Tag Archives: Logical Graphs

Praeclarum Theorema • 3

Posted on October 15, 2023 by Jon Awbrey

Re: Praeclarum Theorema • (1) • (2) The steps of the proof are replayed in the following animation. Reference Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 6 Comments

Praeclarum Theorema • 2

Posted on October 14, 2023 by Jon Awbrey

Re: Praeclarum Theorema • 1 And here’s a neat proof of that nice theorem — Reference Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz : Logical Papers, … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 8 Comments

Praeclarum Theorema • 1

Posted on October 13, 2023 by Jon Awbrey

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W. Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. This … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 9 Comments

Logical Graphs • Discussion 9

Posted on October 12, 2023 by Jon Awbrey

Re: Logical Graphs • Formal Development Re: Laws of Form • Lyle Anderson LA: The Gestalt Switch from parenthesis to graphs is stimulating.  There are probably things in Laws of Form that we didn’t see because we were blinded by … Continue reading →

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, Painted Cacti, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Sign Relations, Spencer Brown, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Praeclarum Theorema

Posted on October 5, 2023 by Jon Awbrey

Introduction The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W. Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 8 Comments

Logical Graphs • Discussion 8

Posted on October 2, 2023 by Jon Awbrey

Re: Logical Graphs • Formal Development Re: Laws of Form • Alex Shkotin Hi Alex, I got my first brush with graph theory in a course on the Foundations of Mathematics Frank Harary taught at the University of Michigan in 1970.  … Continue reading →

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, Painted Cacti, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Sign Relations, Spencer Brown, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Logical Graphs • Discussion 7

Posted on October 1, 2023 by Jon Awbrey

Re: Logical Graphs • Formal Development Re: Laws of Form • Alex Shkotin AS: When we look at undirected graph it is usual, before describing a rules of graph transformation, to describe exactly what kind of graphs we are working … Continue reading →

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, Painted Cacti, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Sign Relations, Spencer Brown, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Logical Graphs • Formal Development 8

Posted on September 30, 2023 by Jon Awbrey

Exemplary Proofs Using no more than the axioms and theorems recorded so far, it is possible to prove a multitude of much more complex theorems.  A couple of all‑time favorites are linked below. Peirce’s Law Praeclarum Theorema cc: FB | … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 3 Comments

Logical Graphs • Formal Development 7

Posted on September 29, 2023 by Jon Awbrey

Frequently Used Theorems (concl.) C3.  Dominant Form Theorem The third of the frequently used theorems of service to this survey is one Spencer Brown annotates as Consequence 3 (C3) or Integration.  A better mnemonic might be dominance and recession theorem (DART), but … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 3 Comments

Logical Graphs • Formal Development 6

Posted on September 28, 2023 by Jon Awbrey

Frequently Used Theorems (cont.) C2.  Generation Theorem One theorem of frequent use goes under the nickname of the weed and seed theorem (WAST).  The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 3 Comments