15 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] |
16641 | Whiteness does not exist, but by it something can exist-as-white [Aquinas] |
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] |
6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
22170 | Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas] |
22169 | Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas] |
22168 | Minds take in a likeness of things, which activates an awaiting potential [Aquinas] |