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Nov 25, 2018, 9:28:33 AM11/25/18

to Ontolog Forum, Systems Science, Structural Modeling

A first mention of semiotics (and cybersemiotics) in another group afforded me a chance to begin a fresh introduction to the area. Then I thought it might be useful to share that here.

InterSciWiki

http://intersci.ss.uci.edu/wiki/index.php/Semeiotic

Wikiversity

https://en.wikiversity.org/wiki/Semeiotic

Folks already registered on Wikipedia would find it easy to use the talk page on Wikiversity if they wanted to engage in additional discussion there.

Regards,

Jon

Nov 25, 2018, 11:16:15 AM11/25/18

to Ontolog Forum, Systems Science, Structural Modeling

Here are links to fuller discussions of semiotics.

InterSciWiki

http://intersci.ss.uci.edu/wiki/index.php/Sign_relation

Wikiversity

https://en.wikiversity.org/wiki/Sign_relation

The approach described here is based on what I regard as the core definition of sign relations, one explicit enough to support a consequential theory of signs.

C.S. Peirce • On the Definition of Logic (as depending on the definition of a sign)

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

C.S. Peirce • Logic as Semiotic

https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-•-logic-as-semiotic/

Regards,

Jon

Nov 25, 2018, 4:15:26 PM11/25/18

to ontolo...@googlegroups.com

The sign domain is the representamen domain. Peirce was fussy about terminology. The sign is the unity of the 3 domains (object, representamen, interpretant).

__ __

Mihai Nadin

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Nov 25, 2018, 6:45:35 PM11/25/18

to ontolo...@googlegroups.com, Systems Science, Structural Modeling

Dear Mihai,

Peirce sometimes fussed over that term but more often not. The shorter word will serve us well enough as it did him and it has the benefit of being far less off-putting.

The more important thing is to understand triadic sign relations as a defined species of triadic relations, which are in turn a species of mathematical relations denoted by relative terms.

For a taste of how Peirce treated the logic of relative terms see my discussion of his 1870 Logic Of Relatives, which is where I first cut my teeth on the subject. Historically speaking this is also where we got our

first real breakthrough in reasoning about the mathematics of relations.

Peirce’s 1870 Logic Of Relatives

http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives

Regards,

Jon

To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/35ae8bd40cc7402fa8b7a57fae77385b%40utdallas.edu.

Nov 28, 2018, 5:35:04 PM11/28/18

to ontolog-forum

For ease of reference, here are two variants of Peirce’s 1902 definition of a sign, which he gives in the process of defining logic.

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).

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, 13–73. Online.

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).

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, 13–73. Online.

Dec 9, 2018, 11:22:19 AM12/9/18

to Ontolog Forum, Systems Science, Structural Modeling

Dear Mihai, All —

It's possible my previous reply was succinct to a fault,

but it did give the gist of a well-considered choice of

terms, one that Peirce made on many occasions and maybe

even in the end.

Peirce invented the term “representamen” as a part of his

“non-psychlogical” program to detach logic and the concept

of a sign from their traditional embedding in psychological

material where signs are interpreted by mental ideas in the

mind, psyche, or soul of their interpretive agent. That is

a reasonable rhetorical strategy, at least in the beginning.

Another tactic, one often seen in the history of mathematics, is simply

to generalize the meaning of the original term, achieving the required

precision by attaching the definition that befits the context in view.

Peirce used both tactics on different occasions and for different audiences.

A fair sample of the full variorum can be found in the Commens Dictionary:

Representamen

http://www.commens.org/dictionary/term/representamen

Regards,

Jon

--

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

isw: http://intersci.ss.uci.edu/wiki/index.php/JLA

facebook page: https://www.facebook.com/JonnyCache

It's possible my previous reply was succinct to a fault,

but it did give the gist of a well-considered choice of

terms, one that Peirce made on many occasions and maybe

even in the end.

Peirce invented the term “representamen” as a part of his

“non-psychlogical” program to detach logic and the concept

of a sign from their traditional embedding in psychological

material where signs are interpreted by mental ideas in the

mind, psyche, or soul of their interpretive agent. That is

a reasonable rhetorical strategy, at least in the beginning.

Another tactic, one often seen in the history of mathematics, is simply

to generalize the meaning of the original term, achieving the required

precision by attaching the definition that befits the context in view.

Peirce used both tactics on different occasions and for different audiences.

A fair sample of the full variorum can be found in the Commens Dictionary:

Representamen

http://www.commens.org/dictionary/term/representamen

Regards,

Jon

--

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

isw: http://intersci.ss.uci.edu/wiki/index.php/JLA

facebook page: https://www.facebook.com/JonnyCache

Apr 30, 2019, 9:02:19 AM4/30/19

to Ontolog Forum, Systems Science, Structural Modeling

Questions about the nature of concepts and their action in sign relations

arose in discussions elsewhere, prompting me to pick up this thread again.

Here is the context:

Re: Semiotic Triangle

At: https://www.academia.edu/s/82ada7ef2e/semiotic-triangle-zero-update-2-0

Re: John Corcoran

At: https://www.facebook.com/groups/peircesociety/permalink/1569171163218870

Here is my comment:

Cf: Semiotics, Semiosis, Sign Relations ??? 4

At: https://inquiryintoinquiry.com/2019/04/29/semiotics-semiosis-sign-relations-%e2%80%a2-4/

Concepts for Peirce are mental symbols, so they fall under the general designation

of signs. For triadic sign relations in general, then, we are considering a triadic

relation among objects of signs, signs of objects, and what Peirce calls interpretant

signs, or interpretants for short. It is critical to regard the designations of objects,

signs, and interpretants as relational roles not ontological essences. It is also critical

to distinguish (a) extended sign relations, (b) elementary sign relations, (c) the slots of

an ordered triple, and (d) the things that fill those slots.

Triangles like the one linked above have long been used to introduce the idea of

a triadic sign relation. They have the unintended consequence, however, of leading

people to miss all the points I mentioned above. So it's wise to move quickly on to

better pictures and more detailed descriptions.

Regards,

Jon

arose in discussions elsewhere, prompting me to pick up this thread again.

Here is the context:

Re: Semiotic Triangle

At: https://www.academia.edu/s/82ada7ef2e/semiotic-triangle-zero-update-2-0

Re: John Corcoran

At: https://www.facebook.com/groups/peircesociety/permalink/1569171163218870

Here is my comment:

Cf: Semiotics, Semiosis, Sign Relations ??? 4

At: https://inquiryintoinquiry.com/2019/04/29/semiotics-semiosis-sign-relations-%e2%80%a2-4/

Concepts for Peirce are mental symbols, so they fall under the general designation

of signs. For triadic sign relations in general, then, we are considering a triadic

relation among objects of signs, signs of objects, and what Peirce calls interpretant

signs, or interpretants for short. It is critical to regard the designations of objects,

signs, and interpretants as relational roles not ontological essences. It is also critical

to distinguish (a) extended sign relations, (b) elementary sign relations, (c) the slots of

an ordered triple, and (d) the things that fill those slots.

Triangles like the one linked above have long been used to introduce the idea of

a triadic sign relation. They have the unintended consequence, however, of leading

people to miss all the points I mentioned above. So it's wise to move quickly on to

better pictures and more detailed descriptions.

Regards,

Jon

Oct 26, 2019, 3:05:13 PM10/26/19

to Ontolog Forum, Systems Science, Structural Modeling, Peirce List, Cybernetic Communications, Laws Of Form Group

Cf: Semiotics, Semiosis, Sign Relations : 5

At: https://inquiryintoinquiry.com/2019/10/26/semiotics-semiosis-sign-relations-%e2%80%a2-5/

Re: Recursion Again

At: https://richardcoyne.com/2019/10/26/recursion-again/

A recurring correction of a recurring mistake:

It's a common mistake to confound infinite with unbounded.

A process can continue without end and still be "bounded

in a nutshell". So a sign process can pass from sign to

interpretant sign to next interpretant sign ad infinitum

without ever leaving a finite set of signs.

So let that be the end of that.

Regards,

Jon

At: https://inquiryintoinquiry.com/2019/10/26/semiotics-semiosis-sign-relations-%e2%80%a2-5/

Re: Recursion Again

At: https://richardcoyne.com/2019/10/26/recursion-again/

A recurring correction of a recurring mistake:

It's a common mistake to confound infinite with unbounded.

A process can continue without end and still be "bounded

in a nutshell". So a sign process can pass from sign to

interpretant sign to next interpretant sign ad infinitum

without ever leaving a finite set of signs.

So let that be the end of that.

Regards,

Jon

Oct 30, 2019, 2:36:43 PM10/30/19

to Ontolog Forum, Systems Science, Structural Modeling, Peirce List, Laws Of Form Group, Cybernetic Communications

Cf: Semiotics, Semiosis, Sign Relations : 4

At: https://inquiryintoinquiry.com/2019/04/29/semiotics-semiosis-sign-relations-%e2%80%a2-4/

All,

Questions about the use of "semiotic triangles" and/or "semiotic triskelia"

to represent triadic sign relations have come up again, as they often do

in the wider world, prompting me to revisit an earlier comment on the

subject and tri, tri again to render the issues as clear as I can,

otherwise we appear doomed never to get off triangle one.

Re: Semiotic Triangle

1 : https://www.academia.edu/s/82ada7ef2e/semiotic-triangle-zero-update-2-0

2 : https://www.academia.edu/34149912/Semiotic_Triangle_Charting_the_expression-sense-reference_distinction

Re: John Corcoran

At: https://www.facebook.com/groups/peircesociety/permalink/1569171163218870/

At: https://www.facebook.com/groups/peircesociety/permalink/1735601909909127/

Concepts for Peirce are mental symbols, so they fall under the general

designation of signs. For triadic sign relations in general, then, we

are dealing with a triadic relation among (1) "objects" of signs, (2)

"signs" of objects, and (3) what Peirce calls "interpretant signs", or

"interpretants" for short. It is critical to regard the 3 designations

* The extended sign relation L as a subset of a cartesian product O x S x I,

* The elementary sign relation as an ordered triple (o, s, i) in O x S x I,

* The places forming an ordered triple (o, s, i),

* The elements o, s, i filling those places.

Triangles like the one linked above have long been used to introduce the

idea of a triadic sign relation. They have the unintended consequence,

however, of leading people to miss all the points I mentioned above.

So it's wise to move quickly on to better pictures and more detailed

descriptions.

Resources

=========

* Survey of Semiotics, Semiosis, Sign Relations

* https://inquiryintoinquiry.com/2019/10/29/survey-of-semiotics-semiosis-sign-relations-%e2%80%a2-1/

At: https://inquiryintoinquiry.com/2019/04/29/semiotics-semiosis-sign-relations-%e2%80%a2-4/

All,

Questions about the use of "semiotic triangles" and/or "semiotic triskelia"

to represent triadic sign relations have come up again, as they often do

in the wider world, prompting me to revisit an earlier comment on the

subject and tri, tri again to render the issues as clear as I can,

otherwise we appear doomed never to get off triangle one.

Re: Semiotic Triangle

1 : https://www.academia.edu/s/82ada7ef2e/semiotic-triangle-zero-update-2-0

2 : https://www.academia.edu/34149912/Semiotic_Triangle_Charting_the_expression-sense-reference_distinction

Re: John Corcoran

At: https://www.facebook.com/groups/peircesociety/permalink/1569171163218870/

At: https://www.facebook.com/groups/peircesociety/permalink/1735601909909127/

Concepts for Peirce are mental symbols, so they fall under the general

designation of signs. For triadic sign relations in general, then, we

"signs" of objects, and (3) what Peirce calls "interpretant signs", or

"interpretants" for short. It is critical to regard the 3 designations

of objects, signs, and interpretants as relational roles not ontological

essences. It is also critical to distinguish the following things:
* The extended sign relation L as a subset of a cartesian product O x S x I,

* The elementary sign relation as an ordered triple (o, s, i) in O x S x I,

* The places forming an ordered triple (o, s, i),

* The elements o, s, i filling those places.

Triangles like the one linked above have long been used to introduce the

idea of a triadic sign relation. They have the unintended consequence,

however, of leading people to miss all the points I mentioned above.

So it's wise to move quickly on to better pictures and more detailed

descriptions.

=========

* Survey of Semiotics, Semiosis, Sign Relations

* https://inquiryintoinquiry.com/2019/10/29/survey-of-semiotics-semiosis-sign-relations-%e2%80%a2-1/

Oct 30, 2019, 3:16:03 PM10/30/19

to Jon Awbrey, Ontolog Forum, Systems Science, Structural Modeling, Peirce List, Cybernetic Communications, Laws Of Form Group

Jon,

JA> It's a common mistake to confound infinite with unbounded. A process can continue without end and still be "bounded in a nutshell". So a sign process can pass from sign to interpretant sign to next interpretant sign ad infinitum without ever leaving a finite set of signs.

That's not a mistake. It's the definition of countably infinite: I'm sure you know that, but it's important to state the definition in a way that distinguishes countably infinite sets (e.g., the integers) from uncountable sets (e.g., the real numbers).

The set of integers is countably infinite. Therefore, any set of integers that you can reach by counting is always finite. But the last sentence above is confusing because it's impossible to count "ad infinitum". However, you could specify an ordering of the integers that could produce an infinite set if you could run the machine "ad infinitum".

The real numbers are uncountably infinite. If you tried to count them, as you would with the integers, you could only get a finite set. And even if you had a machine that could run "ad infinitum", you could only get a countable subset. You could never get all the real numbers.

John

Oct 30, 2019, 4:04:19 PM10/30/19

to ontolo...@googlegroups.com

On Wed, October 30, 2019 15:16, John F. Sowa wrote:

> Jon,

>

> JA> It's a common mistake to confound infinite with unbounded.

> A process can continue without end and still be "bounded in a nutshell".

In the real world, of course, no process can continue without end.
> Jon,

>

> JA> It's a common mistake to confound infinite with unbounded.

> A process can continue without end and still be "bounded in a nutshell".

Infinities can be bounded in a nutshell. Just imagine that the worm in

the center of a coconut eats its way halfway to the shell each second.

The worm's physical travel has an infinite number of steps and is bounded.

> So a sign process can pass from sign to interpretant sign to next

> interpretant sign ad infinitum without ever leaving a finite set of

> signs.

> countably infinite:Â I'm sure you know that, but it's important to state

> the definition in a way that distinguishes countably infinite sets (e.g.,

> the integers) from uncountable sets (e.g., the real

> numbers).

>

> The set of integers is countably infinite.

> Therefore, any set of integers that you can reach by counting is always

> finite. But the last sentence above is confusing because it's

> impossible

> to count "ad infinitum". However, you could specify an ordering

> of the integers that could produce an infinite set if you could run the

> machine "ad infinitum".

The same with the rational numbers, which are countably infinite.
> the integers) from uncountable sets (e.g., the real

> numbers).

>

> The set of integers is countably infinite.

> Therefore, any set of integers that you can reach by counting is always

> finite. But the last sentence above is confusing because it's

> impossible

> to count "ad infinitum". However, you could specify an ordering

> of the integers that could produce an infinite set if you could run the

> machine "ad infinitum".

> The real numbers are

> uncountably infinite. If you tried to count them, as you would with the

> integers, you could only get a finite set. And even if you had a machine

> that could run "ad infinitum", you could only get a countable

> subset. You could never get all the real numbers.

identify a irrational real number by listing all its digits. One can only

identify one by specifying an equation with arguments being named rational

numbers and named irrationals. One could design an ordering of the

identifiable real numbers so that for any one identified, its position in

the ordering could be identified.

-- doug

> John

>

> --

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Nov 7, 2019, 6:55:06 PM11/7/19

to Ontolog Forum, Systems Science, Structural Modeling, Peirce List, Cybernetic Communications, Laws Of Form Group

Cf : Semiotics, Semiosis, Sign Relations : 7

At : http://inquiryintoinquiry.com/2019/11/07/semiotics-semiosis-sign-relations-%e2%80%a2-7/

Re: Semiotics, Semiosis, Sign Relations : 5

At: https://inquiryintoinquiry.com/2019/10/26/semiotics-semiosis-sign-relations-%e2%80%a2-5/

Re: It's a common mistake to confound infinite with unbounded.

have delineated the context in which it was set a little more fully.

A "sign process" in this context is simply a sequence of signs, of the

sort we might observe in communicational, computational, or experimental

settings. For people who remember the more ancient arts of AI, cognitive

science, and cybernetics, it may help to recall the orders of considerations

arising in protocol analysis.

It goes with this territory to assume the formal equivalent of "categorical

perception". This means we can set aside the subtleties of token haecceity --

the fact each instance of a sign is distinct from every other instance --

along with the possibility of signs being sampled from a continuous medium.

In this setting we are left with two interpretations for "infinite and bounded",

depending on whether the sign domain has a quantitative measure defined on it,

or not. In the first case, "bounded" means the sequence never exceeds a finite

bound in the relevant measure. In the second case, "bounded" means the sequence

never leaves a finite set.

Regards,

Jon

At : http://inquiryintoinquiry.com/2019/11/07/semiotics-semiosis-sign-relations-%e2%80%a2-7/

Re: Semiotics, Semiosis, Sign Relations : 5

At: https://inquiryintoinquiry.com/2019/10/26/semiotics-semiosis-sign-relations-%e2%80%a2-5/

Re: It's a common mistake to confound infinite with unbounded.

A process can continue without end and still be "bounded

in a nutshell". So a sign process can pass from sign to

interpretant sign to next interpretant sign ad infinitum

without ever leaving a finite set of signs.

The number of questions I got about that statement tells me I should
in a nutshell". So a sign process can pass from sign to

interpretant sign to next interpretant sign ad infinitum

without ever leaving a finite set of signs.

have delineated the context in which it was set a little more fully.

A "sign process" in this context is simply a sequence of signs, of the

sort we might observe in communicational, computational, or experimental

settings. For people who remember the more ancient arts of AI, cognitive

science, and cybernetics, it may help to recall the orders of considerations

arising in protocol analysis.

It goes with this territory to assume the formal equivalent of "categorical

perception". This means we can set aside the subtleties of token haecceity --

the fact each instance of a sign is distinct from every other instance --

along with the possibility of signs being sampled from a continuous medium.

In this setting we are left with two interpretations for "infinite and bounded",

depending on whether the sign domain has a quantitative measure defined on it,

or not. In the first case, "bounded" means the sequence never exceeds a finite

bound in the relevant measure. In the second case, "bounded" means the sequence

never leaves a finite set.

Regards,

Jon

Nov 9, 2019, 1:02:38 PM11/9/19

to Ontolog Forum, Systems Science, Structural Modeling, Peirce List, Cybernetic Communications, Laws Of Form Group

Cf: Semiotics, Semiosis, Sign Relations : 8

At: http://inquiryintoinquiry.com/2019/11/09/semiotics-semiosis-sign-relations-%e2%80%a2-8/

Continuing questions about "infinite semiosis" vs. "unbounded semiosis"

prompt me to make another comment by way of bringing our focus to bear

on the empirical context of semiosis and sign relations.

The semiotic question goes back to a line from Peirce and the uses later

writers like Eco and Derrida made of it. But the real issue is not about

the cardinality or topology of any sub-posed continuum, "signiferous ether",

or semiotic medium so much as the empirical data streams we actually have,

which are captured categorically and coded discretely as sequences of signs.

Regards,

Jon

At: http://inquiryintoinquiry.com/2019/11/09/semiotics-semiosis-sign-relations-%e2%80%a2-8/

Continuing questions about "infinite semiosis" vs. "unbounded semiosis"

prompt me to make another comment by way of bringing our focus to bear

on the empirical context of semiosis and sign relations.

The semiotic question goes back to a line from Peirce and the uses later

writers like Eco and Derrida made of it. But the real issue is not about

the cardinality or topology of any sub-posed continuum, "signiferous ether",

or semiotic medium so much as the empirical data streams we actually have,

which are captured categorically and coded discretely as sequences of signs.

Regards,

Jon

Apr 13, 2020, 9:54:18 AM4/13/20

to Cybernetic Communications, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Semiotics, Semiosis, Sign Relations • 9

At: http://inquiryintoinquiry.com/2020/04/12/semiotics-semiosis-sign-relations-%e2%80%a2-9/

All,

Just a note to record this citation by Jon Alan Schmidt of an important theme in Peirce.

It touches on one of those recurring questions which has come up time and again on the

Peirce List over the last 20 years, more acutely in recent Facebook discussions about

"universes of discourse", and more obliquely in the Ontolog Forum in connection with

the AI-CogSci-DataBase issue of "open vs. closed worlds". In another life I might

have mentioned the Central Limit Theorem at this point as that would have brought

us nearer Peirce's core insight into the matter, but maybe another time ...

Jon Alan Schmidt wrote:

<QUOTE>

Every proposition is collective and copulative; as I stated in a recent post (

https://list.iupui.edu/sympa/arc/peirce-l/2020-03/msg00028.html ) , its dynamical object is “the entire universe” (CP

5.448n, EP 2:394, 1906), which is “the totality of all real objects” (CP 5.152, EP 2:209, 1903), while its immediate

object is “the logical universe of discourse” (CP 2.323, EP 2:283, 1903).

</QUOTE>

Thanks are due to JAS for calling attention to a critical point. I'm occupied with another train of thought at the

moment so I'll just stop to flag it for a later discussion. Incidentally, or synchronistically, lack of care in

distinguishing different objects of the same signs, in particular, immediate and ultimate objects and their

corresponding universes or object domains, has been the source of many misunderstandings in scattered discussions on

Facebook of late.

Another issue arising here has to do with the difference between the “dimensionality of a relation” and the “number of

correlates”. Signs may have any number of correlates in the object domain without requiring the dimensionality of the

relevant sign relation to be greater than three. This is one of the consequences of “triadic relation irreducibility”.

Resources

=========

Logic Syllabus

( https://inquiryintoinquiry.com/logic-syllabus/ )

Semeiotic

( https://oeis.org/wiki/Semeiotic )

Universe of Discourse

( https://oeis.org/wiki/Universe_of_discourse )

Peirce’s 1870 Logic Of Relatives

( https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives )

Sign Relation

( https://oeis.org/wiki/Sign_relation )

Triadic Relation

( https://oeis.org/wiki/Triadic_relation )

Relation Theory

( https://oeis.org/wiki/Relation_theory )

Relation Reduction

( https://oeis.org/wiki/Relation_reduction )

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

facebook page: https://www.facebook.com/JonnyCache

At: http://inquiryintoinquiry.com/2020/04/12/semiotics-semiosis-sign-relations-%e2%80%a2-9/

All,

Just a note to record this citation by Jon Alan Schmidt of an important theme in Peirce.

It touches on one of those recurring questions which has come up time and again on the

Peirce List over the last 20 years, more acutely in recent Facebook discussions about

"universes of discourse", and more obliquely in the Ontolog Forum in connection with

the AI-CogSci-DataBase issue of "open vs. closed worlds". In another life I might

have mentioned the Central Limit Theorem at this point as that would have brought

us nearer Peirce's core insight into the matter, but maybe another time ...

Jon Alan Schmidt wrote:

<QUOTE>

Every proposition is collective and copulative; as I stated in a recent post (

https://list.iupui.edu/sympa/arc/peirce-l/2020-03/msg00028.html ) , its dynamical object is “the entire universe” (CP

5.448n, EP 2:394, 1906), which is “the totality of all real objects” (CP 5.152, EP 2:209, 1903), while its immediate

object is “the logical universe of discourse” (CP 2.323, EP 2:283, 1903).

</QUOTE>

Thanks are due to JAS for calling attention to a critical point. I'm occupied with another train of thought at the

moment so I'll just stop to flag it for a later discussion. Incidentally, or synchronistically, lack of care in

distinguishing different objects of the same signs, in particular, immediate and ultimate objects and their

corresponding universes or object domains, has been the source of many misunderstandings in scattered discussions on

Facebook of late.

Another issue arising here has to do with the difference between the “dimensionality of a relation” and the “number of

correlates”. Signs may have any number of correlates in the object domain without requiring the dimensionality of the

relevant sign relation to be greater than three. This is one of the consequences of “triadic relation irreducibility”.

Resources

=========

Logic Syllabus

( https://inquiryintoinquiry.com/logic-syllabus/ )

Semeiotic

( https://oeis.org/wiki/Semeiotic )

Universe of Discourse

( https://oeis.org/wiki/Universe_of_discourse )

Peirce’s 1870 Logic Of Relatives

Sign Relation

( https://oeis.org/wiki/Sign_relation )

Triadic Relation

( https://oeis.org/wiki/Triadic_relation )

Relation Theory

( https://oeis.org/wiki/Relation_theory )

Relation Reduction

( https://oeis.org/wiki/Relation_reduction )

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

Aug 9, 2021, 12:40:36 PM8/9/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

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

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).

=========

Charles S. Peirce (1902),

“Parts of Carnegie Application” (L 75), published in Carolyn Eisele (ed., 1976),

Online ( https://arisbe.sitehost.iu.edu/menu/library/bycsp/L75/l75.htm )

Regards,

Jon

Aug 10, 2021, 7:15:26 PM8/10/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

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.

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

Regards,

Jon

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.

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

Regards,

Jon

Aug 12, 2021, 6:20:34 PM8/12/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

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

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

Aug 13, 2021, 8:45:19 AM8/13/21

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

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

Aug 13, 2021, 7:00:39 PM8/13/21

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

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

Aug 14, 2021, 6:46:05 AM8/14/21

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

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

<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

Aug 14, 2021, 12:45:15 PM8/14/21

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,

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

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

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

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

Aug 22, 2021, 12:45:17 PM8/22/21

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.

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

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.

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

Aug 23, 2021, 4:44:41 PM8/23/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG

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

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

Aug 25, 2021, 11:15:46 AM8/25/21

Cf: Semiotics, Semiosis, Sign Relations • Discussion 12

https://inquiryintoinquiry.com/2021/08/25/semiotics-semiosis-sign-relations-discussion-12/

::: Robert Marty (quoted)

https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00292.html

<QUOTE RM:>

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

( https://oeis.org/wiki/Sign_relation#Six_ways_of_looking_at_a_sign_relation )

which begins as follows.

<QUOTE Article:>

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:

<QUOTE CSP:>

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).

</QUOTE>

“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

https://inquiryintoinquiry.com/2021/08/25/semiotics-semiosis-sign-relations-discussion-12/

::: Robert Marty (quoted)

https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00292.html

<QUOTE RM:>

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.

<QUOTE Article:>

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:

<QUOTE CSP:>

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).

</QUOTE>

“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

Aug 30, 2021, 3:26:31 PM8/30/21

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

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

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

Aug 31, 2021, 3:40:17 PM8/31/21

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/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