35 ideas
| 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] |
| 23928 | Good art produces exaltation and detachment [Bell,C] |
| 23922 | The word 'beauty' leads to confusion, because it denotes distinct emotions [Bell,C] |
| 23921 | Our feeling for natural beauty is different from the aesthetic emotion of art [Bell,C] |
| 23929 | We only see landscapes as artistic if we ignore their instrumental value [Bell,C] |
| 23923 | Visual form can create a sublime mental state [Bell,C] |
| 23932 | Art is the expression of an emotion for ultimate reality [Bell,C] |
| 23927 | Aestheticism invites artist to create beauty, but with no indication of how to do it [Bell,C] |
| 8115 | Only artists can discern significant form; other people must look to art to find it [Bell,C, by Gardner] |
| 23924 | Maybe significant form gives us a feeling for ultimate reality [Bell,C] |
| 23931 | Significant form is the essence of art, which I believe expresses an emotion about reality [Bell,C] |
| 20434 | 'Form' is visual relations, and it is 'significant' if it moves us aesthetically; art needs both [Bell,C, by Feagin] |
| 23934 | The only expression art could have is the emotion resulting from pure form [Bell,C] |
| 23925 | Mere copies of pictures are not significant - unless the copies are very exact [Bell,C] |
| 23926 | Art is distinguished by its aesthetic emotion, which produces appropriate form [Bell,C] |
| 23933 | Aesthetic contemplation is the best and most intense mental state [Bell,C] |
| 23935 | Aesthetic experience is an exaltation which increases the possibilities of life [Bell,C] |
| 22691 | Only artistic qualities matter in art, because they also have the highest moral value [Bell,C] |
| 21236 | Instead of gravitational force, we now have a pervasive gravitational field [Farmelo] |
| 21235 | The Schrödinger waves are just the maths of transforming energy values to positions [Farmelo] |
| 21234 | Experiments show that fundamental particles of one type are identical [Farmelo] |
| 23930 | Religion sees infinite value in some things, and irrelevance in the rest [Bell,C] |