Combining Texts

All the ideas for 'Leibniz', 'Sets and Numbers' and 'There is No A Priori (and reply)'

expand these ideas     |    start again     |     specify just one area for these texts

11 ideas

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]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
7566 The Identity of Indiscernibles is really the same as the verification principle [Jolley]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
19565 How could the mind have a link to the necessary character of reality? [Devitt]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
19564 Some knowledge must be empirical; naturalism implies that all knowledge is like that [Devitt]