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, 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.

2 Responses to Animated Logical Graphs • 8

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

  2. Pingback: Survey of Animated Logical Graphs • 2 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.