Combining Philosophers

All the ideas for Archimedes, George Boole and Max Black

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9 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]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

10196

The Axiom of Choice needs a criterion of choice [Black]

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 / B. Foundations for Mathematics / 3. Axioms for Geometry

13007

Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]

9. Objects / A. Existence of Objects / 5. Individuation / b. Individuation by properties

10194

Two things can only be distinguished by a distinct property or a distinct relation [Black]

9. Objects / F. Identity among Objects / 5. Self-Identity

10193

The 'property' of self-identity is uselessly tautological [Black]

9. Objects / F. Identity among Objects / 7. Indiscernible Objects

10195

If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles [Black]