Category Archives: Logic

Sign Relational Manifolds • 1

Posted on October 31, 2022 by Jon Awbrey

Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation. I will have to wait for my present train of thought to stop at a station before I can hop … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 6 Comments

Zeroth Law Of Semiotics • Discussion 2

Posted on October 27, 2022 by Jon Awbrey

Re: All Liar, No Paradox • Zeroth Law Of Semiotics Re: FB | Charles S. Peirce Society • Joseph Harry Paradoxes star among my first loves in logic.  So enamored was I with tricks of the mind’s eye I remember … Continue reading →

Posted in Animata, C.S. Peirce, Denotation, Information = Comprehension × Extension, Liar Paradox, Logic, Logical Graphs, Mathematics, Nominalism, Pragmatic Maxim, Semiositis, Semiotics, Sign Relations, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , | 6 Comments

Abduction, Deduction, Induction, Analogy, Inquiry • 31

Posted on October 14, 2022 by Jon Awbrey

Re: Scott Aaronson • Explanation-Gödel and Plausibility-Gödel Scott Aaronson asks a question arising from Gödel’s First Incompleteness Theorem, namely, what are its consequences for the differential values of explanation, plausibility, and proof?  I add the following thoughts. A general heuristic … Continue reading →

Posted in Abduction, Analogy, Animata, Aristotle, Artificial Intelligence, C.S. Peirce, Deduction, Induction, Inquiry, Inquiry Driven Systems, Intelligent Systems Engineering, Logic, Mathematics, Scientific Method, Semiotics, Visualization | Tagged , , , , , , , , , , , , , , , | 5 Comments

Theme One Program • Exposition 8

Posted on October 8, 2022 by Jon Awbrey

Transformation Rules and Equivalence Classes The abstract character of the cactus language relative to its logical interpretations makes it possible to give abstract rules of equivalence for transforming cacti among themselves and partitioning the space of cacti into formal equivalence … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Exposition 7

Posted on September 30, 2022 by Jon Awbrey

Mathematical Structure and Logical Interpretation The main things to take away from the previous post are the following two ideas, one syntactic and one semantic. Syntax.  The compositional structures of cactus graphs and cactus expressions are constructed from two kinds of connective … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Exposition 6

Posted on September 29, 2022 by Jon Awbrey

Quickly recapping the discussion so far, we started with a data structure called an idea‑form flag and adopted it as a building block for constructing a species of graph-theoretic data structures called painted and rooted cacti.  We showed how to code … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Theory and Therapy of Representations • 4

Posted on September 17, 2022 by Jon Awbrey

Re: Theory and Therapy of Representations • 3 Re: Ontolog Forum • Paola Di Maio JA: What are the forces distorting our representations of what’s observed, what’s expected, and what’s intended? PDM: The short answer is …. the force behind all … Continue reading →

Posted in Accountability, Adaptive Systems, C.S. Peirce, Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Justice, Law, Logic, Max Weber, Observation, Plato, Pragmata, Representation, Science, Semiotics, Society, Statistics, Systems Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Theory and Therapy of Representations • 3

Posted on September 16, 2022 by Jon Awbrey

Representation is a concept we find at the intersection of cybernetics, epistemology, logic, mathematics, psychology, and sociology.  In my studies it led me from math to psych and back again, with sidelong glances at the history of democratic governance.  Its … Continue reading →

Posted in Accountability, Adaptive Systems, C.S. Peirce, Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Justice, Law, Logic, Max Weber, Observation, Plato, Pragmata, Representation, Science, Semiotics, Society, Statistics, Systems Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Theory and Therapy of Representations • 2

Posted on September 14, 2022 by Jon Awbrey

December 19, 2011 In a complex society, people making decisions and taking actions at places remote from you have the power to affect your life in significant ways.  Those people govern your life, they are your government, no matter what … Continue reading →

Posted in Accountability, Adaptive Systems, C.S. Peirce, Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Justice, Law, Logic, Max Weber, Observation, Plato, Pragmata, Representation, Science, Semiotics, Society, Statistics, Systems Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Theory and Therapy of Representations • 1

Posted on September 13, 2022 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 Accountability, Adaptive Systems, C.S. Peirce, Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Justice, Law, Logic, Max Weber, Observation, Plato, Pragmata, Representation, Science, Semiotics, Society, Statistics, Systems Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments