Tag Archives: C.S. Peirce

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 , , , , , , , , , , , , , , , , | Leave a comment

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 , , , , , , , , , , , , , , , , | 2 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

Differential Logic • Discussion 17

Posted on March 18, 2026 by Jon Awbrey

Re: Differential Logic • The Logic of Change and Difference Re: Systems Science Working Group • Paola Di Maio PDM: Subject: Differential Logic — A point of contact with AI Knowledge Representation Dear Jon, Thank you for keeping the bell … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Logic • The Logic of Change and Difference

Posted on March 14, 2026 by Jon Awbrey

Differential logic is the logic of variation — the logic of change and difference. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 18

Posted on March 6, 2026 by Jon Awbrey

Tangent and Remainder Maps If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition in the following way. The next venn diagram shows the differential … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic • 17

Posted on March 5, 2026 by Jon Awbrey

Enlargement and Difference Maps Continuing with the example the following venn diagram shows the enlargement or shift map in the same style of field picture we drew for the tacit extension A very important conceptual transition has just occurred here, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic • 16

Posted on March 4, 2026 by Jon Awbrey

Propositions and Tacit Extensions Now that we’ve introduced the field picture as an aid to visualizing propositions and their analytic series, a pleasing way to picture the relationship of a proposition to its enlargement or shift map and its difference … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Logic • 15

Posted on March 2, 2026 by Jon Awbrey

Differential Fields The structure of a differential field may be described as follows.  With each point of there is associated an object of the following type:  a proposition about changes in that is, a proposition   In that frame of … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Cybernetics, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments