48 ideas
4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
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] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [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] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
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] |
3534 | To be is to have causal powers [Alexander,S] |
4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
4461 | Tropes are like Hume's 'impressions', conceived as real rather than as ideal [Moreland] |
4462 | A colour-trope cannot be simple (as required), because it is spread in space, and so it is complex [Moreland] |
4463 | In 'four colours were used in the decoration', colours appear to be universals, not tropes [Moreland] |
4453 | One realism is one-over-many, which may be the model/copy view, which has the Third Man problem [Moreland] |
4464 | Realists see properties as universals, which are single abstract entities which are multiply exemplifiable [Moreland] |
4451 | If properties are universals, what distinguishes two things which have identical properties? [Moreland] |
4450 | The traditional problem of universals centres on the "One over Many", which is the unity of natural classes [Moreland] |
4449 | Evidence for universals can be found in language, communication, natural laws, classification and ideals [Moreland] |
4454 | The One-In-Many view says universals have abstract existence, but exist in particulars [Moreland] |
4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [Moreland] |
4452 | Maybe universals are real, if properties themselves have properties, and relate to other properties [Moreland] |
4467 | A naturalist and realist about universals is forced to say redness can be both moving and stationary [Moreland] |
4469 | There are spatial facts about red particulars, but not about redness itself [Moreland] |
4472 | Redness is independent of red things, can do without them, has its own properties, and has identity [Moreland] |
4459 | Moderate nominalism attempts to embrace the existence of properties while avoiding universals [Moreland] |
4458 | Unlike Class Nominalism, Resemblance Nominalism can distinguish natural from unnatural classes [Moreland] |
4457 | There can be predicates with no property, and there are properties with no predicate [Moreland] |
4471 | We should abandon the concept of a property since (unlike sets) their identity conditions are unclear [Moreland] |
4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
4460 | Abstractions are formed by the mind when it concentrates on some, but not all, the features of a thing [Moreland] |
14494 | Epiphenomenalism is like a pointless nobleman, kept for show, but soon to be abolished [Alexander,S] |
3398 | Epiphenomenalism makes the mind totally pointless [Alexander,S] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
4455 | It is always open to a philosopher to claim that some entity or other is unanalysable [Moreland] |
4473 | 'Presentism' is the view that only the present moment exists [Moreland] |