Category Archives: Triadic Relations

Objects, Models, Theories • 2

Posted on September 12, 2026 by Jon Awbrey

Re: Gödel’s Lost Letter • The Graph Of Math GLL: Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory.  He was of course the greatest architect of Proof Theory, which stands in contrast … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Objects, Models, Theories • 1

Posted on September 10, 2026 by Jon Awbrey

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839 I return once more to a recurring subject. Re: Artem Kaznatcheev • Three Types of Mathematical Models In speaking of models one tends to find denizens of different disciplines talking at … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 2 Comments

Reflective Interpretive Frameworks • Incident 2

Posted on August 27, 2026 by Jon Awbrey

Re: Terence Tao • Modular Arithmetic Challenge Can a neural network learn to do modular multiplication efficiently? Incidental Reflection 1 There are alternative models of neural networks which do not depend on threshold neurons and endlessly fiddling with weights. Incidental … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Reflection On Recursion • Discussion 1

Posted on April 21, 2026 by Jon Awbrey

Re: Reflection On Recursion • 1 Re: Laws of Form • John Mingers 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 … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Reflection On Recursion • 4

Posted on April 18, 2026 by Jon Awbrey

A feature worth noting in the recursion diagram is the function traversing the square from one triadic node to the other.  It preserves an image of the object all the while its precedent is being retrieved and processed — thus … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Reflection On Recursion • 3

Posted on April 13, 2026 by Jon Awbrey

One other feature of syntactic recursion deserves to be brought into higher relief.  Evidence of it can be found in the recursion diagram by examining the places where three paths meet.  On the descending side there is the point where … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Reflection On Recursion • 2

Posted on April 9, 2026 by Jon Awbrey

Turning to the form of a simple recursive function the clause we used to define it earns the title of “syntactic recursion” due to the way the function name occurring in the defined phrase re‑occurs in the defining phrase It … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Reflection On Recursion • 1

Posted on April 6, 2026 by Jon Awbrey

Ongoing conversations with Dan Everett on Facebook have me backtracking to recurring questions about the relationship between formal language theory (as I once learned it) and the properties of natural languages as they are found occurring in the field.  A … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Reflective Interpretive Frameworks • Incident 1

Posted on March 26, 2026 by Jon Awbrey

Re: William Waites • The Agent That Doesn’t Know Itself WW:  ❝Why Has Nobody Done This?❞ People who study C.S. Peirce would say reflective reasoning requires triadic relations at core and there is work being done on that.  One of … Continue reading →

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | 2 Comments

Sign Relations • Graphical Representations

Posted on January 15, 2026 by Jon Awbrey

The dyadic components of sign relations have graph‑theoretic representations, as digraphs (or directed graphs), which provide concise pictures of their structural and potential dynamic properties. By way of terminology, a directed edge is called an arc from point to point … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 2 Comments