Combining Texts

All the ideas for 'fragments/reports', 'Persons, Character and Morality' and 'Sets and Numbers'

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12 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
The master science is physical objects divided into sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Sets exist where their elements are, but numbers are more like universals [Maddy]
Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
It is important that a person can change their character, and not just be successive 'selves' [Williams,B]
Kantians have an poor account of individuals, and insist on impartiality, because they ignore character [Williams,B]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
For utilitarians states of affairs are what have value, not matter who produced them [Williams,B]
28. God / A. Divine Nature / 1. God
There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara]