Animated Logical Graphs : 8

Re: Ken ReganThe Shapes of Computations

The most striking example of a “Primitive Insight Proof” (PIP❢) known to me is the Dawes–Utting proof of the Double Negation Theorem from the CSP–GSB axioms for propositional logic. There is a graphically illustrated discussion at the following location:

I cannot hazard a guess what order of insight it took to find that proof — for me it would have involved a whole lot of random search through the space of possible proofs, and that’s even if I got the notion to look for one in the first place.

There is of course a much deeper order of insight into the mathematical form of logical reasoning that it took C.S. Peirce to arrive at his maximally elegant 4-axiom set.

This entry was posted in Amphecks, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Diagrammatic Reasoning, Graph Theory, Inquiry Driven Education, 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.

One Response to Animated Logical Graphs : 8

  1. Pingback: Survey of Animated Logical Graphs • 1 | Inquiry Into Inquiry

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