Combining Texts
Ideas for
'The Lagoon: how Aristotle invented science', 'The Aim and Structure of Physical Theory' and 'The Principles of Mathematics'
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8 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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14124
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Axiom of Archimedes: a finite multiple of a lesser magnitude can always exceed a greater [Russell]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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7530
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Russell tried to replace Peano's Postulates with the simple idea of 'class' [Russell, by Monk]
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18246
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Dedekind failed to distinguish the numbers from other progressions [Shapiro on Russell]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
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14147
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Denying mathematical induction gave us the transfinite [Russell]
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14125
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Finite numbers, unlike infinite numbers, obey mathematical induction [Russell]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
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14116
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Numbers were once defined on the basis of 1, but neglected infinities and + [Russell]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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14117
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Numbers are properties of classes [Russell]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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9977
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Ordinals can't be defined just by progression; they have intrinsic qualities [Russell]
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