38 ideas
| 11147 | Naturalistic philosophers oppose analysis, preferring explanation to a priori intuition [Margolis/Laurence] |
| 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] |
| 11141 | Modern empiricism tends to emphasise psychological connections, not semantic relations [Margolis/Laurence] |
| 11142 | Body-type seems to affect a mind's cognition and conceptual scheme [Margolis/Laurence] |
| 11121 | Language of thought has subject/predicate form and includes logical devices [Margolis/Laurence] |
| 11120 | Concepts are either representations, or abilities, or Fregean senses [Margolis/Laurence] |
| 11122 | A computer may have propositional attitudes without representations [Margolis/Laurence] |
| 11124 | Do mental representations just lead to a vicious regress of explanations [Margolis/Laurence] |
| 11123 | Maybe the concept CAT is just the ability to discriminate and infer about cats [Margolis/Laurence] |
| 11125 | The abilities view cannot explain the productivity of thought, or mental processes [Margolis/Laurence] |
| 11140 | Concept-structure explains typicality, categories, development, reference and composition [Margolis/Laurence] |
| 11128 | Classically, concepts give necessary and sufficient conditions for falling under them [Margolis/Laurence] |
| 11130 | Typicality challenges the classical view; we see better fruit-prototypes in apples than in plums [Margolis/Laurence] |
| 11129 | The classical theory explains acquisition, categorization and reference [Margolis/Laurence] |
| 11131 | It may be that our concepts (such as 'knowledge') have no definitional structure [Margolis/Laurence] |
| 11132 | The prototype theory is probabilistic, picking something out if it has sufficient of the properties [Margolis/Laurence] |
| 11133 | Prototype theory categorises by computing the number of shared constituents [Margolis/Laurence] |
| 11134 | People don't just categorise by apparent similarities [Margolis/Laurence] |
| 11135 | Complex concepts have emergent properties not in the ingredient prototypes [Margolis/Laurence] |
| 11136 | Many complex concepts obviously have no prototype [Margolis/Laurence] |
| 11137 | The theory theory of concepts says they are parts of theories, defined by their roles [Margolis/Laurence] |
| 11138 | The theory theory is holistic, so how can people have identical concepts? [Margolis/Laurence] |
| 11139 | Maybe concepts have no structure, and determined by relations to the world, not to other concepts [Margolis/Laurence] |
| 11146 | People can formulate new concepts which are only named later [Margolis/Laurence] |
| 8066 | Butler exalts conscience, but it may be horribly misleading [Anscombe on Butler] |