Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 19
https://inquiryintoinquiry.com/2021/10/05/semiotics-semiosis-sign-relations-discussion-19/

All,

I included this note in a series where I may more easily find it again
and added the Figure which always helps me stay oriented in this arena.

Figure.  Normative Science, Phenomenology, Mathematics, Metaphysics
http://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg

Caption.  “Normative science rests largely on phenomenology and on
mathematics;  metaphysics on phenomenology and on normative science.”

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)
Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)
ttp://web.archive.org/web/2005121054/http://www.princeton.edu/~batke/peirce/cl_o_sci_03.htm

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-10/thrd1.html#00013
::: John Sowa
https://list.iupui.edu/sympa/arc/peirce-l/2021-10/msg00013.html


Questions for everybody to consider:  In the 1903 classification of the
sciences, Peirce did not mention semeiotic, the most important science
that he introduced.  Why not?  Where does it belong in the classification?


The short schrift on this subject may be summed up in the following syllogism.

Logic = Formal Semiotic
===

C.S. Peirce • On the Definition of Logic
https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-on-the-definition-of-logic/

Formal = Quasi-Necessary = Normative


C.S. Peirce • Logic as Semiotic
https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-logic-as-semiotic/
(It's a peculiar use, but it's Peirce's peculiar use in this context.)

Conclusion.  Logic = Normative Semiotic.


Corollary.  This leaves room for Descriptive Semiotic.
==

Additional Notes


Definition and Determination • 5
https://inquiryintoinquiry.com/2012/06/02/definition-and-determination-5/

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jerry LR Chandler]

List:

> On Sep 28, 2021, at 9:30 AM, Jon Awbrey  wrote:
> 
> The likeness theory of reference has the same problem as the
> correspondence theory of truth, namely, as used in those theories
> both terms refer to dyadic relations and dyadic relations are not
> adequate to the task of accounting for the complex of activities
> composing the intellect, for example, inquiry, learning, reasoning,
> speech, thought,

The applications of the principles of correspondence relations, in three forms, 
1:1 and 1:many and many:1are intrinsic to the logic of chemical notation as 
used by CSP.

These correspondence relations are necessary to express the truth functions of 
chemical reactions, chemical equilibrium, chemical thermodynamics and the Law 
of mass action.

And, by the way, all of these chemical processes for necessary to generate 
embryogenesis and neurogenesis and hence mentation.

Cheers
Jerry _ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 18
https://inquiryintoinquiry.com/2021/09/28/semiotics-semiosis-sign-relations-discussion-18/

Re: FB | Medieval Logic
https://www.facebook.com/groups/medievallogic
::: Edward Buckner
https://www.facebook.com/groups/medievallogic/posts/1840849412784222
https://www.facebook.com/groups/medievallogic/posts/1841508382718325

On Pragmata
===

The object of a sign is any object of discussion or thought.
It is relational not ontological.  This is the beginning of
pragmatic semiotics.

On Homoiomata
=

The likeness theory of reference has the same problem as the
correspondence theory of truth, namely, as used in those theories
both terms refer to dyadic relations and dyadic relations are not
adequate to the task of accounting for the complex of activities
composing the intellect, for example, inquiry, learning, reasoning,
speech, thought, in short, Information Development/Exchange Activities.

In actuality, Aristotle comes closer to recognizing the triadic relation of
Objects, Signs, and Ideas than the majority of later writers before Peirce.
Here is the figure Susan Awbrey and I cut in our first hack at the matter.

Figure 1.  The Sign Relation in Aristotle
https://inquiryintoinquiry.files.wordpress.com/2021/09/the-sign-relation-in-aristotle.png

Resources
=

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.
Archive
https://web.archive.org/web/19970626071826/http://chss.montclair.edu/inquiry/fall95/awbrey.html
Journal
https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
Online
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry

πρᾶγμα
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpra%3Dgma
Liddell, H.G., and Scott, R. (1925), A Greek-English Lexicon (1940 edition),
Perseus Digital Library ( http://www.perseus.tufts.edu )

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 17
https://inquiryintoinquiry.com/2021/09/12/semiotics-semiosis-sign-relations-discussion-17/

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/thrd5.html#00090
::: Robert Marty
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00141.html
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00151.html
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00178.html

Dear Robert,

I've been reviewing the discussions of August on this topic
and I think it might be possible to advance our inquiry and
even establish new levels of competence in our theory of signs
if we examined the main points again and dedicated ourselves to
clearing up the subject's more persistent enigmas.

As I was preparing to recap our earlier discussions, it gradually
dawned on me how one issue more than any other is the source of major
misunderstanding and a whole lot of “people talking past each other”,
as the saying goes.  To put it succinctly if very roughly, it has to do
with the difference between people who have tests and are seeking answers
and people who have answers and are seeking tests.  I say “very roughly”
because it's clear all of us are all of those people *some* of the time.
And yet we do see cognitive bifurcations and cultural divides persisting
over time, to one basin or the other of which people often find themselves
resorting for extended periods if not the duration of a lifetime.

I'll take up a tactic for dealing with this issue next time.

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 16
https://inquiryintoinquiry.com/2021/09/02/semiotics-semiosis-sign-relations-discussion-16/

Re: FB | Semeiotics
https://www.facebook.com/Semeiotic/posts/4441505199249593
::: Marius V. Constantin
https://www.facebook.com/groups/964364967280710/posts/1502285400155328/

Marius Constantin asked a series of questions
which allow me to clear up a number of points.


Have you taken into consideration the difference
between weak negation and strong negation?


I always begin classically where logic is concerned — I guess that means
“strong” negation — we make a stronger start and get better mileage on
that basis before we run into the specialized circumstances, mainly
in computational and generalized semiotic settings, which force us
to weaken our logic.


It is so-called semiotic negation, which, by the way, was an aspect, for me,
in so-called resolution logic (Ch. Sanders Peirce is mentioned on that one).


I had a computer science course on resolution-unification theorem provers
at U. Illinois in the mid 1980s.  If that’s the same sort of resolution,
it generalizes the modus ponens inference rule, all of which exemplify
implicational inference.  Peirce’s logical graphs allow a degree of
equational or information-preserving inference, a fact which
Spencer Brown drew out and made more clear.

Regards,

Jon

_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 15
https://inquiryintoinquiry.com/2021/09/01/semiotics-semiosis-sign-relations-discussion-15/

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/thrd5.html#00090
::: Robert Marty (quoted)
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00292.html


I persist in the idea that in your six combinations [O, S, I] only one
is relevant for semiotics, the others being out of the field […] On the
projections, there is also matter for discussion … but to discuss well
one must reserve a rather large agenda … I thus wait for your reply
dealing with semiosis to resume a debate well-centered on the essential …

Dear Robert,

Returning to our discussion of 3-place relations and the 6 conversions
they enjoy under the action of the symmetric group S₃ permuting their
places, it’s been a while so I’ll extract the substance of my last
reply and continue from there.

We had been contemplating Peirce's variations on a theme of giving
as presented in the section of the Sign Relation article titled
“Six Ways of Looking at a Sign Relation”.

That section begins as follows.

https://oeis.org/wiki/Sign_relation#Six_ways_of_looking_at_a_sign_relation 
>

In the context of 3-adic relations in general, Peirce provides the
following illustration of the six converses of a 3-adic relation,
that is, the six differently ordered ways of stating what is
logically the same 3-adic relation:



So in a triadic fact, say, for example

• A gives B to C

we make no distinction in the ordinary logic of relations between
the subject nominative, the direct object, and the indirect object.
We say that the proposition has three logical subjects.  We regard
it as a mere affair of English grammar that there are six ways of
expressing this:

[Display.  Six Ways of Looking at a Sign Relation]
https://inquiryintoinquiry.files.wordpress.com/2021/04/six-ways-of-looking-at-a-triadic-relation-e28cac-1.png

These six sentences express one and the same indivisible phenomenon.
(C.S. Peirce, “The Categories Defended”, MS 308 (1903), EP 2, 170–171).



I called attention to the moral Peirce draws.

• “These six sentences express one and the same indivisible phenomenon.”

With that one statement Peirce draws the clearest possible
line of demarcation between affairs of grammar and affairs
of logic, mathematics, and phenomena.

The same lesson applies to any relation whose places are not
in general reserved for fixed types of entities, in particular,
it applies to triadic sign relations.  As we say, “objects, signs,
and interpretants are roles not essences”.

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 14
https://inquiryintoinquiry.com/2021/08/31/semiotics-semiosis-sign-relations-discussion-14/

Re: Animated Logical Graphs • 81
https://inquiryintoinquiry.com/2021/08/26/animated-logical-graphs-81/
Re: Semiotics, Semiosis, Sign Relations • Discussion 13
https://inquiryintoinquiry.com/2021/08/30/semiotics-semiosis-sign-relations-discussion-13/

All,

Topics arising in various circles I traverse on the web
are flashing me back to my earliest influences in the ways
of inquiry driven systems.  Dick Lipton and Ken Regan brought
to mind the generative power of negative operations and the
specific limits of perceptrons.  Peiyuan Zhu and Henry Story
discussed a paper by Michael Heller and Jerzy Król titled
“How Logic Interacts with Geometry : Infinitesimal Curvature
of Categorical Spaces”.  It was over my head, just a bit,
but it reminded me of early questions about logical atoms,
individuals, nominalism vs. realism, and quantum logics,
not to mention current pursuits in differential logic,
all of which feedback into the ouroborian ampheckbaena
of NAND and NNOR among negative ops.

It will be interesting to see what evolves …

Resources
=

Survey of Animated Logical Graphs
https://inquiryintoinquiry.com/2021/05/01/survey-of-animated-logical-graphs-4/

Survey of Differential Logic
https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

Survey of Inquiry Driven Systems
https://inquiryintoinquiry.com/2020/12/27/survey-of-inquiry-driven-systems-3/

Survey of Semiotics, Semiosis, Sign Relations
https://inquiryintoinquiry.com/2019/10/29/survey-of-semiotics-semiosis-sign-relations-1/

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 13
https://inquiryintoinquiry.com/2021/08/30/semiotics-semiosis-sign-relations-discussion-13/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
::: Peiyuan Zhu
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/251113234
::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/251115511

Zulip Inivitation Link:
https://categorytheory.zulipchat.com/join/uez4ystfwhbwazggfurgxkm7/

Dear Peiyuan, Henry …

Way back during my first foundation + identity crisis I explored every
alternative, deviant, non-standard version of logic and set theory
I could scrape up — I remember saying to one of my professors,
“How come we’re still talking about logical atoms in the quantum era?” —
and he sent me off to read about quantum logics, which had apparently
already fallen out of fashion at the time.  Remarkably enough, I did
find one Peircean scholar who had done a lot of work on them, but
they didn’t seem to be what I needed right then.

My present, still pressing applications require me to start from much more
elementary grounds, stuff I can build up from boolean sources and targets,
universes with coordinate spaces of type (Bⁿ, Bⁿ → B).

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 12
https://inquiryintoinquiry.com/2021/08/25/semiotics-semiosis-sign-relations-discussion-12/

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/thrd5.html#00090
::: Robert Marty (quoted)
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00292.html


I persist in the idea that in your six combinations [O, S, I]
only one is relevant for semiotics, the others being out of the
field […] On the projections, there is also matter for discussion …
but to discuss well one must reserve a rather large agenda …
I thus wait for your reply dealing with semiosis to resume
a debate well-centered on the essential …

Dear Robert,

A bit of calm today — and feeling slaked after a day spent
minding Voltaire's advice and pulling weeds from our garden —
I'll take up one of your last problems first as it may be
the one most quickly resolved.

I take it you are referring to the section of the
Sign Relation ( https://oeis.org/wiki/Sign_relation )
article titled “Six Ways of Looking at a Sign Relation”
( https://oeis.org/wiki/Sign_relation#Six_ways_of_looking_at_a_sign_relation )
which begins as follows.


In the context of 3-adic relations in general, Peirce provides the
following illustration of the six converses of a 3-adic relation,
that is, the six differently ordered ways of stating what is
logically the same 3-adic relation:


So in a triadic fact, say, for example

• A gives B to C

we make no distinction in the ordinary logic of relations between
the subject nominative, the direct object, and the indirect object.
We say that the proposition has three logical subjects.  We regard
it as a mere affair of English grammar that there are six ways of
expressing this:

[Display.  Six Ways of Looking at a Sign Relation]
https://inquiryintoinquiry.files.wordpress.com/2021/04/six-ways-of-looking-at-a-triadic-relation-e28cac-1.png

These six sentences express one and the same indivisible phenomenon.
(C.S. Peirce, “The Categories Defended”, MS 308 (1903), EP 2, 170–171).


“These six sentences express one and the same indivisible phenomenon.”

It's a statement telling of the difference between affairs of grammar
and affairs of logic, mathematics, and phenomena.

To be continued …

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

ah, what do mathematicians know of life's exigency?
proof is our rock and our soul necessity.
we don't just make abstractions, we are abstractions.
it's coffee and doughnuts all the way down ...
no one disturbs our vain diagrams
till human voices wake us, and we drown.

 also sprach 0*
   23 august 2021

On 8/23/2021 3:57 AM, robert marty wrote:

Dear Jon,
I myself am concerned by several deluges ( 5 urgent reviews to finish, a
fight to fight on the slow read, a synopsis for an article to provide,
another for a treatise, etc...) ... but I don't complain because I like it!
But I also like to be precise in my arguments. I persist in the idea that
in your six combinations O, S, only one is relevant for semiotics, the
others being out of the field ... I made the same criticism to Gary R. with
his strange "trikons" ... on the projections, there is also matter for
discussion  but to discuss well one must reserve a rather large agenda
.. I thus wait for your reply dealing with semiosis to resume a debate
well centered on the essential ...

Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *

_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 11
https://inquiryintoinquiry.com/2021/08/22/semiotics-semiosis-sign-relations-discussion-11/

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/thrd1.html#9
::: Robert Marty
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00132.html


Dear Jon,

You evoke many concepts with their relations, the explanation of which would take a considerable amount of time, to the 
point that you are reduced to answering yourself.  I want to question you on the point that interests me particularly, 
which concerns your entry into Peirce's semiotics.  I found it among all your links here:


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

You will tell me if this is the right reference.  If it is so, then I think you have made a bad choice, and of course, I 
explain myself.  To be clear and precise, I must reproduce the entirety of your “Definition“ paragraph:


• Definition ( https://oeis.org/wiki/Sign_relation#Definition )


Dear Robert,

I'm just beginning to get out from under the deluge of tasks
put off by the pandemic ... I think I can finally return to
your remarks of August 12 on my sketch of Peirce's theory
of signs for the general reader interested in semiotics.

Your message to the List had many detailed quotations, so I'm
in the process of drafting an easier-on-the-eyes blog version.
When I get done with that — it may be a day — I'll post my reply
on the thread dealing with Semiotics, Semiosis, Sign Relations,
so as to keep focused on signs.

Semiotics, Semiosis, Sign Relations
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/thrd5.html#00090

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[robert marty]

Jon, excuse me for "John" ...
Honorary Professor ; PhD Mathematics ; PhD Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le dim. 15 août 2021 à 12:18, robert marty  a
écrit :

> Dear John,
>
> I think that the text "*Modeling in Humanities: the case of Peirce's
> Semiotics (Part A*)" that I just published answers your question. I
> maintain that retaining a definition of the sign that does not incorporate
> the internal determinations of the sign by the object and the interpreter
> by the sign does not allow us to classify signs. But you can still try to
> find a meaning to each of the 6 combinations of S, O, I by not using the
> interdependence of the categories, which translates into the
> phenomenological constraint according to which::* "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.*" (EP2: 481).
> This constraint is the only one that allows us to control the combinatory
> explosion.
> ...
> Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
> fr.wikipedia.org/wiki/Robert_Marty
> *https://martyrobert.academia.edu/ *
>
>
>
> Le sam. 14 août 2021 à 18:45, Jon Awbrey  a écrit :
>
>> Cf: Semiotics, Semiosis, Sign Relations • Discussion 10
>>
>> https://inquiryintoinquiry.com/2021/08/14/semiotics-semiosis-sign-relations-discussion-10/
>>
>> Re: Semiotics, Semiosis, Sign Relations • Discussion 8
>>
>> https://inquiryintoinquiry.com/2021/08/13/semiotics-semiosis-sign-relations-discussion-8/
>>
>> Re: Category Theory
>>
>> https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
>> ::: Morgan Rogers
>>
>> https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/249456735
>>
>>  Please clearly state at least one “distinctive quality of
>> sign relations”. 
>>
>> Dear Morgan,
>>
>> Sign relations are triadic relations.
>>
>> Can any triadic relation be a sign relation?
>>
>> I don’t know.  I have pursued the question myself whether any
>> triadic relation could be used somehow or other in a context
>> of communication, information, inquiry, learning, reasoning,
>> and so on where concepts of signs and their meanings are
>> commonly invoked — there’s the rub — it’s not about what
>> a relation is “intrinsically” or “ontologically” at all
>> but a question of “suitability for a particular purpose”
>> as they say in all the standard disclaimers.
>>
>> What Peirce has done is to propose a definition intended to capture an
>> intuitive, pre-theoretical, traditional concept of signs and their uses.
>> To put it on familiar ground, it’s like Turing’s proposal of his namesake
>> machine to capture the intuitive concept of computation.  That is not a
>> matter to be resolved by à priori dictates but by trying out candidate
>> models in the intended applications.
>>
>> I gave you what I consider Peirce’s best definition of a “sign”
>> in relational terms and I pointed out where it needs filling out
>> to qualify as a proper mathematical definition, most pointedly in
>> the further definitions of “correspondence” and “determination”.
>>
>> That is the current state of the inquiry as it stands at this site …
>>
>> Regards,
>>
>> Jon
>> _ _ _ _ _ _ _ _ _ _
>> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
>> PEIRCE-L to this message. PEIRCE-L posts should go to
>> peirce-L@list.iupui.edu .
>> ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to
>> l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the
>> message and nothing in the body.  More at
>> https://list.iupui.edu/sympa/help/user-signoff.html .
>> ► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;
>> and co-managed by him and Ben Udell.
>>
>
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[robert marty]

Dear John,

I think that the text "*Modeling in Humanities: the case of Peirce's
Semiotics (Part A*)" that I just published answers your question. I
maintain that retaining a definition of the sign that does not incorporate
the internal determinations of the sign by the object and the interpreter
by the sign does not allow us to classify signs. But you can still try to
find a meaning to each of the 6 combinations of S, O, I by not using the
interdependence of the categories, which translates into the
phenomenological constraint according to which::* "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.*" (EP2: 481).
This constraint is the only one that allows us to control the combinatory
explosion.
...
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le sam. 14 août 2021 à 18:45, Jon Awbrey  a écrit :

> Cf: Semiotics, Semiosis, Sign Relations • Discussion 10
>
> https://inquiryintoinquiry.com/2021/08/14/semiotics-semiosis-sign-relations-discussion-10/
>
> Re: Semiotics, Semiosis, Sign Relations • Discussion 8
>
> https://inquiryintoinquiry.com/2021/08/13/semiotics-semiosis-sign-relations-discussion-8/
>
> Re: Category Theory
>
> https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
> ::: Morgan Rogers
>
> https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/249456735
>
>  Please clearly state at least one “distinctive quality of sign
> relations”. 
>
> Dear Morgan,
>
> Sign relations are triadic relations.
>
> Can any triadic relation be a sign relation?
>
> I don’t know.  I have pursued the question myself whether any
> triadic relation could be used somehow or other in a context
> of communication, information, inquiry, learning, reasoning,
> and so on where concepts of signs and their meanings are
> commonly invoked — there’s the rub — it’s not about what
> a relation is “intrinsically” or “ontologically” at all
> but a question of “suitability for a particular purpose”
> as they say in all the standard disclaimers.
>
> What Peirce has done is to propose a definition intended to capture an
> intuitive, pre-theoretical, traditional concept of signs and their uses.
> To put it on familiar ground, it’s like Turing’s proposal of his namesake
> machine to capture the intuitive concept of computation.  That is not a
> matter to be resolved by à priori dictates but by trying out candidate
> models in the intended applications.
>
> I gave you what I consider Peirce’s best definition of a “sign”
> in relational terms and I pointed out where it needs filling out
> to qualify as a proper mathematical definition, most pointedly in
> the further definitions of “correspondence” and “determination”.
>
> That is the current state of the inquiry as it stands at this site …
>
> Regards,
>
> Jon
> _ _ _ _ _ _ _ _ _ _
> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
> peirce-L@list.iupui.edu .
> ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to
> l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the
> message and nothing in the body.  More at
> https://list.iupui.edu/sympa/help/user-signoff.html .
> ► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and
> co-managed by him and Ben Udell.
>
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 10
https://inquiryintoinquiry.com/2021/08/14/semiotics-semiosis-sign-relations-discussion-10/

Re: Semiotics, Semiosis, Sign Relations • Discussion 8
https://inquiryintoinquiry.com/2021/08/13/semiotics-semiosis-sign-relations-discussion-8/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
::: Morgan Rogers
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/249456735

 Please clearly state at least one “distinctive quality of sign 
relations”. 

Dear Morgan,

Sign relations are triadic relations.

Can any triadic relation be a sign relation?

I don’t know.  I have pursued the question myself whether any
triadic relation could be used somehow or other in a context
of communication, information, inquiry, learning, reasoning,
and so on where concepts of signs and their meanings are
commonly invoked — there’s the rub — it’s not about what
a relation is “intrinsically” or “ontologically” at all
but a question of “suitability for a particular purpose”
as they say in all the standard disclaimers.

What Peirce has done is to propose a definition intended to capture an
intuitive, pre-theoretical, traditional concept of signs and their uses.
To put it on familiar ground, it’s like Turing’s proposal of his namesake
machine to capture the intuitive concept of computation.  That is not a
matter to be resolved by à priori dictates but by trying out candidate
models in the intended applications.

I gave you what I consider Peirce’s best definition of a “sign”
in relational terms and I pointed out where it needs filling out
to qualify as a proper mathematical definition, most pointedly in
the further definitions of “correspondence” and “determination”.

That is the current state of the inquiry as it stands at this site …

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 9
http://inquiryintoinquiry.com/2021/08/14/semiotics-semiosis-sign-relations-discussion-9/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
::: Morgan Rogers
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/248952679


Okay, I may have mixed up the meanings of “object” and “interpretant”
in my plain language translations above?  Re determination, I read
“B is determined by A” as meaning the conjunction of

∀a ∈ A, ∃b ∈ B, ∃c ∈ C, R(a,b,c)

and

∀a ∈ A, ∀c ∈ C, R(a,b,c) ∧ R(a,b',c) ⇒ b = b' ?

Whether this is right depends on the answers to my previous questions.


Dear Morgan,

Let's look at the gloss I gave for Determination under the Definition
( https://oeis.org/wiki/Sign_relation#Definition )  of a Sign Relation
( https://oeis.org/wiki/Sign_relation ).

• Determination.  Peirce's concept of determination is broader in several
  directions than the sense of the word that refers to strictly deterministic
  causal-temporal processes.  First, and especially in this context, he is
  invoking a more general concept of determination, what is called a formal
  or informational determination, as in saying “two points determine a line”,
  rather than the more special cases of causal and temporal determinisms.
  Second, he characteristically allows for what is called “determination in
  measure”, that is, an order of determinism that admits a full spectrum of
  more and less determined relationships.

Other words for this general order of determination are structure,
pattern, law, form, and one coming up especially in cybernetics and
systems theory, constraint.  It's what happens when not everything
that might happen actually does.  (The stochastic mechanic or the
quantum technician will probably quip at this point, “At least,
not with equal probability.”)

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 8
https://inquiryintoinquiry.com/2021/08/13/semiotics-semiosis-sign-relations-discussion-8/

Re: Peirce List
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/thrd5.html#00090
::: Robert Marty
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00151.html


Thank you for reminding me of the definition of a group that I have taught for 45 years … I think you work with the 
permutations of symmetrical groups that do not fit well with the interdependence of categories and which make us go out 
of the Peircian theory, which is not forbidden as long as we point it out.  I'll look at the use you make of them when 
you've answered my previous questions with something other than a stream of links and the definition of a group!  (my 
Ph.D. Math is on Abelian Groups) … formulating my questions correctly takes me time, especially to grasp your thought … 
I would like a reciprocal … I always thought that you had the capacity to do it without giving up your certainties, but 
I must say that today I am disappointed …



Dear Robert,

Auld acquaintance is not forgot 
I will convey your thanks to one who reminded me.

My reason for encoring mathematical groups as a class of
triadic relations and elsewhere casting divisibility in
the role of a dyadic relation was not so much for their
own sakes as for the critical exercise my English Lit
teachers used to style as “Compare and Contrast”.
For the sale of our immediate engagement, then, we
tackle that exercise all the better to highlight
the distinctive qualities of triadic relations
and sign relations.

A critical point of the comparison is to grasp sign relations
as *collections* of ordered triples — collections endowed with
collective properties extending well beyond the properties of
individual triples and their components.

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Discussion 7
https://inquiryintoinquiry.com/2021/08/13/semiotics-semiosis-sign-relations-discussion-7/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
::: Morgan Rogers
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/248860697


Okay, this is hard to parse, but I’ve looked at it a few times now framed with discussion from a few different sources, 
and it seems that if we fix some sets A of signs, B of interpretants and C of objects, and treating the sign relation as 
R ⊆ A × B × C, there are some reasonable restrictions/assumptions we could place on R.  For example:


1a.
∀a ∈ A, ∀b ∈ B, ∃c ∈ C, (a,b,c) ∈ R,
“every sign means something to every interpretant”,
1b.
∀a ∈ A, ∃b ∈ B, ∃c ∈ C, (a,b,c) ∈ R, a weaker alternative,
“every sign means something to some interpretant”,
2a.
∀c ∈ C, ∀b ∈ B, ∃a ∈ A, (a,b,c) ∈ R,
“every interpretant has a name for every object”,
2b.
∀c ∈ C, ∃b ∈ B, ∃a ∈ A, (a,b,c) ∈ R, a weaker alternative,
“every object has at least one name assigned to it by each 
interpretant”,

and so on.

However, none of these seem strictly necessary to me;  there could be meaningless symbols or nameless objects.  Does 
Peirce assume any of these things or similar?  If not, I suspect the answer to my question regarding mathematical 
distinguishing features of sign relations is that there aren’t any:  that any ternary relation can be understood as a 
sign relation if one squints hard enough.



Dear Morgan,

As far as meaningless signs go, we do encounter them in theoretical analysis (“resolving conundra” and “steering around 
nonsense”) and empirical or computational applications (“missing data” and “error types”).  The defect of meaning can 
affect either denotative objects or connotative interpretants or both.  In those events we have to generalize sign 
relations to what are called “sign relational complexes”.


Signless objects are a different matter since cognitions and concepts count as signs in pragmatic semiotics and Peirce 
maintains we have no concept of inconceivable objects.


If you fancy indulging in a bit of cosmological speculation you could imagine the whole physical universe to be a sign 
of itself to itself, making O = S = I, but this far downstream from the Big Bang we mortals usually have more pressing 
business to worry about.


In short, what we need sign relations for is not for settling big questions about cosmology or metaphysics but for 
organizing our thinking about object domains and constructing models of what goes on and what might go better in 
practical affairs like communication, inquiry, learning, and reasoning.


Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[robert marty]

Jon, List

  Thank you for reminding me of the definition of a group that I have
taught for 45 years ... I think you work with the permutations of
symmetrical groups that do not fit well with the interdependence of
categories and which make us go out of the Peircian theory, which is not
forbidden as long as we point it out. I'll look at the use you make of them
when you've answered my previous questions with something other than a
stream of links and the definition of a group! (my Ph.D. Math is on Abelian
Groups)... formulating my questions correctly takes me time, especially to
grasp your thought... I would like a reciprocal... I always thought that
you had the capacity to do it without giving up your certainties, but I
must say that today I am disappointed...
Regards,

Robert Marty

Honorary Professor ; Ph.D. Mathematics ; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le ven. 13 août 2021 à 00:20, Jon Awbrey  a écrit :

> Cf: Semiotics, Semiosis, Sign Relations • Comment 3
>
> https://inquiryintoinquiry.com/2021/08/12/semiotics-semiosis-sign-relations-comment-3/
>
> All,
>
> It helps me to compare sign relations with my other favorite class
> of triadic relations, namely, groups.  Applications of mathematical
> groups came up just recently in the Laws of Form discussion group,
> so it will save a little formatting time to adapt the definition
> used there.
>
> Cf: Animated Logical Graphs • 60
> https://inquiryintoinquiry.com/2021/02/21/animated-logical-graphs-60/
>
> Definition 1.  A group (G, ∗) is a set G together with
> a binary operation ∗ : G × G → G satisfying the following
> three conditions.
>
> 1.  Associativity.
>  For any x, y, z in G, we have (x ∗ y) ∗ z  =  x ∗ (y ∗ z).
>
> 2.  Identity.
>
>  There is an identity element 1 in G such that for all g in G,
>  we have 1 ∗ g  =  g ∗ 1  =  g.
>
> 3.  Inverses.
>  Each element has an inverse, that is, for each g in G,
>  there is some h in G such that g ∗ h  =  h ∗ g  =  1.
>
> Regards,
>
> Jon
>
> _ _ _ _ _ _ _ _ _ _
> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
> peirce-L@list.iupui.edu .
> ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to
> l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the
> message and nothing in the body.  More at
> https://list.iupui.edu/sympa/help/user-signoff.html .
> ► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and
> co-managed by him and Ben Udell.
>
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Comment 3
https://inquiryintoinquiry.com/2021/08/12/semiotics-semiosis-sign-relations-comment-3/

All,

It helps me to compare sign relations with my other favorite class
of triadic relations, namely, groups.  Applications of mathematical
groups came up just recently in the Laws of Form discussion group,
so it will save a little formatting time to adapt the definition
used there.

Cf: Animated Logical Graphs • 60
https://inquiryintoinquiry.com/2021/02/21/animated-logical-graphs-60/

Definition 1.  A group (G, ∗) is a set G together with
a binary operation ∗ : G × G → G satisfying the following
three conditions.

1.  Associativity.
For any x, y, z in G, we have (x ∗ y) ∗ z  =  x ∗ (y ∗ z).

2.  Identity.

There is an identity element 1 in G such that for all g in G,
we have 1 ∗ g  =  g ∗ 1  =  g.

3.  Inverses.
Each element has an inverse, that is, for each g in G,
there is some h in G such that g ∗ h  =  h ∗ g  =  1.

Regards,

Jon

_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[robert marty]

Jon, List

  I am familiar with this type of confusion, and it is not because it has
been in Wikipedia for 15 years that it is validated. It existed in my
immediate environment that I finally break.  I will first make some remarks
and then ask you a question.

The remark: you spend without justification six different grammatical forms
allowing six different predicates to describe the same phaneron by linking
the letters A, B, C, in six ways to the six purely formal combinations of
the three letters S, O, and I. For each of the six combinations, which
predicate? A Y diagram with three free ends where the letters S, O, I
circulate might be the answer? (I can't think of any other, but you tell
me...) But then you spend from the six different ways given by Pierce to
express a single phaneron grammatically = the fact that an object in the
world has changed ownership (in all six grammatical cases, it is the same
fact that has happened in the real world) to the semiotic with six
combinations of three letters O, S, I which one wonders about the relation
with what precedes. Indeed, if O is the object of a sign, S the sign itself
(= the concrete thing that represents) and I the interpreter, that makes
three distinct elements possibly present to the mind according to the
focus, so three distinct phanerons, two out of mind and the third is a
determination of this mind. In passing, I note that you illustrate by
quotations from Peirce only three combinations (what about the other
three?) whose coherence is open to discussion.  Finally, you quote
2.228-229 (1902) and 2.230 (1910) from which it seems that Liszka would
have drawn (by observation?) four normative conditions that a sign should
fulfill, in which, if he retains that the sign determines the interpretant,
and represents the object thanks to ground, he still ignores that the
object determines the sign, although almost all the definitions after
1904-1905 expressly stipulate it.  Now, because we have a sign with three
elements, each of which can also be present in mind, Peirce can classify
the signs according to the categorial belonging of each of them (I have
modeled it).
So my question is: How will you get the 10 classes of signs, let alone the
28 (and I'm not talking about the 66 that are still not defined)? With OSI,
I presume? What will be the use of the 5 others?
  Best regards,
Robert Marty
NB: just now, I see that you had posted before I finished reacting. At
first glance, I see that the Cartesian product O x Sx I partially answers
my question above but does not inform me about the rest.
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ *



Le mer. 11 août 2021 à 01:15, Jon Awbrey  a écrit :

> Cf: Semiotics, Semiosis, Sign Relations • Comment 2
>
> https://inquiryintoinquiry.com/2021/08/10/semiotics-semiosis-sign-relations-comment-2/
>
> Re: Semiotics, Semiosis, Sign Relations • Comment 1
>
> https://inquiryintoinquiry.com/2021/08/09/semiotics-semiosis-sign-relations-comment-1/
>
> All,
>
> Definitions tend to call on other terms in need of their own definitions,
> and so on till the process terminates at the level of primitive terms.
> The main two concepts requiring supplementation in Peirce's definition
> of a sign relation are the ideas of “correspondence” and “determination”.
> We can figure out fairly well what Peirce had in mind from things he wrote
> elsewhere, as I explained in the Sign Relation article I added to Wikipedia
> 15 years ago.
>
> Sign Relation
> https://en.wikipedia.org/w/index.php?title=Sign_relation=68541642
>
> Not daring to look at what's left of that, here's the relevant section
> from the OEIS Wiki fork.
>
> Sign Relation ( https://oeis.org/wiki/Sign_relation )
> • Definition ( https://oeis.org/wiki/Sign_relation#Definition )
>
> Regards,
>
> Jon
> _ _ _ _ _ _ _ _ _ _
> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
> peirce-L@list.iupui.edu .
> ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to
> l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the
> message and nothing in the body.  More at
> https://list.iupui.edu/sympa/help/user-signoff.html .
> ► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and
> co-managed by him and Ben Udell.
>
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Comment 2
https://inquiryintoinquiry.com/2021/08/10/semiotics-semiosis-sign-relations-comment-2/

Re: Semiotics, Semiosis, Sign Relations • Comment 1
https://inquiryintoinquiry.com/2021/08/09/semiotics-semiosis-sign-relations-comment-1/

All,

Definitions tend to call on other terms in need of their own definitions,
and so on till the process terminates at the level of primitive terms.
The main two concepts requiring supplementation in Peirce's definition
of a sign relation are the ideas of “correspondence” and “determination”.
We can figure out fairly well what Peirce had in mind from things he wrote
elsewhere, as I explained in the Sign Relation article I added to Wikipedia
15 years ago.

Sign Relation
https://en.wikipedia.org/w/index.php?title=Sign_relation=68541642

Not daring to look at what's left of that, here's the relevant section
from the OEIS Wiki fork.

Sign Relation ( https://oeis.org/wiki/Sign_relation )
• Definition ( https://oeis.org/wiki/Sign_relation#Definition )

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.

Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations

[Jon Awbrey]

Cf: Semiotics, Semiosis, Sign Relations • Comment 1
https://inquiryintoinquiry.com/2021/08/09/semiotics-semiosis-sign-relations-comment-1/

All,

I opened a topic on Sign Relations in the Logic stream of
Category Theory Zulipchat to work on Peirce's theory of
triadic sign relations in a category-theoretic framework.

Invitation Link
https://categorytheory.zulipchat.com/join/jsvtolybonggfwxiodsktbkz/

Topic Link
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations

I had been reading Peirce for a decade or more before I found a math-strength
definition of signs and sign relations.  A lot of the literature on semiotics
takes almost any aperçu Peirce penned about signs as a “definition” but barely
a handful of those descriptions are consequential enough to support significant
theory.  For my part, the definition of a sign relation coming closest to the
mark is one Peirce gave in the process of defining logic itself.  Two variants
of that definition are linked and copied below.

C.S. Peirce • On the Definition of Logic

https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-on-the-definition-of-logic/

Selections from C.S. Peirce, “Carnegie Application” (1902)

No. 12.  On the Definition of Logic

Logic will here be defined as formal semiotic.  A definition of a sign will be given which no more refers to human 
thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. 
 Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the 
same sort of correspondence with something, C, its object, as that in which itself stands to C.  It is from this 
definition, together with a definition of “formal”, that I deduce mathematically the principles of logic.  I also make a 
historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no 
novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally 
recognized.  (NEM 4, 20–21).


No. 12.  On the Definition of Logic [Earlier Draft]

Logic is formal semiotic.  A sign is something, A, which brings something, B, its interpretant sign, determined or 
created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in 
which itself stands to C.  This definition no more involves any reference to human thought than does the definition of a 
line as the place within which a particle lies during a lapse of time.  It is from this definition that I deduce the 
principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of 
Weierstrassian severity, and that is perfectly evident.  The word “formal” in the definition is also defined.  (NEM 4, 54).


Reference
=

Charles S. Peirce (1902),
“Parts of Carnegie Application” (L 75), published in Carolyn Eisele (ed., 1976),
“The New Elements of Mathematics by Charles S. Peirce”, vol. 4, pp. 13–73.
Online ( https://arisbe.sitehost.iu.edu/menu/library/bycsp/L75/l75.htm )

Regards,

Jon
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON 
PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . 
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 
with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the 
body.  More at https://list.iupui.edu/sympa/help/user-signoff.html .
► PEIRCE-L is owned by THE PEIRCE GROUP;  moderated by Gary Richmond;  and 
co-managed by him and Ben Udell.