Animated Logical Graphs • 52

Peirce's Law

Re: Richard J. LiptonThe Future Of Mathematics?Is The End Near?
Re: Peirce ListJon Alan Schmidt

Peirce’s explorations in logic and the theory of signs opened several directions of generalization from logics of complete information (LOCI) to theories of partial information (TOPI).  Naturally we hope these avenues of approach will eventually converge on a unified base camp from which to reach greater heights of understanding, but that is still a work in progress, at least for me.

Any passage from logic as a critical, formal, or normative theory of controlled semiotic conduct to the descriptive study of signs “in the wild” involves relaxing logical norms to statistical norms.

One of the headings under which Peirce expands the scope of logic to something more general — whether keeping or losing the name of “logic” is a secondary consideration — is found in his study of Generality and Vagueness as affecting signs not fully primed for logical use.  There’s a bit about that at the following places.

As you can see, in this direction of generalization Peirce considers relaxing both the principle of contradiction and the principle of excluded middle.

Resources

cc: Cybernetics Communications (1) (2)FB | Logical Graphs • Ontolog Forum (1) (2)
• Peirce (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) • Structural Modeling (1) (2) • Systems (1) (2)

This entry was 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 and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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