45 ideas
| 21634 | Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber] |
| 21666 | 'Fundamentality' is either a superficial idea, or much too obscure [Hofweber] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 21640 | 'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber] |
| 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] |
| 21657 | Since properties can have properties, some theorists rank them in 'types' [Hofweber] |
| 21653 | Maybe not even names are referential, but are just by used by speakers to refer [Hofweber] |
| 21636 | 'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber] |
| 21637 | If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber] |
| 21643 | The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber] |
| 21644 | Numbers are used as singular terms, as adjectives, and as symbols [Hofweber] |
| 21646 | The Amazonian Piraha language is said to have no number words [Hofweber] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |
| 21649 | How can words be used for counting if they are objects? [Hofweber] |
| 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] |
| 21647 | Logicism makes sense of our ability to know arithmetic just by thought [Hofweber] |
| 21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |
| 21664 | Supervenience offers little explanation for things which necessarily go together [Hofweber] |
| 21660 | Reality can be seen as the totality of facts, or as the totality of things [Hofweber] |
| 21661 | There are probably ineffable facts, systematically hidden from us [Hofweber] |
| 21652 | Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber] |
| 21663 | Counterfactuals are essential for planning, and learning from mistakes [Hofweber] |
| 21654 | The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber] |
| 21641 | Inferential role semantics is an alternative to semantics that connects to the world [Hofweber] |
| 21638 | Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber] |
| 21658 | Properties can be expressed in a language despite the absence of a single word for them [Hofweber] |
| 21659 | 'Being taller than this' is a predicate which can express many different properties [Hofweber] |
| 21655 | Compositonality is a way to build up the truth-conditions of a sentence [Hofweber] |
| 21656 | Proposition have no content, because they are content [Hofweber] |
| 21635 | Without propositions there can be no beliefs or desires [Hofweber] |
| 21662 | Do there exist thoughts which we are incapable of thinking? [Hofweber] |
| 21645 | 'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber] |
| 21639 | 'Background deletion' is appropriately omitting background from an answer [Hofweber] |
| 22511 | Some reasonings are stronger than we are [Philolaus] |