Combining Texts

Ideas for 'Parmenides', 'Utopia' and 'Review of Chihara 'Struct. Accnt of Maths''

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7 ideas

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

10185

Set theory is the standard background for modern mathematics [Burgess]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

10184

Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]

10189

There is no one relation for the real number 2, as relations differ in different models [Burgess]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique

10186

If set theory is used to define 'structure', we can't define set theory structurally [Burgess]

10187

Abstract algebra concerns relations between models, not common features of all the models [Burgess]

10188

How can mathematical relations be either internal, or external, or intrinsic? [Burgess]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

16150

One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]