37 ideas
| 21584 | A sense of timelessness is essential to wisdom [Russell] |
| 21572 | Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell] |
| 21571 | Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell] |
| 21574 | Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell] |
| 21587 | Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell] |
| 21582 | Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell] |
| 21573 | When problems are analysed properly, they are either logical, or not philosophical at all [Russell] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 21588 | Logic gives the method of research in philosophy [Russell] |
| 21586 | The logical connectives are not objects, but are formal, and need a context [Russell] |
| 21585 | The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 21684 | Atomic facts may be inferrable from others, but never from non-atomic facts [Russell] |
| 22316 | A positive and negative fact have the same constituents; their difference is primitive [Russell] |
| 21576 | With asymmetrical relations (before/after) the reduction to properties is impossible [Russell] |
| 21575 | When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell] |
| 21580 | Science condemns sense-data and accepts matter, but a logical construction must link them [Russell] |
| 21583 | When sense-data change, there must be indistinguishable sense-data in the process [Russell] |
| 21577 | Empirical truths are particular, so general truths need an a priori input of generality [Russell] |
| 21579 | Objects are treated as real when they connect with other experiences in a normal way [Russell] |
| 21578 | Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell] |
| 5987 | Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von] |
| 6416 | Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling] |
| 21581 | We never experience times, but only succession of events [Russell] |
| 24043 | Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle] |