Replacing truth tables and Boolean equivalences | MathFoundations274 | N J Wildberger

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 NOTE: The important topic of BOX ARITHMETIC is now also being further developed at the Wild Egg Maths channel: see the first two Playlists below (for Members of that channel) ************** Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon:   / njwildberger   Your support would be much appreciated. Insights into Mathematics YT channel:    / njwildberger   Insights into Mathematics Playlists:    • The Algebra of Boole, Logic and Circuit An...   (31 videos)    • Box Arithmetic: a new framework for Mathem...   (18 videos)    • Hypergroups and Diffusion Symmetry: an int...   (6 videos)    • Rational Trigonometry for maths, physics a...   (4 videos)    • Sociology and Pure Maths   (44 videos)    • Old Babylonian mathematics and Plimpton 322   (8 videos)    • Math Foundations   (226 videos)    • Math Seminars N J Wildberger   (26 videos)    • Math History (ancient to modern)   (45 videos)    • Geometric Linear Algebra   (43 videos)    • Algebraic Topology   (40 videos)    • Universal Hyperbolic Geometry   (55 videos)    • Differential Geometry   (34 videos)    • Elementary Probability and Statistics   (8 videos)    • Math Terminology for Incoming Uni Students   (9 videos)    • Famous Math Problems   ( 46 videos) Wild Egg Maths Playlists:    • Box Arithmetic Book: A finite multiset fou...   (NEW!!)    • Intro to Algebraic Calculus with Box Arith...   (4 videos)    • Classical to Quantum (for Members)   (64 videos)    • Solving Polynomial Equations and the Geode...   (45 videos)    • De Casteljau Bezier curves and associated ...   (20 videos)    • Exploring q-series (for Members)   (8 videos)    • Six: A mathematical exploration   (9 videos)    • Algebraic Calculus One: a new foundation f...   (52 videos)    • Advice to prospective research mathematici...   (9 videos)    • The Hexagrammum Mysticum: a Geometric Gem ...   (14 videos)    • Algebraic Calculus Two   (8 videos)    • Special (Polynomial) Functions and Maxel N...   (25 videos)    • Dynamics on Graphs: The ADE Phenomenon & B...   (30 videos)