with a formalization of the "percipuum" in the
category of relational structures. But that's another story...
For now I am sorry to find that I submitted my nicotine analysis to
the criticism on May 3rd and that I did not get any reaction. I
believe that I show and demonstrate how a positive image of semiotics
is formed and how it gains in "semioticity" until it becomes able to
compete with the negative image of nicotine installed in a Dicent
Symbol, at the top of the lattice.
See
https://www.academia.edu/42930701/Nicotine_a_semiotic_confrontation_between_life_and_death
Best regards,
Robert Marty
Le mer. 6 mai 2020 à 06:47, Gary Richmond a écrit :
Jon, Robert, List,
JAS: Overall, we seem to be more or less on the same page.GR: I
think that's so.
JAS: I understand the impetus for using "presupposition" rather
than "involution," since the former term is more familiar to modern
mathematicians and logicians than the latter.GR: I too understand the
impetus for Robert's using "presupposition" as being more familiar to
modern mathematicians than "involution." But how many of them are
familiar with Peirce's three category theory at all? I continue to
believe that in consideration of Peirce's semeiotic (and all that
follows from it) that "involution" is the more accurate and evocative
term.
JAS: I have no objection to saying that 3ns involves 2ns and 1ns,
while 2ns involves 1ns. I just find it more succinct and equally
accurate to say that 3ns involves 2ns, which involves 1ns; this
already entails that 3ns also involves 1ns.GR: Logically, of course,
you are correct and your more succinct version is equivalent. But
saying that " 3ns involves 2ns and 1ns" brings the fundamental
trichotomy into high relief immediately. But it is a minor point,
perhaps one merely of emphasis.
JAS: I am not wedded to Peirce's adaptation of Aristotelian
terminology (1ns/2ns/3ns = form/matter/entelechy), which is most
prevalent in his writings around 1904--e.g., in "New Elements" (EP
2:303-305) and "Sketch of Dichotomic Mathematics" (NEM
4:292-300)--but I find it helpful in certain contexts.
GR: I suppose it is helpful in certain contexts to employ Peirce's
tricategorial adaptation of Aristotelian terminology. But is it
possible that the movement from one equivalent terminology to another
-- especially, but not only, within a single analysis -- has impeded
the more general acceptance of some core Peircean ideas? I don't
think there's an easy solution to this or any of the terminological
questions we've taken up on the list over the last few years, but I
think that there may be a communicational problematic here worth
considering.
JAS: I share Gary R.'s interest in learning more about "the
conceptual relationship between Peirce's trichotomic category theory
and contemporary mathematical category theory if any." I am more
familiar with Fernando Zalamea's opinion (which I share) that
Peirce's mathematical conception of continuity is more consistent
with category theory (synthetic/top-down) than set theory
(analytic/bottom-up). GR: Zalamea is, in my estimation, one of, if
not the leading contemporary expert writing on mathematical
continuity today. Again, I would be most interested in your thoughts,
Robert, about "the conceptual relationship between Peirce's
trichotomic category theory and contemporary mathematical category
theory if any."
Best.
Gary R
"TIME IS NOT A RENEWABLE RESOURCE." GNOX
Gary Richmond
Philosophy and Critical ThinkingCommunication StudiesLaGuardia
College of the City University of New York
On Tue, May 5, 2020 at 9:29 PM Jon Alan Schmidt <
[email protected] [2]> wrote:
Gary R., Robert, List:
Overall, we seem to be more or less on the same page.
I understand the impetus for using "presupposition" rather than
"involution," since the former term is more familiar to modern
mathematicians and logicians than the latter.
I have no objection to saying that 3ns involves 2ns and 1ns, while
2ns involves 1ns. I just find it more succinct and equally accurate
to say that 3ns involves 2ns, which involves 1ns; this already
entails that 3ns also involves 1ns.
I am not wedded to Peirce's adaptation of Aristotelian terminology
(1ns/2ns/3ns = form/matter/entelechy), which is most prevalent in his
writings around 1904--e.g., in "New Elements" (EP 2:303-305) and
"Sketch of Dichotomic Mathematics" (NEM 4:292-300)--but I find it
helpful in certain contexts.
I share Gary R.'s interest in learning more about "the conceptual
relationship between Peirce's trichotomic category theory and
contemporary mathematical category theory if any." I am more
familiar with Fernando Zalamea's opinion (which I share) that
Peirce's mathematical conception of continuity is more consistent
with category theory (synthetic/top-down) than set theory
(analytic/bottom-up).
Thanks,
Jon Alan Schmidt - Olathe, Kansas, USAProfessional Engineer, Amateur
Philosopher, Lutheran Laymanwww.LinkedIn.com/in/JonAlanSchmidt [3] -
twitter.com/JonAlanSchmidt [4]
On Tue, May 5, 2020 at 3:29 PM Gary Richmond wrote:
Robert, List,
Robert wrote:
RM: I spent a year extracting all the definitions of the sign that
Peirce could have imagined and I was not disappointed since I found
76; they're on peirce.org. I have taken this effort when I realized
the incredible number of scholars who thought in a non-critical way
about the definition of the sign they attributed to Peirce. In
particular, I have seen impossible triangles and confusions,
especially with the Saussurian tradition, with the conceptions of
Hjemslev and in the end of Greimas and his Ecole de Paris. It would
have taken a titanic job to denounce all distortions, fanciful
borrowings and undue annexations.
That was certainly time very well spent by you! I know of no Peirce
scholar who isn't aware of your list of Peirce's 76 definitions of
'sign', and many who have referenced it in their own work. I myself
have read through it several times over the years. It is surely a
major contribution, especially since, as you commented, there were
any "number of scholars who thought in a non-critical way about the
definition of the sign they attributed to Peirce."
Your scholarship has certainly contributed to dispelling the many
"distortions, fanciful borrowings and undue annexations" regarding
Peirce's semeiotic. I sometimes think, how much better Peirce's
semeiotic might today be known, understood, further developed and
applied, had it not been for Sassurean thinking having taken hold and
rooting itself so deeply in Continental thinking for most of the 20th
century; and, as a consequence, drawing attention away from Peirce's
triadic semeiotic, distorting it with Sassurean concepts and
language, dyadic and nominalistic thinking, etc. To some extent it
seems to me that that remains the case to this very day.
Shifting to an entirely different topic prompted by your most recent
off-list email to me (I'm afraid the math in it, as the American
English idiom has it, was "above my pay grade"), a question which has
come upon the list before, albeit infrequently, concerns the
conceptual relationship between Peirce's trichotomic category theory
and contemporary mathematical category theory if any. What, may I
ask, are your thoughts about that?
Best,
Gary R
"Time is not a renewable resource." gnox
Gary Richmond
Philosophy and Critical ThinkingCommunication StudiesLaGuardia
College of the City University of New York
On Tue, May 5, 2020 at 6:19 AM Robert Marty wrote:
Gary, Jon Alan, List
I fully respect yours concerns and of course it is clear that
everyone can invest them in the podium that is quite honored. For the
part concerning me I see no difficulty in using "involution" rather
than "presupposition" and I do not think I have strayed too far from
Peirce with "presupposition" since I think I have shown on the basis
of Frege's definition that the relationships of determination between
the elements of the phenomena as stated by Peirce verified this
assertion. For I just need to inscribe the abstract arrows of the
mathematical object that I build "without reference to their real
existence", within Peirce's empirical discourse. C.S. Peirce, 1976:
NEM, vol. IV, 1122 :
"It is obvious that a Possible cannot determine anything other
than a Possible, and likewise a Necessitant cannot be determined by
anything other than a Necessitant " ( letter to Lady Welby of
December 23, 1908)
I understood very early on that I had to trace a personal path in
what J.M. Chevalier quite rightly called "Le continent peircien"
(https://www.academia.edu/3383353/La_d%C3%A9couverte_du_continent_peircien)
but by justifying at every step a very close and verifiable
proximity to the fundamental conceptions of phaneroscopy and
semiotics. And when we received in Perpignan the MS microfilms that
we had ordered from the Harvard Library (32 reels of 100m each - 3.2
km!) I don't regret my decision ... I spent a year extracting all the
definitions of the sign that Peirce could have imagined and I was not
disappointed since I found 76; they're on peirce.org [7]. I have
taken this effort when I realized the incredible number of scholars
who thought in a non-critical way about the definition of the sign
they attributed to Peirce. In particular, I have seen impossible
triangles and confusions, especially with the Saussurian tradition,
with the conceptions of Hjemslev and in the end of Greimas and his
Ecole de Paris. It would have taken a titanic job to denounce all
distortions, fanciful borrowings and undue annexations.
A practical consequence is that I have not acquired the skill to
discuss the relevance of the intellectual investments that can be
made on the podium. Let me reveal the picture came to mind when I
read Jon Alan's first and almost immediate reaction above; it is not
derogatory: I saw a child jumping from level 3 on the steps of the
podium and I imagined all the possible choices he could make to get
down. Obviously there are 10 and even there are 6 in the inner
cylinder 3 in the outside cylinder and only 1 outside the two
cylinders. To each his obsessions! Since this (dynamic) image no
longer leaves my mind because I wonder if it does not open another
way to go to the lattice of the classes of signs that would not go
through the constraints of purely algebraic formalization. I think
about it often ...
Best regards
RobertLe mar. 5 mai 2020 à 06:04, Gary Richmond <
[email protected] [8]> a écrit :
Jon, Robert, List,
I began a draft response to your post, Jon, shortly after you wrote
it, but things began to move so quickly on the list that my initial
thoughts soon seemed to be superseded in the rapid fire exchanges
following. So I am glad that you reposted it as it gives me another
chance to respond (if I can complete it soon enough not to lose it
again as things move on).
I certainly agree with Jon that your paper, Robert, is most
interesting and that your podium diagram effectively represents the
relations holding among the three categories. But I also agree with
you, Jon, that 'involution' is not only Peirce's term, but indeed
expresses the concept of the logical relations holding among the
categories more accurately than does 'presupposition', really
optimally . I would very slightly modify Jon's expression of these
involutional relations: 3ns involves 2ns and 1ns; 2ns involves 1ns.
JAS: Applying this to the "podium" diagram, 1=essence, 2=existence,
and 3=reality. What about the inner portions? I suggest that
1/2=inherence, 2/3=persistence, and 1/2/3=governance.
GR: I think that inherence, persistence and governance make good
terminological sense in consideration of "the inner portions" of the
podium based on CP 1.175. But as I see it the Aristotelian
terminology of NEM 4:292-300, "form for 1ns, matter for 2ns, and
entelechy for 3ns" is potentially misleading, especially if we forget
that for Peirce 'form' is, as you commented, Jon, "whatever it is in
itself, irrespective of anything else/" (1=essence), matter as "all
that it is in reference to something else than itself" (2=existence),
and entelechy as "that which brings things together" (3=reality)."
In short, I see no reason to employ the Aristotelian terminology,
loaded as it is with pre-Peircean notions especially of form.
'Matter' and 'entelechy' fare somewhat better, but still bring with
them the Aristotelian associations. I think that it is possible and
desirable to move beyond these in Peircean scholarship.
Indeed, I found it helpful to my own understanding to substitute
Peirce's terms for Aristotle's in distinguishing the inner relations.
So: "the determination of "[the existent] by [essence]"
(1/2=inherence), "the reaction of [existent] with [existent] "
(2=existence), and "a determination of [an existent] to [an
essential form]" (1/2/3=governance).
Jon, your quoting Colapietro helped clarify the following, I think,
truly important notion: that "reality, is persistence, is regularity
(or, persistence in/as regularity?).
VC: Existence is the mode of being of an individual substance
considered as a continuity of reactions; insofar as it is actually
reacting against other things, it exists. Persistence is the mode of
being of such a substance seen as a continuity of reactions; insofar
as it endures throughout a series of reactions, it persists. In other
words, existence (because it is an instance of opposition) designates
the aspect of secondness exhibited by any individual substance, while
persistence (because it is a case of continuity) designates one of the
ways in which it manifests thirdness. ( Vincent Colapietro, Peirce's
Approach to the Self: A Semiotic Perspective on Human Subjectivity,
83).
In a word, 'persistence' is the existential form of continuity.
JAS: Peirce describes two different classes of possible states of
things that may be realized at a lapse of time--prolonged states,
which are realized at any instant within a lapse; and gradual
states, which are realized only at an entire lapse during which a
change occurs from one prolonged state to another, these two states
being "logically incompossible" (see NEM 3:1074-1077, c.1905). Such
diversity requires real qualities to be continuous (1/2/3), rather
than isolated (1), and real things to persist (2/3), not merely
exist (2). (Boldface and underlining as emphasis added by GR.)
To repeat: In a nutshell, real qualities are continuous (not
isolated); real things persist (not just exist).
I expect to spend more time reflecting on the following quotations
(which I've read numerous times over the years) and your succinct
comment which separates them.
CSP: Time with its continuity logically involves some other kind of
continuity than its own. Time, as the universal form of change, cannot
exist unless there is something to undergo change [2/3] and to undergo
a change continuous in time there must be a continuity of changeable
qualities [1/2/3]. (CP 6.132, EP 1:323, 1892)
JAS: This is one specific sense in which all three categories are
always present within our existing universe.
CSP: I chiefly insist upon continuity, or Thirdness, and, in order
to secure to thirdness its really commanding function, I find it
indispensable fully [to] recognize that it is a third, and that
Firstness, or chance, and Secondness, or Brute reaction, are other
elements, without the independence of which Thirdness would not have
anything upon which to operate. (CP 6.202, 1898)
Best,
Gary
"TIME IS NOT A RENEWABLE RESOURCE." GNOX
Gary Richmond
Philosophy and Critical ThinkingCommunication StudiesLaGuardia
College of the City University of New York
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