Combining Texts

All the ideas for 'Mathematics without Numbers', 'The Laws of Thought' and 'Letter to Weber'

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8 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
8083 Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
7727 Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
8686 Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
22277 Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18244 I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
8698 Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
9557 Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
10263 Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]