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] |
9148 | I think of variables as objects rather than as signs [Fine,K] |
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] |
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] |
9152 | If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K] |
9149 | To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K] |
9150 | We should define abstraction in general, with number abstraction taken as a special case [Fine,K] |
9146 | After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |