Tag Archives: Mathematics

Sign Relations • Signs and Inquiry

Posted on February 9, 2024 by Jon Awbrey

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry.  In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity | Tagged , , , , , , , , | 4 Comments

Sign Relations • Definition

Posted on February 8, 2024 by Jon Awbrey

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting. Logic will here be defined … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity | Tagged , , , , , , , , | 4 Comments

Sign Relations • Anthesis

Posted on February 7, 2024 by Jon Awbrey

Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity | Tagged , , , , , , , , | 4 Comments

Survey of Semiotics, Semiosis, Sign Relations • 5

Posted on January 26, 2024 by Jon Awbrey

C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play.  Understanding logic as Peirce understands … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity | Tagged , , , , , , , , | 29 Comments

Survey of Cybernetics • 4

Posted on January 25, 2024 by Jon Awbrey

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? — Plato … Continue reading →

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 13 Comments

Survey of Definition and Determination • 3

Posted on January 24, 2024 by Jon Awbrey

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Logic, Mathematics, Scientific Method, Semiotics, Sign Relations, Structure | Tagged , , , , , , , , , , , , , , , | Leave a comment

Differential Propositional Calculus • Discussion 9

Posted on January 21, 2024 by Jon Awbrey

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have.  Then, your conception of those effects is the whole of your conception of the object. — C.S. Peirce • The Maxim of … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Riffs and Rotes • Happy New Year 2024

Posted on January 2, 2024 by Jon Awbrey

No information is lost by dropping the terminal 1s.  Thus we may write the following form. The article referenced below tells how forms like these correspond to a family of digraphs called riffs and a family of graphs called rotes.  … Continue reading →

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | 1 Comment

Differential Propositional Calculus • 37

Posted on January 1, 2024 by Jon Awbrey

Foreshadowing Transformations • Extensions and Projections of Discourse And, despite the care which she took to look behind her at every moment, she failed to see a shadow which followed her like her own shadow, which stopped when she stopped, … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Propositional Calculus • 36

Posted on December 31, 2023 by Jon Awbrey

Transformations of Discourse It is understandable that an engineer should be completely absorbed in his speciality, instead of pouring himself out into the freedom and vastness of the world of thought, even though his machines are being sent off to … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments