Combining Texts

All the ideas for 'Basic Problems of Phenomenology', 'Frege's Theory of Numbers' and 'Sets and Numbers'

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11 ideas

4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17824 The master science is physical objects divided into sets [Maddy]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
15571 The idea of an atemporal realm of validity is as implausible as medieval theology [Heidegger]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17825 Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
17826 Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
17828 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
17827 Sets exist where their elements are, but numbers are more like universals [Maddy]
17830 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
17823 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
17829 Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
23. Ethics / F. Existentialism / 6. Authentic Self
15581 Dasein is always only that which it has chosen to be [Heidegger]