Combining Texts

All the ideas for 'fragments/reports', 'Sets and Numbers' and 'Counterpart theory and Quant. Modal Logic'

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


16 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]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 7. Natural Necessity
Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
Counterparts are not the original thing, but resemble it more than other things do [Lewis]
If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
Essential attributes are those shared with all the counterparts [Lewis]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]