Combining Texts

All the ideas for 'fragments/reports', 'The Epistemology of Essentialist Claims' and 'Review of Chihara 'Struct. Accnt of Maths''

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12 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
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]
9. Objects / D. Essence of Objects / 3. Individual Essences
Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael]
Maybe essential properties have to be intrinsic, as well as necessary? [McMichael]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is false, because it implies the existence of necessary singular propositions [McMichael]
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Individuals enter into laws only through their general qualities and relations [McMichael]