Combining Texts

All the ideas for 'Events and Their Names', 'The Myth of the Given' and 'Review of Chihara 'Struct. Accnt of Maths''

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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]
7. Existence / B. Change in Existence / 4. Events / c. Reduction of events
Events are made of other things, and are not fundamental to ontology [Bennett]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
The 'doctrine of the given' is correct; some beliefs or statements are self-justifying [Chisholm]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Facts are about the world, not in it, so they can't cause anything [Bennett]