18 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] |
14620 | Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [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] |
14530 | The role of semantic necessity in semantics is like metaphysical necessity in metaphysics [Fine,K, by Hale/Hoffmann,A] |
14618 | Semantics is either an assignment of semantic values, or a theory of truth [Fine,K] |
14621 | Semantics is a body of semantic requirements, not semantic truths or assigned values [Fine,K] |
14622 | Referential semantics (unlike Fregeanism) allows objects themselves in to semantic requirements [Fine,K] |
14619 | The Quinean doubt: are semantics and facts separate, and do analytic sentences have no factual part? [Fine,K] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |