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All the ideas for 'Review of Chihara 'Struct. Accnt of Maths'', 'Survival and Identity, with postscript' and 'Bayesianism'

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9 ideas

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]
10. Modality / A. Necessity / 4. De re / De dicto modality
De re modal predicates are ambiguous [Lewis, by Rudder Baker]
14. Science / C. Induction / 6. Bayes's Theorem
Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich]
Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich]