27 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] |
4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
5492 | How can essences generate the right powers to vary with distance between objects? [Armstrong] |
4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |