Animated Logical Graphs • 13

Cf: Survey of Animated Logical Graphs

The blog post linked above updates my Survey of Resources for Animated Logical Graphs.  It contains links to basic expositions and extended discussions of the graphs themselves, deriving from the Alpha Graphs C.S. Peirce used for propositional logic, more recently revived and augmented by G. Spencer Brown in his Laws of Form.  What I contributed to their development was an extension from tree-like forms to what graph theorists know as cacti, and thereby hangs many a tale yet to be told.  I hope to add more proof animations as time goes on.

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

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 , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Animated Logical Graphs • 2

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing and revising the assembled material with an eye toward developing more polished articles.

Beginnings

Elements

Examples

Excursions

Applications

Blog Dialogs

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Conceptual Barriers • 3

Re: Ontolog ForumPaola Di Maio

Partly this discussion and partly just the mood I’m in brought to mind a motley assortment of old reminiscences.  My first years in college I oscillated (or vacillated) between math and physics, eventually returning to grad school in math, but only after a decade of cycling through majors from communications — of which I recall only a course in Aristotle — to psychology to philosophy to a “radical-liberal arts college” where I got to craft my own Bachelor’s degree in Mathematical and Philosophical Method.

But I’m getting ahead of the story.  The course in physics took off with a bang right away, moving quickly from classical to relativity to quantum physics.  My professors often took a Read the Masters! approach, giving us readings in Bohr, Dirac, Feynman, Heisenberg, and others, in addition to our regular textbooks.  Among the forces that drove me back to math, I remember Dirac’s algebraic symbolism, Heisenberg’s matrix mechanics, and above all Peirce, especially his use of logical matrices, that made me realize I needed to learn a lot more math before I could comprehend what any of them were talking about.

To be continued …

Posted in Artificial Intelligence, C.S. Peirce, Conceptual Barriers, Conceptual Integration, Constraint, Indication, Information, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intentionality, Knowledge Representation, Peirce, Pragmatic Semiotic Information, Scholarship of Integration, Semiotics, Sign Relations, Systems Theory, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Conceptual Barriers • 2

Re: Ontolog ForumPaola Di Maio

Synchronicity being what it is, here for your contemplation are two pictures from a current discussion on Facebook.

See Tables 8 and 9 in the following article and section:

Posted in Artificial Intelligence, C.S. Peirce, Conceptual Barriers, Conceptual Integration, Constraint, Indication, Information, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intentionality, Knowledge Representation, Peirce, Pragmatic Semiotic Information, Scholarship of Integration, Semiotics, Sign Relations, Systems Theory, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Conceptual Barriers • 1

Re: Ontolog ForumJohn Sowa

My first year at college the university held a cross-campus colloquium taking its theme from C.P. Snow’s Two Cultures about the need for and difficulties of cross-disciplinary communication and collaboration in our day.  The university had recently created three residential colleges focused on the arts, sciences, and government/history but designed to provide future citizens with an integrated perspective on how these concentrations fit into the bigger picture of the modern world.

Long time passing, I found myself returning to these questions around the turn of the millennium, addressing the “problem of silos” and the “scholarship of integration” from the perspective of Peirce’s and Dewey’s pragmatism and semiotics.  Here’s a couple of contributions Susan Awbrey and I made to the area:

Conference Presentation

  • Awbrey, S.M., and Awbrey, J.L. (1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re-Organizing Knowledge, Trans-Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.

Published Paper

  • Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  AbstractOnline.

I don’t know if the brands of ontologies being cranked out today are going to be the ultimate answer to these problems, but I do think there are applications of logic, mathematical modeling, and pragmatic semiotics that would certainly help a lot.

Resources

  • Constraints and Indications ☞ (1)(2)

cc: Structural ModelingSystems Science

Posted in Artificial Intelligence, C.S. Peirce, Conceptual Barriers, Conceptual Integration, Constraint, Indication, Information, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intentionality, Knowledge Representation, Peirce, Pragmatic Semiotic Information, Scholarship of Integration, Semiotics, Sign Relations, Systems Theory, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Semiotics, Semiosis, Sign Relations • 4

Re: Semiotic TriangleJohn Corcoran

Concepts for Peirce are mental symbols, so they fall under the general designation of signs.  For triadic sign relations in general, then, we are considering a triadic relation among objects of signs, signs of objects, and what Peirce calls interpretant signs, or interpretants for short.  It is critical to regard the designations of objects, signs, and interpretants as relational roles not ontological essences.  It is also critical to distinguish (a) extended sign relations, (b) elementary sign relations, (c) the slots of an ordered triple, and (d) the things that fill those slots.

Triangles like the one linked above have long been used to introduce the idea of a triadic sign relation.  They have the unintended consequence, however, of leading people to miss all the points I mentioned above.  So it’s wise to move quickly on to better pictures and more detailed descriptions.

Resources

  • Semiotics, Semiosis, Sign Relations ☞ (1)(2)(3)

cc: CyberneticsOntolog ForumStructural ModelingSystems Science

Posted in C.S. Peirce, Cybernetics, Logic, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , , | Leave a comment

Abductive Inference, Concept Formation, Hypothesis Formation • 1

In pragmatic semiotics, concept formation like hypothesis formation falls under the heading of abductive inference.  A lot has been said and there’s a lot more to say about that, but things are too much in flux right now to allow for an organized exposition.

So here’s just a teaser from Peirce on how concepts evolve from one level of complexity to the next, using incidentally a paradigm from the world of physics.

cc: Ontolog ForumStructural ModelingSystems Science

Posted in Abduction, C.S. Peirce, Concept Formation, Differential Calculus, Differential Logic, Dyadic Relations, Dynamical Systems, Dynamics, Geometry, Hypothesis, Hypothesis Formation, Inference, Logic, Logic of Relatives, Mathematics, Mental Models, Peirce, Physics, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment