#### Semiotics, Semiosis, Sign Relations

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.

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

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

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.

Regards,

Jon

Lyle Anderson

On Mon, Aug 9, 2021 at 09:40 AM, Jon Awbrey wrote:
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.
Why, when writing this sentence as the result of human thought, does Pierce then assert that it has nothing to do with human thought?  At the time, Newtonian Mechanics were in vogue and particles thought to occupy a defined place in time.  Now we know that particles act as a mass wave function, and have only a probability that they are at any particular place at a particular time.  He then proceeds to present an unintelligible word salad for a "definition" to be understood by human thought processes.

Apparently, Pierce, equivocated on this, according to Hardwick: "The concept ‘interpretant’ derives its meaning from its role in Peirce’s theory of semiosis. Semiotic is the study of relations between signs, which are triadic by definition. A sign stands for its object to an interpretant sign, at least potentially. Peirce distinguishes two objects of the sign: the immediate object within the sign, which is the object as mentally represented by the sign, and the mediate or dynamoid object without, which is the object in itself (Hardwick 1977: 83f., 32)."
https://thereitis.org/the-classification-of-peirces-interpretants/
This interesting article goes on to discuss "emotional" interpretants, "energetic" interpretants, "logical" interpretants, and "ultimate" logical interpretants.  The later being a concept's 'living definition,' and interpretant which itself has no further interpretant, and must be a habit, and hence "the most perfect account of a concept that words can convey."  But wait! There's more! In 1909, Pierce presented another classification of interpretants: immediate, dynamical, and final interpretants, and all of these refer to the effect of the interpretants on the mind!

Seriously, gang, the Creator has given us Laws of Form so we can go through the muddled thinking of the past and prune out all the dead branches in the Tree of Knowledge.  Just painting the dead branches green doesn't really do anything for anybody.

May the Form be with you!
Best regards,
Lyle

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&oldid=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

Lyle Anderson

On Tue, Aug 10, 2021 at 04:15 PM, Jon Awbrey wrote:
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.
Jon,
How does one analyse this sentence using Semiotics?  What words or concepts represent the sign?  What words or concepts represent the interpretant sign?  What words or concepts represent the object?  What condition causes the process to terminate?  Is the "level of primitive terms" the same a Pierce's concept of habit?  How does something get to be a habit?

George Spencer-Brown starts with the ideas of distinction and indication and the relationship between them as given.
"We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction."

"We take, therefore, the form of distinction for the form." This is the primitive "triadic" relationship in Laws of Form: Observer, Indication, Distinction.  Would it be equivalent to say: "The observer indicates that the form of the distinction is the form?   How do these words map into Pierce's Semiotics?  Does it map to Semiotics?  Is the act of mapping part of Semiotics?

Stanford has a nice piece on Pierce.  https://plato.stanford.edu/entries/peirce-semiotics/

Best regards,
Lyle

johncm22

It seems to me fairly clear

As gsb says, the mark is a token of the first distinction, so the first distinction is the object and the mark is the representamen. The value for an observer is the interpretent.

Or does anyone not agree
john

On Wed, 11 Aug 2021 at 18:09, Lyle Anderson <LylePhone@...> wrote:
On Tue, Aug 10, 2021 at 04:15 PM, Jon Awbrey wrote:
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.
Jon,
How does one analyse this sentence using Semiotics?  What words or concepts represent the sign?  What words or concepts represent the interpretant sign?  What words or concepts represent the object?  What condition causes the process to terminate?  Is the "level of primitive terms" the same a Pierce's concept of habit?  How does something get to be a habit?

George Spencer-Brown starts with the ideas of distinction and indication and the relationship between them as given.
"We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction."

"We take, therefore, the form of distinction for the form." This is the primitive "triadic" relationship in Laws of Form: Observer, Indication, Distinction.  Would it be equivalent to say: "The observer indicates that the form of the distinction is the form?   How do these words map into Pierce's Semiotics?  Does it map to Semiotics?  Is the act of mapping part of Semiotics?

Stanford has a nice piece on Pierce.  https://plato.stanford.edu/entries/peirce-semiotics/

Best regards,
Lyle

Lyle Anderson

Based on John's mapping:
"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."

Translates into:

1.  "Namely, a mark is something,
A, which brings something, B, its observer determined or created by the mark, into the same sort of correspondence with something, C, its First Distinction, as that in which the mark stands to C."

At first glance, the idea of the mark determining or creating the observer might feel a little off, so we might permutate the terms to explore other nuances of meaning:

2. "Namely, an observer is something,
A, which brings something, B, its mark determined or created by the observer, into the same sort of correspondence with something, C, its First Distinction, as that in which the observer stands to C."

3. "Namely, a First Distinction is something, A, which brings something, B, its mark determined or created by the First Distinction, into the same sort of correspondence with something, C, its observer, as that in which the First Distinction stands to C."

4. "Namely, a mark is something,
A, which brings something, B, its First Distinction determined or created by the mark, into the same sort of correspondence with something, C, its observer, as that in which the mark stands to C."

5. "Namely, an observer is something, A, which brings something, B, its First Distinction determined or created by the observer, into the same sort of correspondence with something, C, its mark, as that in which the observer stands to C."

6. "Namely, an First Distinction is something, A, which brings something, B, its observer determined or created by the First Distinction, into the same sort of correspondence with something, C, its mark, as that in which the First Distinction stands to C."

All of these seem equally valid.  This includes #1 and #6 where the observer is determined or created by either the mark or the first distinction.  (When I write (mark) a program to monitor a particular input value from a sensor, I am using my mark to create an observer.)

From all of these permutations it follows that: "We see now that the first distinction, the mark, and the observer are not only interchangeable, but, in the form, identical.""}

I think we have now connected Peirce's Semiotics to both the beginning and end of Laws of Form.  Other than the endorphins which are generated by using familiar habits to traveling over familiar roads,  What is the point of revisiting the 19th Century when we have the 20th Century exposition of the same thing, with added benefit that the study appears to begin and the actual beginning: The drawing of the First Distinction.

May the Form be with you!
Best regards,
Lyle

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

Lyle Anderson

Jon,
I am a trained mathematician.  My undergraduate degree was in Mathematics and Physics.  At one time I was certified as a Mathematician GS-13 because a government bureaucrat decided that a Physicist GS-13 couldn't do my job.  My Master's Degree in Computer Science involved a lot of mathematics and number theory.

Yes, I did introduce group theory into the discussion of Laws of Form.  That was before I found out that not everyone on this forum is a mathematician.  As GSB points out, Contraction of Reference only works if one can still follow the steps after the contraction of reference.  When you slip into set theoretic notation so quickly you are loosing people who aren't mathematicians.

What I am asking you to do is to explain what you are saying to non-mathematicians.
Best regards,
Lyle

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

<QUOTE MR:>
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.
</QUOTE>

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

Lyle Anderson

On Fri, Aug 13, 2021 at 05:45 AM, Jon Awbrey wrote:
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.
Jon,
What your are writing here, in the first clause of your first sentence, before the "but,' is that "We see now that the first distinction, the mark, and the observer are not only interchangeable, but, in the form, identical."  You then proceed to cast this profound observation aside in order to take up "more pressing business."

You identify that "more pressing business" as doing better "in practical affairs like communication, inquiry, learning, and reasoning."  What I find interesting is that you always leave out "history."  You ask "what could go better?" without providing the answer to the implicit antecedent "then what."  You never seem to examine the consequences of various theories that have been held by various establishments in the past, and what those establishments did to the people who discovered the next correct approximation on our way to the answer to the "big questions."  Ignoring history has lead to untold amounts of human misery.

I would give several examples from current events, but I am "self-censoring" to keep from becoming "politically incorrect."

Here is a Twitter thread from Kareem Carr, a former mathematician turned statistician, on "everything you need to know about 2+2=5."  Who knows if Kareem is being satirical, but may people didn't think so.   https://twitter.com/kareem_carr/status/1289724475609501697

Best regards,
Lyle

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

<QUOTE RM:>
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 …
</QUOTE>

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

Mauro Bertani

Hi Jon, Lyle,

<quote Jon Awbrey>
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.
</quote>

I write this simple note:

I'm not a mathematician and it is only an idea

Mauro

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

<QUOTE MR:>
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.
</QUOTE>

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

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

<QUOTE MR:> Please clearly state at least one “distinctive quality of sign relations”. </QUOTE>

Dear Morgan,

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

Lyle Anderson

Mauro,
It is not surprising that common arithmetic can be derived from one operation based on the fact that all of mathematics can be derived using the Laws of Form, starting from the drawing of the first distinction that encompass a trinity relationship, distinction, mark, and observer, using two axioms that can be interpreted in different ways, depending on what one intends to do.

That is the question I have for you:  What are you trying to do?  What are you trying to understand?

Best regards,
Lyle

bruceschuman@...

All of mathematics can be derived using the Laws of Form

- Lyle Anderson, Saturday, August 14, 2021 10:20 AM

Ok, sounds very exciting.

So Lyle, how about you take up the request you just made of Jon, and explain this doctrine/claim in terms that can be understood by a non-mathematician.

To the extent you are able, please list the sequence of steps, and the objects defined.  Don’t leave any gaps in the definition chain.

I’d like to see this framework responding to Jon’s previous quote that you cited:

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.

- Jon Awbrey, Tue, Aug 10, 2021

What I am calling for is a definition chain that terminates in stable unambiguous primitives.    I’d say this is the great mathematical/philosophical task.

In this below quote from you and GSB, I do not understand what is meant by “given”.  For me, that concept is confusing and ambiguous, like an implicit but undefined postulate or axiom – which makes it intolerable in this context.  We are looking for a foundation we can trust and safely build on, not another swamp of implicit and undefined or confusing and controversial abstractions.

Perhaps we can backtrack from this idea of “the given” by looking at your Kabballah cosmology.

George Spencer-Brown starts with the ideas of distinction and indication and the relationship between them as given.
"We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction."

- Lyle Anderson, Wed 8/11/2021

All of mathematics can be derived using the Laws of Form

Based on your Kabbalistic theology, in very broad strokes, a defense of your claim might appear in this form:

The Creator => Creates a “conceptual space” => Makes a distinction in that space => All mathematics can be constructed from that distinction

If that is close, please show how.  If it is wrong, please say why.

If you could actually build this construction in unambiguous terms comprehensible to non-mathematicians, that would be a very great accomplishment.  Please do not define ungrounded abstractions in terms of ungrounded abstractions.  All definitions must be constructed in terms of primitives derived from your thesis.

If anybody can do this, it would be you, Lyle.  But you must hammer out all undefined abstractions and ambiguities.

Truly, I would be thrilled to see this.  Thanks.

The tzimtzum or tsimtsum (Hebrew "contraction/constriction/condensation") is a term used in the Lurianic Kabbalah to explain Isaac Luria's doctrine that God began the process of creation by "contracting" his Ohr Ein Sof (infinite light) in order to allow for a "conceptual space" in which finite and seemingly independent realms could exist. This primordial initial contraction, forming a "vacant space" into which new creative light could beam, is denoted by general reference to the tzimtzum.

Bruce Schuman

Santa Barbara CA USA

bruceschuman@... / 805-705-9174

From: lawsofform@groups.io <lawsofform@groups.io> On Behalf Of Lyle Anderson
Sent: Saturday, August 14, 2021 10:20 AM
To: lawsofform@groups.io
Subject: Re: [lawsofform] Semiotics, Semiosis, Sign Relations

Mauro,
It is not surprising that common arithmetic can be derived from one operation based on the fact that all of mathematics can be derived using the Laws of Form, starting from the drawing of the first distinction that encompass a trinity relationship, distinction, mark, and observer, using two axioms that can be interpreted in different ways, depending on what one intends to do.

That is the question I have for you:  What are you trying to do?  What are you trying to understand?

Best regards,
Lyle

Lyle Anderson

On Sat, Aug 14, 2021 at 01:08 PM, <bruceschuman@...> wrote:
In this below quote from you and GSB, I do not understand what is meant by “given”.  For me, that concept is confusing and ambiguous, like an implicit but undefined postulate or axiom – which makes it intolerable in this context.  We are looking for a foundation we can trust and safely build on, not another swamp of implicit and undefined or confusing and controversial abstractions.
Bruce,
According to https://dictionary.cambridge.org/us/dictionary/english/given , "given" as a noun, means "something that is certain to happen or to be."  Using the technique of substituting the definition for the word in a sentence, we have: "We take as something that is certain to be the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction."  Maybe rearranging the clauses will make it easier to understand: "We take the idea of distinction and the idea of indication as something that is certain to be, and that we cannot make an indication without drawing a distinction."

Your definition for indication is circular.  Here is is the Cambridge Dictionary definition of indication: "a sign that something exists, is true, or is likely to happen."   It is very close to their definition of "sign" which is "something showing that something else exists or might happen or exist in the future."  So one could think of a "indication" as a more certain "sign."

This is the starting point in Laws of Form.  The question for you now is: do you understand what these words mean?  Before we add the two axioms to the definition, you must understand the definition.  These are the "primitives" from which the thesis derives.  Do you accept them as being true, at least for the sake of argument?

We need to settle this beginning place, first, before we go on to cosmology and theology.

Best regards,
Lyle

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#00009
::: Robert Marty
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00132.html

<QUOTE RM:>
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 )
</QUOTE>

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.

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

Cf: Semiotics, Semiosis, Sign Relations • Comment 4
https://inquiryintoinquiry.com/2021/08/23/semiotics-semiosis-sign-relations-comment-4/

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

Cf: (Context : Ironic)(Apology : T.S. Eliot)
https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00292.html

Lyle Anderson

These, then, are the two points I wanted to make. First, that human beings, all over the earth, have this curious idea that they ought to behave in a certain way, and cannot really get rid of it. Secondly, that they do not in fact behave in that way. They know the Law of Nature; they break it. These two facts are the foundation of all clear thinking about ourselves and the universe we live in.

Lewis, C. S.. Mere Christianity (C.S. Lewis Signature Classics) (p. 8). HarperCollins. Kindle Edition.

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