17 ideas
| 9161 | Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 9390 | Logic guides thinking, but it isn't a substitute for it [Rumfitt] |
| 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] |
| 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] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 9389 | Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt] |
| 9160 | Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H] |
| 9164 | We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H] |
| 9165 | Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H] |
| 9162 | Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H] |
| 9166 | People vary in their epistemological standards, and none of them is 'correct' [Field,H] |
| 9163 | If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H] |