25 ideas
8877 | We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa] |
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] |
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] |
8884 | The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa] |
8878 | It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa] |
8880 | In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa] |
8881 | Most of our knowledge has insufficient sensory support [Sosa] |
8882 | Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa] |
8883 | Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa] |
8885 | Some features of a thought are known directly, but others must be inferred [Sosa] |
8876 | Much propositional knowledge cannot be formulated, as in recognising a face [Sosa] |
8879 | Fully comprehensive beliefs may not be knowledge [Sosa] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |