Aristotle's syllogisms revisited with the Algebra of Boole | MathFoundations 280 | N J Wildberger

We have another look at the syllogisms of Aristotle, now from the Algebra of Boole point of view. Two of his logical forms are quite different from the other two, and by restating the sylllogisms using modern Propositional Logic we can then convert exactly four of them into the Algebra of Boole --- and then give easy mechanical proofs.

The remaining syllogisms present more of a challenge!

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Here are all the Insights into Mathematics Playlists:

Elementary Mathematics (K-6) Explained: playlist
list=PL8403C2F0C89B1333
Year 9 Maths: Year9Maths
Ancient Mathematics: Ancient Mathematics
Wild West Banking: Wild West Banking
Sociology and Pure Mathematics: Sociology and Pure Mathematics
Old Babylonian Mathematics (with Daniel Mansfield): playlist
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: MathHistory: A course in the History ...
Wild Trig: Intro to Rational Trigonometry: WildTrig: Intro to Rational Trigonometry
MathFoundations: Math Foundations
Wild Linear Algebra: Wild Linear Algebra
Famous Math Problems: Famous Math Problems
Probability and Statistics: An Introduction: Probability and Statistics: an introd...
Boole's Logic and Circuit Analysis: Boole's Logic and Circuit Analysis
Universal Hyperbolic Geometry: Universal Hyperbolic Geometry
Differential Geometry: Differential Geometry
Algebraic Topology: Algebraic Topology
Math Seminars: MathSeminars
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And here are the Wild Egg Maths Playlists:

Triangle Centres: ENCYCLOPEDIA OF TRIANGLE CENTERS
Six: An elementary course in pure mathematics: Six: An elementary course in Pure Mat...
Algebraic Calculus One: Algebraic Calculus One
Algebraic Calculus Two: Algebraic Calculus Two

Video Contents:
00:00 Aristotle via the Algebra of George Boole
02:29 Aristotle's four logical forms
05:07 Example: Properties on a population (original)
10:50 Aristotle's two perfect logical forms
14:21 First figure syllogisms and second figure syllogisms
16:41 Barbara
20:55 Celarant
22:13 Camestres