Tag Archives: Form

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

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

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#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: , , , , , , , , , , , , Form, , , , , , , , , , , , , , , , , , ,   

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 7:20 am on November 5, 2025
Tags: , Comprehension, Constraint, , , Extension, Form, Indication, , , , , , , , , Structure, Systems Theory,   

Survey of Definition and Determination • 4

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from signs and scientific inquiry to logic and information theory.

Two of the first questions calling for fresh examination were the closely related concepts of definition and determination, not only as Peirce used them in his logic and semiotics but as researchers in areas as diverse as computer science, cybernetics, physics, and systems science would find themselves forced to reconsider the concepts in later years.  That led me to collect a sample of texts where Peirce and a few other writers discuss the issues of definition and determination.  There are copies of those selections at the following sites.

What follows is a Survey of blog and wiki posts on Definition and Determination, with a focus on the part they play in Peirce’s interlinked theories of signs, information, and inquiry.  In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force when we view the overarching concept of constraint from an information-theoretic point of view, as Peirce did beginning in the 1860s.

Blog Dialogs

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#c-s-peirce, #comprehension, #constraint, #definition, #determination, #extension, #form, #indication, #information, #information-comprehension-x-extension, #inquiry-driven-systems, #logic, #mathematics, #scientific-method, #semiotics, #sign-relations, #structure, #systems-theory, #visualization