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Ideas for
'Metaphysics: the logical approach', 'Existentialism and Humanism' and 'Review of Chihara 'Struct. Accnt of Maths''
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9 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
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3332
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Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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3330
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Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA]
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3337
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Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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10185
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Set theory is the standard background for modern mathematics [Burgess]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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10184
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Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
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10189
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There is no one relation for the real number 2, as relations differ in different models [Burgess]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
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10186
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If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
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10187
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Abstract algebra concerns relations between models, not common features of all the models [Burgess]
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10188
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How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
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