Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, George Boole and Arend Heyting

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6 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 / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

8754	Logic is dependent on mathematics, not the other way round [Heyting, by Shapiro]

14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction

20653

Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]