Combining Philosophers

Ideas for Eubulides, Bertrand Russell and Graham Farmelo

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15 ideas

6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17627 It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
10052 Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
14431 The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell]
14124 Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
7530 Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk]
18246 Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell]
14422 Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell]
14423 '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
14147 Denying mathematical induction gave us the transfinite [Russell]
14125 Finite numbers, unlike infinite numbers, obey mathematical induction [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
14116 Numbers were once defined on the basis of 1, but neglected infinities and + [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
14117 Numbers are properties of classes [Russell]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
14425 A number is something which characterises collections of the same size [Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
14434 What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9977 Ordinals can't be defined just by progression; they have intrinsic qualities [Russell]