Combining Texts

All the ideas for 'Knowledge and its Limits', 'Space, Knowledge and Power (interview)' and 'Sets and Numbers'

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11 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
15045 The big issue since the eighteenth century has been: what is Reason? Its effect, limits and dangers? [Foucault]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
17824 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
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
4760 Belief aims at knowledge (rather than truth), and mere believing is a kind of botched knowing [Williamson]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
19512 Don't analyse knowledge; use knowledge to analyse other concepts in epistemology [Williamson, by DeRose]