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4 ideas
8077 | Stoic propositional logic is like chemistry - how atoms make molecules, not the innards of atoms [Chrysippus, by Devlin] |
Full Idea: In Stoic logic propositions are treated the way atoms are treated in present-day chemistry, where the focus is on the way atoms fit together to form molecules, rather than on the internal structure of the atoms. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Keith Devlin - Goodbye Descartes Ch.2 | |
A reaction: A nice analogy to explain the nature of Propositional Logic, which was invented by the Stoics (N.B. after Aristotle had invented predicate logic). |
8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
Full Idea: Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought. | |
From: report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3 | |
A reaction: The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one. |
7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once. | |
From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege | |
A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven? |
20791 | Chrysippus has five obvious 'indemonstrables' of reasoning [Chrysippus, by Diog. Laertius] |
Full Idea: Chrysippus has five indemonstrables that do not need demonstration:1) If 1st the 2nd, but 1st, so 2nd; 2) If 1st the 2nd, but not 2nd, so not 1st; 3) Not 1st and 2nd, the 1st, so not 2nd; 4) 1st or 2nd, the 1st, so not 2nd; 5) 1st or 2nd, not 2nd, so 1st. | |
From: report of Chrysippus (fragments/reports [c.240 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 07.80-81 | |
A reaction: [from his lost text 'Dialectics'; squashed to fit into one quote] 1) is Modus Ponens, 2) is Modus Tollens. 4) and 5) are Disjunctive Syllogisms. 3) seems a bit complex to be an indemonstrable. |