Category Archives: Deduction

Survey of Inquiry Driven Systems • 1

Posted on May 14, 2015 by Jon Awbrey

This is a Survey of blog and wiki posts on Inquiry Driven Systems, material I plan to refine toward a more compact and systematic treatment of the subject. An inquiry driven system is a system having among its state variables … Continue reading →

Posted in Abduction, Action, Adaptive Systems, Aristotle, Artificial Intelligence, Automated Research Tools, Change, Cognitive Science, Communication, Cybernetics, Deduction, Descartes, Dewey, Discovery, Doubt, Education, Educational Systems Design, Educational Technology, Fixation of Belief, Induction, Information, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretation, Invention, Kant, Knowledge, Learning, Learning Theory, Logic, Logic of Science, Mathematics, Mental Models, Peirce, Pragmatic Maxim, Pragmatism, Process Thinking, Scientific Inquiry, Semiotics, Sign Relations, Surveys, Teaching, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs • 6

Posted on March 13, 2015 by Jon Awbrey

Re: Peirce List • Jim Willgoose At root we are dealing with a genre of very abstract formal systems.  They have grammars that determine their well-formed expressions and rules that determine the permissible transformations among expressions, but they lack all … Continue reading →

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Graph Theory, Iconicity, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Mathematical Demonstration and the Doctrine of Individuals • 2

Posted on February 23, 2015 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) In reference to the doctrine of individuals, two distinctions should be borne in mind.  The logical atom, or term not capable of logical division, must be one of which every predicate may … Continue reading →

Posted in C.S. Peirce, Deduction, Doctrine of Individuals, Foundations of Mathematics, Identity, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Relation Theory | Tagged , , , , , , , , , , | 6 Comments

Mathematical Demonstration and the Doctrine of Individuals • 1

Posted on February 22, 2015 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) Demonstration of the sort called mathematical is founded on suppositions of particular cases.  The geometrician draws a figure;  the algebraist assumes a letter to signify a single quantity fulfilling the required conditions.  … Continue reading →

Posted in C.S. Peirce, Deduction, Doctrine of Individuals, Foundations of Mathematics, Identity, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Relation Theory | Tagged , , , , , , , , , , | 5 Comments

Animated Logical Graphs • 5

Posted on January 28, 2015 by Jon Awbrey

Re: Peirce List Discussion • HP A computational problem is defined as a set of problem instances with specified properties.  An algorithm solves a problem if it computes the correct answer to every problem instance in that set. The use … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 4

Posted on January 27, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien It’s fair to say most of my university coursework leaned to the theoretical side but I did cobble together a respectable enough background in computing, statistics, and industrial-organizational styles of systems and simulation that … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 3

Posted on January 26, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien I have a little more leisure now to start climbing back into the saddle, so let me see where we left off … Try looking into the article I linked before: Logical Graphs Or … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Differential Logic, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce's Law, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Logic, Semiotics, Spencer Brown, Theorem Proving, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 2

Posted on January 14, 2015 by Jon Awbrey

Re: Peirce List • Jim Willgoose It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Differential Logic, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce's Law, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Logic, Semiotics, Spencer Brown, Theorem Proving, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 1

Posted on January 8, 2015 by Jon Awbrey

For Your Musement … Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic. Proof Animations Double Negation Peirce’s Law Praeclarum Theorema Two‑Thirds Majority … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Differential Logic, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce's Law, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Logic, Semiotics, Spencer Brown, Theorem Proving, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

“What we’ve got here is (a) failure to communicate” • 6

Posted on November 15, 2013 by Jon Awbrey

Excerpt from Warren S. McCulloch, “What Is a Number, that a Man May Know It, and a Man, that He May Know a Number?” (1960) Please remember that we are not now concerned with the physics and chemistry, the anatomy … Continue reading →

Posted in Abduction, Amphecks, Aristotle, Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Combinatorics, Deduction, Duns Scotus, Induction, Leibniz, Logic, Logic of Relatives, Mathematics, Neural Models, Ockham, Peirce, Propositional Logic, Psychons, Relation Theory, Sources, Triadic Relations, Warren S. McCulloch, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment