16 ideas
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
14217 | The 'standard' view of relations is that they hold of several objects in a given order [Fine,K] |
14216 | The 'positionalist' view of relations says the number of places is fixed, but not the order [Fine,K] |
14218 | A block on top of another contains one relation, not both 'on top of' and 'beneath' [Fine,K] |
14220 | Explain biased relations as orderings of the unbiased, or the unbiased as permutation classes of the biased? [Fine,K] |
14219 | Language imposes a direction on a road which is not really part of the road [Fine,K] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
467 | A virtue is a combination of intelligence, strength and luck [Ion] |