Combining Texts

All the ideas for 'Sets and Numbers', 'The Development of Logic' and 'Intro to Classical Chinese Philosophy'

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12 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
The Dao (Way) first means the road, and comes to mean the right way to live [Norden]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
The hermeneutic circle is either within the text, or between text and biased reader [Norden]
Heremeneutics is either 'faith' (examining truth) or 'suspicion' (looking for hidden motives) [Norden]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism [Kneale,W and M]
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]