Insights into Mathematics | Inference Rules via the Algebra of Boole | MathFoundations 275 | N J Wildberger @njwildberger | Uploaded 4 years ago | Updated 20 hours ago
We show how to introduce Inference Rules in Propositional Logic in the framework of the Algebra of Boole, which provides a cut and dried technology to easily establish all such rules.

Prominent amongst these are Modus Ponens, Modus Tollens, Hypothetical Syllogism and Disjunctive Syllogism. With this new technology we can establish each of these very simply, and even more powerfully -- we can in fact dispense with their use altogether! No more memorization of clever logical rules is required, as our simplified Grade 9 algebra of the Algebra of Boole transcends it all.

As an application, we go back to a Logic Puzzle of Lewis Carroll, which tells us something uncomfortable about ... your poetry.


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