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8083 | Boole applied normal algebra to logic, aiming at an algebra of thought |
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 |
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? |
8686 | Boole made logic more mathematical, with algebra, quantifiers and probability |
Full Idea: Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning. | |||
From: report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics | |||
A reaction: The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet. |