Monthly Archives: April 2018

Theme One • A Program Of Inquiry 14

Posted on April 25, 2018 by Jon Awbrey

As an alternative to piling generalities on generalities, not that there’s anything wrong with that, it also helps to look at issues as they arise in concrete applications. One of the most concrete applications I ever attempted was the program … 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

Definition and Determination • 17

Posted on April 23, 2018 by Jon Awbrey

Re: Ontolog Forum • Richard McCullough RM:  We clearly have some differences in the “definition” of “definition”. I suppose it all depends on the sorts of things one wants to define, something we might call the context of application.  I am … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Indication, Information = Comprehension × Extension, Inquiry, Inquiry Driven Systems, Intension, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Definition and Determination • 16

Posted on April 22, 2018 by Jon Awbrey

Re: Ontolog Forum • Richard McCullough RM:  What is your view of definitions? A recurring question, always worth some thought, so I added my earlier comment to a long-running series on my blog concerned with Definition and Determination. Survey of Definition … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Indication, Information = Comprehension × Extension, Inquiry, Inquiry Driven Systems, Intension, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Definition and Determination • 15

Posted on April 21, 2018 by Jon Awbrey

Re: Ontolog Forum • Richard McCullough In some early math course I learned a fourfold scheme of Primitives (undefined terms), Definitions, Axioms, and Inference Rules.  But later excursions tended to run the axioms and definitions together, speaking for example of … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Indication, Information = Comprehension × Extension, Inquiry, Inquiry Driven Systems, Intension, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Theme One • A Program Of Inquiry 13

Posted on April 16, 2018 by Jon Awbrey

Logical Cacti (cont.) 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 classes.  The … 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

Theme One • A Program Of Inquiry 12

Posted on April 3, 2018 by Jon Awbrey

Logical Cacti (cont.) The main things to take away from the previous post are the following two ideas, one syntactic and one semantic. The compositional structures of cactus graphs and cactus expressions are constructed from two kinds of connective operations. There are … 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