Sign Relations, Triadic Relations, Relation Theory

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • 1
http://inquiryintoinquiry.com/2020/10/10/sign-relations-triadic-relations-relation-theory-1/

To understand how signs work in Peirce's theory of triadic sign relations,
or “semiotics”, we have to understand, in order of increasing generality,
sign relations, triadic relations, and relations in general, each as
conceived in Peirce's logic of relative terms and the corresponding
mathematics of relations.

Toward that understanding, here are the current versions of articles
I long ago contributed to Wikipedia and continue more lately to develop
at a number of other places.

* Sign Relations ( https://oeis.org/wiki/Sign_relation )

* Triadic Relations ( https://oeis.org/wiki/Triadic_relation )

* Relation Theory ( https://oeis.org/wiki/Relation_theory )

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 1
http://inquiryintoinquiry.com/2020/10/11/sign-relations-triadic-relations-relation-theory-discussion-1/

Re: Peirce List ( https://list.iupui.edu/sympa/arc/peirce-l/2020-10/thrd1.html#00004 )
::: Edwina Taborsky ( https://list.iupui.edu/sympa/arc/peirce-l/2020-10/msg00005.html )

ET: I particularly like your comment that “signhood is a role
in a triadic relation, a role that a thing bears or plays
in a given context of relationships — it is not an absolute,
non-relative property of a thing-in-itself, one that it
possesses independently of all relationships to other things”.

ET: I myself emphasize that this context of the role is made up
of relationships (plural) — which gives the triad its capacity
for complexity. Therefore, as we see in Robert Marty's lattice,
a thing is never a thing-in-itself but is an action, a process,
composed of complex relations.

Dear Edwina,

Things grow complex rather quickly once we start to think about
all the roles a sign may play on all the stages where it struts
and frets its parts. There is no unique setting, no one scene,
but concentric and overlapping contexts of relationship all have
their bearing on the sign's significance.

One strategy we have for dealing with these complexities and avoiding
being overwhelmed by them is to build up a stock of well-studied examples,
graded in complexity from the very simplest to the increasingly complex.
The wide world may always present us with situations more complex than
any in our inventory of familiar cases but the better our stock of ready
examples the more aspects of novel situations we can capture and the
greater our odds of coping with them.

Regards,

Jon

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 2
http://inquiryintoinquiry.com/2020/10/12/sign-relations-triadic-relations-relation-theory-discussion-2/

Re: Peirce List ( https://list.iupui.edu/sympa/arc/peirce-l/2020-10/thrd1.html#00004

::: Edwina Taborsky ( https://list.iupui.edu/sympa/arc/peirce-l/2020-10/msg00007.html

Dear Edwina,

Analytic frameworks, our various theories of categories, sets, sorts, and types,
have their uses but they tend to become à priori, autonomous, top-down, and
top-heavy unless they are supported by a robust population of concrete examples
arising in practical experience, one of the things the maxim of pragmatism
( https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/ ) advises us
to remember. That is why Peirce's tackling of information and inquiry is
even-handed with respect to their extensional and intensional sides.
And it's why we need to pay attention when anomalies accumulate and
the population of presenting cases rebels against the dictates of
Procrustean predicates. Times like that tell us we may need to
reconceive our customary conceptual frameworks.

As it happens, I've been thinking a lot lately about a particular class of
sign sequences, namely, proofs in propositional calculus regarded as cases
of sign process, or semiosis. Naturally I've been thinking of delving more
deeply into Robert Marty's work ( https://www.academia.edu/s/4835fb2725 )
on paths through the lattice of sign classes but so far I'm still in the
early stages of that venture.

For what it's worth, here are my blog posts so far on Proof As Semiosis.

• Animated Logical Graphs
https://inquiryintoinquiry.com/2020/08/19/animated-logical-graphs-35/
https://inquiryintoinquiry.com/2020/08/21/animated-logical-graphs-36/
https://inquiryintoinquiry.com/2020/08/22/animated-logical-graphs-37/
https://inquiryintoinquiry.com/2020/08/25/animated-logical-graphs-38/
https://inquiryintoinquiry.com/2020/09/10/animated-logical-graphs-39/
https://inquiryintoinquiry.com/2020/09/26/animated-logical-graphs-40/
https://inquiryintoinquiry.com/2020/09/29/animated-logical-graphs-41/
https://inquiryintoinquiry.com/2020/10/03/animated-logical-graphs-42/

Regards,

Jon

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 3
http://inquiryintoinquiry.com/2020/12/29/sign-relations-triadic-relations-relation-theory-discussion-3/

All,

I decided the issue I discussed under “Adic Versus Tomic” comes up
often enough to deserve a revised text and upgraded figure so I put
a better copy on my blog, adding it to a series on Relation Theory
where I might have an easier time finding it again. Transcript below,
but see the link above for a more readable copy

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2020-11/thrd1.html#00022
::: Helmut Raulien
https://list.iupui.edu/sympa/arc/peirce-l/2020-11/msg00022.html

HR: As Peircean semiotics is a three-valued logic, I think it
bears relevance for the discussion about multiple-valued logic.

Dear Helmut,

The distinction between “k-adic” (involving a span of k dimensions) and “k-tomic” (involving a range of k values) is one
of the earliest questions I remember discussing on the Peirce List and the panoply of other lists we ranged across in
those heady surfer days. It is critical not to confuse the two aspects of multiplicity. In some cases it is possible
to observe what mathematicians call a projective relationship between the two aspects but that does not make them identical.

I'm adding a lightly edited excerpt from one of those earlier discussions as I think it introduces the issues about as
well as I could manage today.

Arisbe List
===========
https://web.archive.org/web/20150211184002/http://stderr.org/pipermail/arisbe/
Re: Inquiry Into Isms • k-adic versus k-tomic
https://web.archive.org/web/20141219190201/http://stderr.org/pipermail/arisbe/2001-August/thread.html#878
Jon Awbrey • 21 Aug 2001
https://web.archive.org/web/20141005035422/http://stderr.org/pipermail/arisbe/2001-August/000878.html

Here is an old note I've been looking for since we started on this bit about isms, as I feel I managed to express in it
my point of view that the key to integrating variant perspectives is to treat their contrasting values as axes or
dimensions rather than so many points on a line to be selected among, each in exclusion of all the others. To express
it briefly, it is the difference between k-tomic decisions among terminal values and k-adic dimensions of extended
variation.

Standard Upper Ontology List • Dyads
====================================
https://web.archive.org/web/20010312172719/http://suo.ieee.org/email/threads.html#02488
Jon Awbrey • 06 Dec 2000
https://web.archive.org/web/20010512091429/http://suo.ieee.org/email/msg02488.html
Jon Awbrey • 08 Dec 2000
https://web.archive.org/web/20010416032310/http://suo.ieee.org/email/msg02518.html

Jon Awbrey:
I think we need to distinguish “dichotomous thinking” from “dyadic thinking”. One has to do with the number of values,
{0, 1}, {F, T}, {evil, good}, and so on, one imposes on the cosmos, the other with the number of dimensions a person
puts on the face of the deep, that is to say, the number of independent axes in the frame of reference one projects on
the scene or otherwise puts up to put the cosmos on.

Tom Gollier:
Your transmission kind of faded out after the “number of values”, but do you mean a difference between, say, two values
of truth and falsity on the one hand, and all things being divided into subjects and predicates, functions and
arguments, and such as that on the other? If so, I'd like to second the notion, as not only are the two values much
less odious, if no less rigorous, in their applications, but they're often maligned as naive or simplistic by arguments
which actually should be applied to the idea, naive and simplistic in the extreme, that there are only two kinds of things.

Jon Awbrey:
There may be a connection — I will have to think about it — but trichotomic, dichotomic, monocotyledonic, whatever,
refer to the number of values, 3, 2, 1, whatever, in the range of a function. In contrast, triadic, dyadic, monadic, as
a series, refer to the number of independent dimensions involved in a relation, which could be represented as the axes
of a coordinate frame or the columns of a data table. As the appearance of the word “independent” should clue you in,
this will be one of those parti-colored woods in which the interpretive paths of mathematicians and normal folks are
likely to diverge.

A particular type of misunderstanding may arise when people imbued in the different ways of thinking try to communicate
with each other. The following figure illustrates the situation for the case where k = 2.

Figure. Dyadic Versus Dichotomic
https://inquiryintoinquiry.files.wordpress.com/2020/12/dyadic-versus-dichotomic.png

This shows how the “number of values” thinker projects the indications of the “number of axes” thinker onto the linear
spectrum of admitted directions, oppositions, or values, tending to reduce the mutually complementing dimensions to a
tug-of-war of strife-torn exclusions and polarizations.

Even when the tomic thinker tries to achieve a balance, a form of equilibrium, or a compromising harmony, the distortion
due to this style of projection will always render the resulting system untenable.

Probably my bias is evident.

But I think it is safe to say, for whatever else it might be good, tomic thinking is of limited use in trying to
understand Peirce's thought.

Just to mention one of the settings where this theme has arisen in my studies recently, you may enjoy the exercise of
reading, in the light of this projective template, Susan Haack's Evidence and Inquiry, where she strives to achieve a
balance or a compromise between foundationalism and coherentism, that is, more or less, objectivism and relativism, and
with some attempt to incorporate the insights of Peirce's POV. But a tomic thinker, per se, will not be able to
comprehend what the heck Peirce was talking about.

Resources
=========

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 4
http://inquiryintoinquiry.com/2020/12/31/sign-relations-triadic-relations-relation-theory-discussion-4/

Re: Previous Post
https://inquiryintoinquiry.com/2020/12/29/sign-relations-triadic-relations-relation-theory-discussion-3/
Re: Cybernetics
https://groups.google.com/g/cybcom/c/Wyz1oRmturc
::: Cliff Joslyn
https://groups.google.com/g/cybcom/c/Wyz1oRmturc/m/nRfUd8SLBwAJ

Dear Cliff,

Many thanks for your thoughtful reply. I copied a transcript
to my blog (see link above) to take up first thing next year.
Here's hoping we all have a better one!

Regards,

Jon

Cliff Joslyn wrote:

<QUOTE>
I think what you have is sound, and can be described in a number of ways.
In years past in seeking ways to both qualify and quantify variety in
systems I characterized this distinction as between “dimensional variety”
and “cardinal variety”. Thankfully, this seems straightforward from
a mathematical perspective, namely in a standard relational system
S = ×_{i=1}^k X_i, where the X_i are dimensions (something that can
vary), typically cast as sets, so that × here is Cartesian product.
Here k is the dimensional variety (number of dimensions, k-adicity),
while n_i = |X_i| is the cardinal variety (cardinality of dimension i,
n_i-tomicity (n_i-tonicity, actually?)). One might think of the two
most classic examples:

• Multiadic diatom/nic: Maximal (finite) dimensionality, minimal
non-trivial cardinality: The bit string (b_1, b_2, …, b_k) where
there are k Boolean dimensions X_i = {0, 1}. One can imagine k → ∞,
an infinite bit string, even moreso.

• Diadic infini-omic: Minimal non-trivial dimensionality,
maximal cardinality: The Cartesian plane ℝ², where there
are 2 real dimensions.

There's another quantity you didn't mention, which is the
overall “variety” or size of the system, so ∏_{n=1}^k n_i,
which is itself a well-formed expression (only) if there
are a finite number of finite dimensions.
</QUOTE>

[Cliff Joslyn]

Thanks, Jon, interested in your's and others' thoughts.

--
O------------------------------------->
| Cliff Joslyn, Cybernetician at Large
V cajo...@gmail.com

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 4
http://inquiryintoinquiry.com/2020/12/31/sign-relations-triadic-relations-relation-theory-discussion-4/

Cliff,

Just checking possible typo. Is that supposed to be ∏_{i=1}^k n_i ?

Jon

On 1/1/2021 11:38 PM, Cliff Joslyn wrote:
> Thanks, Jon, interested in your's and others' thoughts.

<...>
>> Cliff Joslyn wrote:
<...>

[Cliff Joslyn]

Yes, of course, thank you.

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 5
http://inquiryintoinquiry.com/2021/01/15/sign-relations-triadic-relations-relation-theory-discussion-5/

Re: Cybernetics
( https://groups.google.com/g/cybcom/c/Wyz1oRmturc )
::: Cliff Joslyn
( https://groups.google.com/g/cybcom/c/Wyz1oRmturc/m/nRfUd8SLBwAJ )

Dear Cliff,

I’m still collecting my wits from the mind-numbing events
of the past two weeks so I’ll copy your last remarks here
and work through them step by step.

CJ: <QUOTE>

I think what you have is sound, and can be described in a number of ways.
In years past in seeking ways to both qualify and quantify variety in
systems I characterized this distinction as between “dimensional variety”
and “cardinal variety”. Thankfully, this seems straightforward from
a mathematical perspective, namely in a standard relational system
S = ×_{i=1}^k X_i, where the X_i are dimensions (something that can
vary), typically cast as sets, so that × here is Cartesian product.

</QUOTE>

Relational systems are just the context we need. It is usual to
begin at a moderate level of generality by considering a space X
of the following form.

X = ×_{i=1}^k X_i = X_1 × X_2 × ... × X_{k-1} × X_k.

(I’ll use X instead of S here because I want to save the letter “S” for
sign domains when we come to the special case of sign relational systems.)

We can now define a “relation” L as a subset of a cartesian product.

L ⊆ X_1 × X_2 × ... × X_{k-1} × X_k.

There are two common ways of understanding the subset symbol “⊆”
in this context. Using language from computer science I’ll call
them the “weak typing” and “strong typing” interpretations.

• Under “weak typing” conventions L is just a set which happens to be
a subset of the cartesian product X_1 × X_2 × ... × X_{k-1} × X_k but
which could just as easily be cast as a subset of any other qualified
superset. The mention of a particular cartesian product is accessory
but not necessary to the definition of the relation itself.

• Under “strong typing” conventions the cartesian product
X_1 × X_2 × ... × X_{k-1} × X_k in the type-casting
L ⊆ X_1 × X_2 × ... × X_{k-1} × X_k is an essential part of the
definition of L. Employing a conventional mathematical idiom, a
k-adic relation over the nonempty sets X_1, X_2, ..., X_{k-1}, X_k
is defined as a (k+1)-tuple (L, X_1, X_2, ..., X_{k-1}, X_k) where
L is a subset of X_1 × X_2 × ... × X_{k-1} × X_k.

We have at this point opened two fronts of interest in cybernetics,
namely, the generation of variety and the recognition of constraint.
There’s more detail on this brand of relation theory in the resource
article linked below. I’ll be taking the strong typing approach to
relations from this point on, largely because it comports more
naturally with category theory & by which virtue it enjoys more
immediate applications to systems and their transformations.

But my eye-brain system is going fuzzy on me now,
so I’ll break here and continue later ...

Regards,

Jon

Resources
=========

• Relation Theory ( https://oeis.org/wiki/Relation_theory )

• Triadic Relations ( https://oeis.org/wiki/Triadic_relation )

• Sign Relations ( https://oeis.org/wiki/Sign_relation )

> overall “variety” or size of the system, so ∏_{i=1}^k n_i,

[Jon Awbrey]

Azamat, Helmut, John, All ...

We (some of us) have doggedly chased our assorted masters down this road
so many times before I could hardly e-numerate them all especially since
the lion's share of their spoors long ago disapparated from the live web.

But here's just a trace I found of an early relic ...

ONT Inquiry Into Symbolization (29 Aug 2001)
### http://web.archive.org/web/20070320034430/http://suo.ieee.org/ontology/thrd46.html#03201
(1) http://web.archive.org/web/20081204194050/http://suo.ieee.org/ontology/msg03201.html
(2) http://web.archive.org/web/20081204194631/http://suo.ieee.org/ontology/msg03202.html
(3) http://web.archive.org/web/20080906121059/http://suo.ieee.org/ontology/msg03204.html
(4) http://web.archive.org/web/20081011051100/http://suo.ieee.org/ontology/msg03234.html

In the middle of a different discussion now,
will get back to this later when I'm able ...

Regards,

Jon

On 1/17/2021 3:13 AM, Azamat Abdoullaev wrote:> John wrote:
> "Diogenes the Cynic plucked a chicken/cock and threw it into Plato's
> Academy while shouting "Here is Plato's man."
>
> Thanks, John. It is one of the funniest and smartest history memes.
> To extend it a bit.
> When asked about the origin of his epithet, *cynic/*dog, Diogenes replied
> that it was given to him because he “fawns upon those who give him anything
> and barks at those who give him nothing.”
>
> It implies that operational meanings or definitions could be more
> significant than an intension/extension or representation/reference or
> connotation/denotation dichotomy.
>
> On Sun, Jan 17, 2021 at 7:43 AM John F. Sowa <so...@bestweb.net> wrote:
>
>> Helmut,
>>
>> The distinction between intension and extension is important for every
>> version of logic since antiquity. The oldest example is "rational animal"
>> vs. "featherless biped" -- those are two terms with different intensions,
>> but the same extension. Diogenes the Cynic plucked a chicken and threw it
>> into Plato's Academy while shouting "Here is Plato's man."
>>
>> Alonzo Church, who wrote that excerpt I cited, had been the editor of the
>> Journal of Symbolic Logic for many years.
>>
>> It's just as important for the latest work in computer science for both
>> theory and applications.
>>
>> John
>>

[Michael Lissack]

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 6
http://inquiryintoinquiry.com/2022/03/01/sign-relations-triadic-relations-relation-theory-discussion-6/

Re: FB | Charles S. Peirce Society
https://www.facebook.com/groups/peircesociety/posts/2551077815028195/
::: Alain Létourneau
https://www.facebook.com/groups/peircesociety/posts/2551077815028195?comment_id=2552574114878565

All,

Alain Létourneau asks if I have any thoughts
on Peirce's Rhetoric. I venture the following.

Classically speaking, rhetoric (as distinguished from dialectic)
treats forms of argument which “consider the audience” — which
take the condition of the addressee into account. But that is
just what Peirce's semiotic does in extending our theories of
signs from dyadic to triadic sign relations.

We often begin our approach to Peirce's semiotics by saying he puts the
interpreter back into the relation of signs to their objects. But even
Aristotle had already done that much. Peirce's innovation was to apply
the pragmatic maxim, clarifying the characters of interpreters in terms
of their effects — their interpretants — in the flow of semiosis.

Some reading —

Awbrey, J.L., and Awbrey, S.M. (1995),
“Interpretation as Action • The Risk of Inquiry”,
Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Regards,

Jon

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 7
https://inquiryintoinquiry.com/2022/04/05/sign-relations-triadic-relations-relation-theory-discussion-7/

Re: FB | Dan Everett
https://www.facebook.com/dan.everett.1884
::: On the Origin of Symbols and the Descent of Signs
https://www.facebook.com/dan.everett.1884/posts/286365076993646

All,

A conversation with Dan Everett on Facebook led me to explain
the following point about symbols a little better, or at least
in fewer words, than I think I’ve ever managed before.

Symbols are the genus, the equipotential stem cells of all signs.
Icons and indices are the degenerate species, the differentiated
specializations.

This a consequence of triadic relation irreducibility.
A further consequence is that symbols do not evolve from
icons and indices but the latter devolve from symbols.

To say symbols are the genus of signs is to say every sign has
the generic potential of a symbol. This means when we see an
apparent progression from degenerate species to genuine symbols
it is not evolution or even development properly speaking but
more akin to release of inhibition.

Regards,

Jon

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 8
https://inquiryintoinquiry.com/2022/04/08/sign-relations-triadic-relations-relation-theory-discussion-8/

Re: FB | Dan Everett • On the Origin of Symbols and the Descent of Signs
https://www.facebook.com/dan.everett.1884/posts/286365076993646

All,

Continuing a discussion about the autonomous character of symbols.
https://inquiryintoinquiry.com/2022/04/05/sign-relations-triadic-relations-relation-theory-discussion-7/

There are a few passages from Peirce going most quickly to the
root of the matter and working to keep the main ideas in mind —
before one gets too bogged down and bewildered by the full‑blown
classification mania so common in the literature.

The following statement is key.

<QUOTE CSP:>
Thought is not necessarily connected with a brain. It appears in the
work of bees, of crystals, and throughout the purely physical world;
and one can no more deny that it is really there, than that the colors,
the shapes, etc., of objects are really there.

C.S. Peirce, Collected Papers (CP 4.551)
https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#Instrumental_Focus
</QUOTE>

I know this is a Golden Oldie, but as the years go by
I find many people have taken away different messages
from even the most familiar tunes, making it fruitful
every now and again to accord old themes another turn.

Regards,

Jon

[Jon Awbrey]

Cf: Sign Relations, Triadic Relations, Relation Theory • Discussion 9
https://inquiryintoinquiry.com/2022/04/09/sign-relations-triadic-relations-relation-theory-discussion-9/

| Once, there was nothing there, nothing moving on its own,
| just data and people shuffling it around. Then something
| happened, and it … it knew itself.
|
| William Gibson • “Count Zero”
| https://web.archive.org/web/20050426214714/http://stderr.org/pipermail/arisbe/2001-January/000124.html

Re: FB | Dan Everett • On the Origin of Symbols and the Descent of Signs
https://www.facebook.com/dan.everett.1884/posts/286365076993646

All,

Continuing a discussion on the generative power of symbols.

Here’s the skinny on the big three types of signs. Despite its simplicity,
or maybe because of it, the larger implications for the interpretive character
of sign typing still goes widely missed.

Semeiotic • Types of Signs
https://oeis.org/wiki/Semeiotic#Types_of_signs

There are three principal ways a sign may denote its objects.
The modes of representation are often referred to as kinds,
species, or types of signs but it is important to recognize
they are not ontological species, that is, they are not
mutually exclusive features of description, since the
same thing can be a sign in several different ways.

Beginning very roughly, the three main ways of being a sign can be described as follows.

• An icon denotes its objects by virtue of a quality it shares with its objects.

• An index denotes its objects by virtue of an existential connection it has to its objects.

• A symbol denotes its objects solely by virtue of being interpreted to do so.

One of Peirce’s early delineations of the three types of signs affords
a useful first approach to understanding their differences and their
relationships to each other.

<QUOTE CSP:>
In the first place there are likenesses or copies — such as statues,
pictures, emblems, hieroglyphics, and the like. Such representations
stand for their objects only so far as they have an actual resemblance
to them — that is agree with them in some characters. The peculiarity
of such representations is that they do not determine their objects —
they stand for anything more or less; for they stand for whatever
they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by
a convention of men or a decree of God. Such are tallies,
proper names, &c. The peculiarity of these conventional
signs is that they represent no character of their objects.
Likenesses denote nothing in particular; conventional signs
connote nothing in particular.

The third and last kind of representations are symbols or general
representations. They connote attributes and so connote them as
to determine what they denote. To this class belong all words
and all conceptions. Most combinations of words are also symbols.
A proposition, an argument, even a whole book may be, and should be,
a single symbol. (Peirce 1866, Lecture 7, 467–468).
</QUOTE>

Reference
=========

Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”,
in Writings of Charles S. Peirce : A Chronological Edition, Volume 1 (1857–1866),
Peirce Edition Project, Indiana University Press, Bloomington & Indianapolis, IN,
1982. Lowell Lectures of 1866, 357–504.

Regards,

Jon

[Jon Awbrey]

Sign Relations, Triadic Relations, Relation Theory • Discussion 10
https://inquiryintoinquiry.com/2022/04/11/sign-relations-triadic-relations-relation-theory-discussion-10/

Re: FB | Dan Everett • On the Origin of Symbols and the Descent of Signs
https://www.facebook.com/dan.everett.1884/posts/286365076993646

All,

Continuing a discussion on the generative power of symbols (1) (2) (3).
https://inquiryintoinquiry.com/2022/04/09/sign-relations-triadic-relations-relation-theory-discussion-9/

If it’s true what I say about symbols being the genus of all signs
then it must be possible to say what differentia are added to the
genus in order to generate every subtended species, beginning with
icons and indices.

Turning first to icons, we have the following from Peirce.

<QUOTE CSP:>
In the first place there are likenesses or copies —
such as statues, pictures, emblems, hieroglyphics,
and the like. Such representations stand for their
objects only so far as they have an actual resemblance
to them — that is agree with them in some characters.
The peculiarity of such representations is that they
do not determine their objects — they stand for anything
more or less; for they stand for whatever they resemble
and they resemble everything more or less.

(Peirce 1866, Lecture 7, 467).
</QUOTE>

Let’s say we look inside a triadic sign relation L ⊆ O × S × I
and we notice a triple (o, s, i) where o and s have a character χ
in common. We may quite naturally be tempted to make a further leap
and suppose the sign s receives the interpretant sign i precisely by
virtue of the character χ shared by o and s. I know that looks like
a lot of supposing but the fact is we do the like all the time without
hardly giving it a second thought. But critical reflection demands we
bat an i and give it second and third thoughts.

The catch is tucked away in Peirce’s last sentence. “The peculiarity

of such representations is that they do not determine their objects —
they stand for anything more or less; for they stand for whatever

they resemble and they resemble everything more or less.”

There may be a lot of characters shared by o and s in a given
environment or universe of discourse, any selection of which
may account for the linking of o and s to i. As long as we
remain content to operate in a theoretical vacuum devoid of
empirical grounding, who’s to say any number of them do not
qualify?

But a question arises when we use a sign relation L to model
an empirical system of interpretive practice, whether its agent
is a single individual or a whole community of interpretation.
The question is — Do the characters we mark as effective in our
model actually do the job for the agent?

An icon denotes its objects by virtue of qualities it shares with its
objects. But icons are icons solely because they are interpreted as
icons, by dint of particular qualities chosen from many by the very
process of interpretation in view. This gives us a glimmer of the
interpretive character of sign typing, that sign typologies are not
absolute but relative to the sign relation at hand. To paraphrase
William James, The trail of the hermeneutic serpent is over all.

Regards,

Jon

[Jon Awbrey]

Sign Relations, Triadic Relations, Relation Theory • Discussion 11
• https://inquiryintoinquiry.com/2023/09/12/sign-relations-triadic-relations-relation-theory-discussion-11/

Re: Michael Shapiro • Redefining Arbitrariness in Language
• https://languagelore.net/
• https://languagelore.net/2023/04/03/redefi-ning-arbitrariness-in-language/

<QUOTE MS:>
The matter of arbitrariness in language is primarily associated with the
work of the Swiss linguist, Ferdinand de Saussure (1857–1913), whose book
of lectures, Cours de linguistique Générale, is widely recognized to have
laid the foundations of European structural linguistics in the twentieth
century. One of Saussure's most quoted positions points out that the
meaning of words is arbitrary, in that, for instance, the word “arbre” in
French and its equivalent “tree” in English have nothing to do “naturally”
with the object they signify. Any other sequence of sounds could in theory
designate the same object. These are just the words French and English happen
to have inherited from their history.
</QUOTE>

I prefer to think of the word “arbitrary” as reminding us how every aspect
of a sign's functioning is relative to an arbiter, a judge, an interpreter.
That brings semiology more into harmony with Peirce's semiotics — if only
Saussure had realized how it embeds all dyadic sign relations within the
fold of triadic sign relations!

Regards,

Jon