Monthly Archives: May 2015

Signs Of Signs • 4

Re: Michael Harris • Language About Language But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and “fundamental” questions.  There seems to be no logical distinction.  The … Continue reading

Posted in Aesthetics, C.S. Peirce, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Music, Objective Frameworks, Objectivism, Peirce, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Riffs and Rotes, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Signs Of Signs • 3

Re: Michael Harris • Language About Language And if we don’t, who puts us away? One’s answer, or at least one’s initial response to that question will turn on how one feels about formal realities.  As I understand it, reality … Continue reading

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Signs Of Signs • 2

Re: Michael Harris • Language About Language I compared mathematics to a “consensual hallucination,” like virtual reality, and I continue to believe that the aim is to get (consensually) to the point where that hallucination is a second nature. I … Continue reading

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Signs Of Signs • 1

Re: Michael Harris • Language About Language There is a language and a corresponding literature that approaches logic and mathematics as related species of communication and information gathering, namely, the pragmatic-semiotic tradition passed on to us through the lifelong efforts … Continue reading

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs • 9

Re: Ken Regan • The Shapes of Computations The insight that it takes to find a succinct axiom set for a theoretical domain falls under the heading of abductive or retroductive reasoning, a knack as yet refractory to computational attack, … Continue reading

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Animated Logical Graphs • 8

Re: Ken Regan • The Shapes of Computations The most striking example of a “Primitive Insight Proof” (PIP❢) known to me is the Dawes–Utting proof of the Double Negation Theorem from the CSP–GSB axioms for propositional logic.  There is a … Continue reading

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Animated Logical Graphs • 7

Re: Ken Regan • The Shapes of Computations There are several issues of computation shape and proof style that raise their heads already at the logical ground level of boolean functions and propositional calculus.  From what I’ve seen, there are … Continue reading

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Theme One Program • 1

This is a Survey of previous blog and wiki posts on the Theme One Program that I developed all through the 1980s.  The aim of the project was to develop fundamental algorithms and data structures to support an integrated learning … Continue reading

Posted in Algorithms, Animata, Artificial Intelligence, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognitive Science, Computation, Computational Complexity, Computer Science, Computing, Constraint Satisfaction Problems, Cybernetics, Data Structures, Diagrammatic Reasoning, Diagrams, Differential Analytic Turing Automata, Education, Educational Systems Design, Educational Technology, Equational Inference, Functional Logic, Graph Theory, Indicator Functions, Inquiry, Inquiry Driven Education, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Knowledge, Learning, Learning Theory, Logic, Logical Graphs, Machine Learning, Mathematics, Mental Models, Minimal Negation Operators, Painted Cacti, Peirce, Programming, Programming Languages, Propositional Calculus, Propositional Equation Reasoning Systems, Propositions, Research Technology, Semeiosis, Semiosis, Semiotics, Sign Relations, Surveys, Teaching, Theorem Proving, Triadic Relations, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Semiotic Theory Of Information • 1

This is a Survey of previous blog and wiki posts on the Semiotic Theory Of Information.  All my projects are exploratory in essence but this line of inquiry is more open-ended than most.  The question is: What is information and how … Continue reading

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Entropy, Epistemology, Fixation of Belief, Ignorance, Illusion, Induction, Information, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Mental Models, Objective Frameworks, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Thirdness, Triadic Relations, Triadicity, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Relation Theory • 1

In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many … Continue reading

Posted in Algebra, C.S. Peirce, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Logic, Logic of Relatives, Mathematics, Model Theory, Peirce, Proof Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Teridentity, Thirdness, Triadic Relations, Triadicity, Type Theory, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment