Ideas from 'Review of Chihara 'Struct. Accnt of Maths'' by John P. Burgess [2005], by Theme Structure

[found in 'Philosophia Mathematica' (ed/tr -) [- ,]].

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6. Mathematics / B. Foundations for Mathematics / 5. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is the standard background for modern mathematics
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / a. Structuralism
Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure
There is no one relation for the real number 2, as relations differ in different models
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
If set theory is used to define 'structure', we can't define set theory structurally
Abstract algebra concerns relations between models, not common features of all the models
How can mathematical relations be either internal, or external, or intrinsic?