Combining Texts

All the ideas for 'Science and Method', 'Review of Chihara 'Struct. Accnt of Maths'' and 'fragments/reports'

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11 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
One geometry cannot be more true than another [Poincaré]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory is the standard background for modern mathematics [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
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
If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
Abstract algebra concerns relations between models, not common features of all the models [Burgess]
How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
We must choose in which of the virtues we wish to excel [Panaetius]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / b. Living naturally
Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero]