17 ideas
18009 | Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor] |
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] |
14212 | A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis] |
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] |
14213 | Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis] |
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] |
14210 | A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis] |
14215 | Causal theories of reference make errors in reference easy [Lewis] |
14209 | Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis] |
18007 | Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor] |