36 ideas
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 14480 | Maybe analytic truths do not require truth-makers, as they place no demands on the world [Thomasson] |
| 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] |
| 14471 | Analytical entailments arise from combinations of meanings and inference rules [Thomasson] |
| 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] |
| 14493 | Existence might require playing a role in explanation, or in a causal story, or being composed in some way [Thomasson] |
| 14491 | Rival ontological claims can both be true, if there are analytic relationships between them [Thomasson] |
| 14489 | Theories do not avoid commitment to entities by avoiding certain terms or concepts [Thomasson] |
| 14485 | Ordinary objects may be not indispensable, but they are nearly unavoidable [Thomasson] |
| 14487 | The simple existence conditions for objects are established by our practices, and are met [Thomasson] |
| 21651 | It is analytic that if simples are arranged chair-wise, then there is a chair [Thomasson, by Hofweber] |
| 14467 | Ordinary objects are rejected, to avoid contradictions, or for greater economy in thought [Thomasson] |
| 14479 | To individuate people we need conventions, but conventions are made up by people [Thomasson] |
| 14486 | Eliminativists haven't found existence conditions for chairs, beyond those of the word 'chair' [Thomasson] |
| 14481 | Wherever an object exists, there are intrinsic properties instantiating every modal profile [Thomasson] |
| 14482 | If the statue and the lump are two objects, they require separate properties, so we could add their masses [Thomasson] |
| 14483 | Given the similarity of statue and lump, what could possibly ground their modal properties? [Thomasson] |
| 14476 | Identity claims between objects are only well-formed if the categories are specified [Thomasson] |
| 14477 | Identical entities must be of the same category, and meet the criteria for the category [Thomasson] |
| 14478 | Modal Conventionalism says modality is analytic, not intrinsic to the world, and linguistic [Thomasson] |
| 14466 | A chief task of philosophy is making reflective sense of our common sense worldview [Thomasson] |
| 14475 | How can causal theories of reference handle nonexistence claims? [Thomasson] |
| 14474 | Pure causal theories of reference have the 'qua problem', of what sort of things is being referred to [Thomasson] |
| 14488 | Analyticity is revealed through redundancy, as in 'He bought a house and a building' [Thomasson] |
| 22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |