20 ideas
21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
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] |
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] |
23029 | Knowledge is secured by the relations between its parts, through differences and identities [Green,TH, by Muirhead] |
23046 | States only have full authority if they heed the claims of human fellowship [Green,TH] |
23051 | Equality also implies liberty, because equality must be of opportunity as well as possessions [Green,TH] |
23028 | The highest political efforts express our deeper social spirit [Green,TH, by Muirhead] |
23054 | Communism is wrong because it restricts the freedom of individuals to contribute to the community [Green,TH, by Muirhead] |
23047 | Original common ownership is securing private property, not denying it [Green,TH, by Muirhead] |
23042 | National spirit only exists in the individuals who embody it [Green,TH, by Muirhead] |
23048 | The ground of property ownership is not force but the power to use it for social ends [Green,TH, by Muirhead] |
23049 | Property is needed by all citizens, to empower them to achieve social goods [Green,TH] |