The logo is a little too close to the “red crystal” protective symbol IMHO. #semiotics

From: @nasa
https://social.beachcom.org/@nasa/114393229629270470

Higher Order Sign Relations • Discussion 1

Re: FB | Charles S. Peirce Society • John Corcoran

Questions about the proper treatment of use and mention from the standpoint of Peirce’s theory of signs came up recently in discussions on Facebook.  In pragmatic semiotics the trade‑off between “signs-of-objects” and “signs-as-objects” opens up the wider space of higher order sign relations.  In previous work on Inquiry Driven Systems I introduced the subject in the following way.

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections.  They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign relations.  The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.

References

• John Corcoran
• Schemata : The Concept of Schema in the History of Logic
• Use And Mention, Use Without Mention, Mention Without Use

Resources

• Inquiry Driven Systems
• Reflective Interpretive Frameworks
• Higher Order Sign Relations
• Survey of Inquiry Driven Systems
• Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Higher Order Sign Relations • 1
• https://inquiryintoinquiry.com/2025/03/22/higher-order-sign-relations-1-a/

Higher Order Sign Relations • Introduction —

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections. They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign relations. The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.

Some years ago I was formatting my old dissertation proposal on Inquiry Driven Systems for the web when the subject of “signs about signs” arose on the Peirce List. It called to mind the part of my document on Higher Order Sign Relations, on which basis Reflective Interpretive Frameworks are constructed, and the introduction to which begins as above.

Resources —

Inquiry Driven Systems
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview

Reflective Interpretive Frameworks
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_10#Reflective_Interpretive_Frameworks

Higher Order Sign Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Inquiry #Logic #Mathematics #Reflection
#Semiotics #SignRelations #HigherOrderSignRelations
#InquiryDrivenSystems #ReflectiveInterpretiveFrameworks

Higher Order Sign Relations • 1

Higher Order Sign Relations • Introduction

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections.  They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign relations.  The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.

Some years ago I was formatting my old dissertation proposal on Inquiry Driven Systems for the web when the subject of “signs about signs” arose on the Peirce List.  It called to mind the part of my document on Higher Order Sign Relations, on which basis Reflective Interpretive Frameworks are constructed, and the introduction to which begins as above.

Resources

• Inquiry Driven Systems
• Reflective Interpretive Frameworks
• Higher Order Sign Relations
• Survey of Inquiry Driven Systems
• Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Signs Of Signs • 4

Re: Michael Harris • Language About Language

But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and “fundamental” questions.  There seems to be no logical distinction.  The formalist answer might involve algorithmic complexity, but I don’t think that sheds any useful light on the question.  The materialist answer (often? usually?) amounts to just‑so stories involving Darwin, and lions on the savannah, and maybe an elephant, or at least a mammoth.  I don’t find these very satisfying either and would prefer to find something in between, and I would feel vindicated if it could be proved (in I don’t know what formal system) that the capacity to make such a distinction entails appreciation of music.

Peirce proposed a distinction between corollarial and theorematic reasoning in mathematics which strikes me as similar to the distinction Michael Harris seeks between technical and fundamental questions.

I can’t say I have a lot of insight into how the distinction might be drawn but I recall a number of traditions pointing to the etymology of theorem as having to do with the observation of objects and practices whose depth of detail always escapes full accounting by any number of partial views.

On the subject of music, all I have is the following incidental —

🙞 Riffs and Rotes

Perhaps it takes a number theorist to appreciate it …

Resources

• Higher Order Sign Relations
• Survey of Pragmatic Semiotic Information
• Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Signs Of Signs • 3

Re: Michael Harris • Language About Language

And if we don’t [keep our stories straight], who puts us away?

One’s answer, or at least one’s initial response to that question will turn on how one feels about formal realities.  As I understand it, reality is that which persists in thumping us on the head until we get what it’s trying to tell us.  Are there formal realities, forms which drive us in that way?

Discussions like those tend to begin by supposing we can form a distinction between external and internal.  That is a formal hypothesis, not yet born out as a formal reality.  Are there formal realities which drive us to recognize them, to pick them out of a crowd of formal possibilities?

Resources

• Higher Order Sign Relations
• Survey of Pragmatic Semiotic Information
• Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Signs Of Signs • 2

Re: Michael Harris • Language About Language

I compared mathematics to a “consensual hallucination”, like virtual reality, and I continue to believe that the aim is to get (consensually) to the point where that hallucination is a second nature.

I think that’s called coherentism, normally contrasted with or complementary to objectivism.  It’s the philosophy of a gang of co‑conspirators who think, “We’ll get off scot‑free so long as we all keep our stories straight.”

Resources

• Higher Order Sign Relations
• Survey of Pragmatic Semiotic Information
• Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Signs Of Signs • 1
• https://inquiryintoinquiry.com/2025/03/16/signs-of-signs-1-a/

Re: Michael Harris • Language About Language
• https://mathematicswithoutapologies.wordpress.com/2015/05/23/language-about-language/

There is a language and a corresponding literature treating logic and mathematics as related species of communication and information gathering, namely, the pragmatic-semiotic tradition transmitted through the lifelong efforts of C.S. Peirce. It is by no means a dead language but it continues to fly beneath the radar of many trackers in logic and math today. Nevertheless, the resource remains for those who wish to look into it.

Resources —

Higher Order Sign Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

• https://www.academia.edu/community/LpWxoO
• https://www.researchgate.net/post/Signs_Of_Signs

#Peirce #Inquiry #Logic #Mathematics #Reflection
#Semiotics #SignRelations #HigherOrderSignRelations

Signs Of Signs • 1

Re: Michael Harris • Language About Language

There is a language and a corresponding literature treating logic and mathematics as related species of communication and information gathering, namely, the pragmatic‑semiotic tradition transmitted through the lifelong efforts of C.S. Peirce.  It is by no means a dead language but it continues to fly beneath the radar of many trackers in logic and math today.  Nevertheless, the resource remains for those who wish to look into it.

Resources

• Higher Order Sign Relations
• Survey of Pragmatic Semiotic Information
• Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Cactus Language • Overview 1.1
• https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/

❝Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually no knowledge in immediately adjacent areas. If our intellectual gaze could shift slightly, it would alter each quill’s direction, and suddenly our entire reality would change.❞

— Herbert J. Bernstein • “Idols of Modern Science”

The following report describes a calculus for representing propositions as sentences, that is, as syntactically defined sequences of signs, and for working with those sentences in light of their semantically defined contents as logical propositions. In their computational representation the expressions of the calculus parse into a class of graph‑theoretic data structures whose underlying graphs are called “painted cacti”.

Painted cacti are a specialization of what graph‑theorists refer to as “cacti”, which are in turn a generalization of what they call “trees”. The data structures corresponding to painted cacti have especially nice properties, not only useful in computational terms but interesting from a theoretical standpoint. The remainder of the present Overview is devoted to motivating the development of the indicated family of formal languages, going under the generic name of Cactus Language.

#Peirce #Logic #Semiotics #LogicalGraphs #DifferentialLogic
#Automata #FormalLanguages #FormalGrammars #GraphTheory

Ouch❢
• https://inquiryintoinquiry.com/2025/02/27/ouch%e2%9d%a2-a/

❝A child hears it said that the stove is hot. But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold. But he touches it, and finds the testimony confirmed in a striking way. Thus, he becomes aware of ignorance, and it is necessary to suppose a self in which this ignorance can inhere. …

❝In short, error appears, and it can be explained only by supposing a self which is fallible.

❝Ignorance and error are all that distinguish our private selves from the absolute ego of pure apperception.❞

🙞 C.S. Peirce • “Questions Concerning Certain Faculties Claimed For Man”
• https://www.cspeirce.com/menu/library/bycsp/question/qu-frame.htm

Resource —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Retconning the slang expression “That’s dope” to be a shortened exclamation for “That experience is a source of dopamine” as in my brain is going to insist that I do it again.

Which, interestingly enough, is a back door to saying something could potentially be habit forming if not outright addictive.