Tag Archives: Analogy

Unknown's avatar Jon Awbrey 9:44 am on May 3, 2026
Tags: , , Analogy, , , , , , , , , , , , , , , , , , , , , , , , , , , , ,   

Animated Logical Graphs • 2

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 Spencer Brown’s Laws of Form in the Whole Earth Catalog and I sent off for it right away.  I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

So I’ll try to keep focused on that.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#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, #peirces-law, #praeclarum-theorema, #proof-theory, #propositional-calculus, #propositional-logic, #semiotics, #spencer-brown, #theorem-proving, #topology, #visualization

Unknown's avatar Jon Awbrey 10:10 am on April 30, 2026
Tags: , , Analogy, , , , , , , , , , , , , , , , , , , , , , , , , , , , ,   

Animated Logical Graphs • 1

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

      • Double Negation

    • Peirce’s Law

      • Peirce's Law

    • Praeclarum Theorema

      • Praeclarum Theorema

    • Two‑Thirds Majority Function

      • Two‑Thirds Majority Function

A full discussion of logical graphs can be found in the following article.

Additional Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#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, #peirces-law, #praeclarum-theorema, #proof-theory, #propositional-calculus, #propositional-logic, #semiotics, #spencer-brown, #theorem-proving, #topology, #visualization

Unknown's avatar Jon Awbrey 1:00 pm on November 18, 2025
Tags: , Ackermann, Analogy, , , Carnap, , , Hilbert, Hypostatic Abstraction, Kant, , , Propositions As Types Analogy, , Saunders Mac Lane, , , Universals   

Survey of Precursors Of Category Theory • 6

A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of resources on the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

Background

Blog Series

Categories à la Peirce

cc: FB | Peirce Matters • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#abstraction, #ackermann, #analogy, #aristotle, #c-s-peirce, #carnap, #category-theory, #foundations-of-mathematics, #hilbert, #hypostatic-abstraction, #kant, #logic, #mathematics, #propositions-as-types-analogy, #relation-theory, #saunders-mac-lane, #semiotics, #type-theory, #universals

Unknown's avatar Jon Awbrey 12:08 pm on November 3, 2025
Tags: , Adaptive Systems, Analogy, , , , , Cognitive Science, , , Educational Systems Design, Educational Technology, , , , , , , Intelligent Systems, , , , , Mental Models, , , , ,   

Survey of Inquiry Driven Systems • 7

This is a Survey of work in progress 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 some representing its state of information with respect to various questions of interest, for example, its own state and the states of potential object systems.  Thus it has a component of state tracing a trajectory though an information state space.

Anthem

Elements

Background

Blog Series

  • Pragmatic Cosmos • (1)
  • Reflection On Recursion • (1) • (2) • (3) • (4)
    • Discussions • (1)

Blog Dialogs

  • Architectonics of Inquiry • (1)

Developments

Applications

  • Conceptual Barriers to Creating Integrative Universities
    (Abstract) (Online)
  • Interpretation as Action • The Risk of Inquiry
    (Journal) (doc) (pdf)
  • An Architecture for Inquiry • Building Computer Platforms for Discovery
    (Online)
  • Exploring Research Data Interactively • Theme One : A Program of Inquiry
    (Online)

cc: FB | Inquiry Driven Systems • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#abduction, #adaptive-systems, #analogy, #animata, #artificial-intelligence, #automated-research-tools, #c-s-peirce, #cognitive-science, #cybernetics, #deduction, #educational-systems-design, #educational-technology, #fixation-of-belief, #induction, #information-theory, #inquiry, #inquiry-driven-systems, #inquiry-into-inquiry, #intelligent-systems, #interpretation, #logic, #logic-of-science, #mathematics, #mental-models, #pragmatic-maxim, #semiotics, #sign-relations, #triadic-relations, #visualization