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Jon Awbrey

Higher Order Sign Relations • Discussion 1
• inquiryintoinquiry.com/2025/03

Re: FB | Charles S. Peirce Society • John Corcoran
• facebook.com/groups/peircesoci

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
• johncorcoran.academia.edu/

Schemata : The Concept of Schema in the History of Logic
• academia.edu/12691868/SCHEMATA

Use And Mention, Use Without Mention, Mention Without Use
• academia.edu/s/ea64a3484e/sche

Resources —

Higher Order Sign Relations
• oeis.org/wiki/Inquiry_Driven_S

Survey of Inquiry Driven Systems
• inquiryintoinquiry.com/2024/02

Survey of Semiotics, Semiosis, Sign Relations
• inquiryintoinquiry.com/2024/01




Inquiry Into Inquiry · Higher Order Sign Relations • Discussion 1
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"My main guide in my work was the constant search for a perfect coherence, a complete harmony that I could see behind the turbulent surface of things, and which I patiently strove to uncover, without ever being tired of it. It was a keen sense of "beauty", surely, that was my flair and my only compass. My greatest joy was not so much to contemplate it when it appeared in full light [...]" – Alexandre Grothendieck (1928-2014)

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Soh Kam Yung

"Henry Dudeney [...] asked his readers to dissect an equilateral triangle into the smallest number of pieces that could be rearranged into a square.
[...]
Kamata and two other mathematicians have finally proved that a solution with fewer [than four] pieces is impossible. Their result was posted to the server arXiv.org in a December 2024 preprint entitled “Dudeney’s Dissection Is Optimal.”"

scientificamerican.com/article

On arXiv [ arxiv.org/abs/2412.03865 ]

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Watch Dylan Iwakuni demonstrate six beautiful connections including dovetail and gooseneck joints—each showcasing a marriage of #mathematics, #engineering, and patient craftsmanship.

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Inquiry Into Inquiry

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

Resources

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

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