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

• Logical Graphs • First Impressions
• Logical Graphs • Formal Development
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon
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

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 Function

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

• Logical Graphs

Additional Resources

• Logical Graphs • First Impressions
• Logical Graphs • Formal Development

cc: Academia.edu • Cybernetics • Laws of Form • Ma^thstodon
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