Reflection On Recursion • Discussion

[Jon Awbrey]

Reflection On Recursion • Discussion 1
• https://inquiryintoinquiry.com/2026/04/21/reflection-on-recursion-discussion-1/

Re: Reflection On Recursion • 1
• https://inquiryintoinquiry.com/2026/04/06/reflection-on-recursion-1/
Re: Laws of Form • John Mingers
• https://groups.io/g/lawsofform/message/4943

JM:
❝This is a very important and interesting topic.
I think you should consider the relationship to
self‑reference, indeed are they really the same thing?

❝Also the work of Maturana and Varela on autopoiesis and
the neurophysiology of cognition which also has recursion
at its heart.❞

Thanks, John. Yes, we certainly find the whole array of
self concepts coming into play here — selfhood, autopoiesis
or self creation, self reference and self transformation, just
to name a few. But one thing I need to emphasize from the start
is how radically different such concepts appear when viewed under
x‑rays of Peirce's pragmatic semiotics.

I forget where I first heard it, but it's fairly common observation
that the persistence of a recurring problem is a symptom of how
unlikely it is to be solved in the paradigm where it keeps occurring.

After a while, it simply becomes time to change the paradigm …

Just by way of a first example, take the very idea of “self‑reference”.
The moment we place it in the medium of triadic sign relations we realize
signs do not refer to anything at all except insofar as an interpreter
refers them.

And when we think to ask, “What is this that we call an interpreter?”,
the pragmatic theory of signs tells us we cannot tell when we turn out
the light but under the x‑ray of the pragmatic maxim the sum of its
effects is effectively modeled by an extended triadic sign relation.

Everything I'll be working at here will be done within a framework like that.

Resources —

Inquiry Driven Systems • Inquiry Into Inquiry
• 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#RIF_1

The Phenomenology of Reflection
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_11#The_Phenomenology_of_Reflection

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

Regards,

Jon

cc: https://mathstodon.xyz/@Inquiry/116444045211570341