29 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] |
2584 | Lobotomised patients can cease to care about a pain [Block] |
2582 | A brain looks no more likely than anything else to cause qualia [Block] |
2574 | Behaviour requires knowledge as well as dispositions [Block] |
2576 | In functionalism, desires are internal states with causal relations [Block] |
2575 | Functionalism is behaviourism, but with mental states as intermediaries [Block] |
2583 | You might invert colours, but you can't invert beliefs [Block] |
2578 | Could a creature without a brain be in the right functional state for pain? [Block] |
2585 | Not just any old functional network will have mental states [Block] |
2586 | In functionalism, what are the special inputs and outputs of conscious creatures? [Block] |
2579 | Physicalism is prejudiced in favour of our neurology, when other systems might have minds [Block] |
2577 | Simple machine-functionalism says mind just is a Turing machine [Block] |
2580 | A Turing machine, given a state and input, specifies an output and the next state [Block] |
2581 | Intuition may say that a complex sentence is ungrammatical, but linguistics can show that it is not [Block] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |