Insights into Mathematics | Replacing truth tables and Boolean equivalences | MathFoundations274 | N J Wildberger @njwildberger | Uploaded 4 years ago | Updated 6 hours ago
While Propositional Logic is a branch of philosophy, concerned with systematizing reasoning using connectives such as AND, OR, NOT, IMPLIES and EQUIVALENT, the Algebra of Boole provides a mathematical framework for modelling some of this. With this approach we ignore the issue of the meanings of the various atomic propositions, and replace philosophical discussion of the meaning of "true (T)" and "false (F)" with a cut and dried algebraic approach using just 0's and 1's.

With the Algebra of Boole framework, we move away from using Truth Tables and Boolean equivalences to verify statements: it is simpler and preferable to just compute Boole polynumbers for ingredient clauses. We illustrate this technology with specific examples, including the non-obvious Distributive Law, and also Transitivity of Implication, otherwise known as Hypothetical Syllogism.

Correction: On slide 3, the last column (not P) should be 1,1,0,0.

Video Content:
00:00 Introduction
4:49 Imbedding PL into the Algebra of Boole
10:52 Example: The non - obvious distributive law
18:40 Example: Transitivity of lmplication
21:50 Hypothetical syllogism
27:13 Evaluating using the Algebra of Boole


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