23 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] |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
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] |
9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
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] |
10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |