39 ideas
| 8868 | Objective truth arises from interpersonal communication [Davidson] |
| 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] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
| 15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
| 15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
| 15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
| 15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
| 15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
| 15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
| 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] |
| 15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
| 15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
| 8867 | A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson] |
| 10347 | Objectivity is intersubjectivity [Davidson] |
| 8866 | If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson] |
| 10346 | Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett] |
| 15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
| 15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
| 15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
| 15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
| 15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
| 15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
| 15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
| 15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
| 15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |
| 8870 | Content of thought is established through communication, so knowledge needs other minds [Davidson] |
| 8869 | The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson] |