50 ideas
| 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] |
| 9038 | We must distinguish what the speaker denotes by a name, from what the name denotes [Evans] |
| 5824 | How can an expression be a name, if names can change their denotation? [Evans] |
| 9042 | A private intention won't give a name a denotation; the practice needs it to be made public [Evans] |
| 9041 | The Causal Theory of Names is wrong, since the name 'Madagascar' actually changed denotation [Evans] |
| 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] |
| 16129 | Evans argues (falsely!) that a contradiction follows from treating objects as vague [Evans, by Lowe] |
| 16459 | Is it coherent that reality is vague, identities can be vague, and objects can have fuzzy boundaries? [Evans] |
| 16460 | Evans assumes there can be vague identity statements, and that his proof cannot be right [Evans, by Lewis] |
| 16457 | There clearly are vague identity statements, and Evans's argument has a false conclusion [Evans, by Lewis] |
| 14484 | If a=b is indeterminate, then a=/=b, and so there cannot be indeterminate identity [Evans, by Thomasson] |
| 16224 | There can't be vague identity; a and b must differ, since a, unlike b, is only vaguely the same as b [Evans, by PG] |
| 14895 | 'Superficial' contingency: false in some world; 'Deep' contingency: no obvious verification [Evans, by Macià/Garcia-Carpentiro] |
| 11881 | Rigid designators can be meaningful even if empty [Evans, by Mackie,P] |
| 7639 | The Homunculus Fallacy explains a subject perceiving objects by repeating the problem internally [Evans] |
| 12580 | Experiences have no conceptual content [Evans, by Greco] |
| 7643 | We have far fewer colour concepts than we have discriminations of colour [Evans] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 23794 | Some representational states, like perception, may be nonconceptual [Evans, by Schulte] |
| 16366 | The Generality Constraint says if you can think a predicate you can apply it to anything [Evans] |
| 12575 | Concepts have a 'Generality Constraint', that we must know how predicates apply to them [Evans, by Peacocke] |
| 5825 | Speakers intend to refer to items that are the source of their information [Evans] |
| 5823 | The intended referent of a name needs to be the cause of the speaker's information about it [Evans] |
| 9039 | If descriptions are sufficient for reference, then I must accept a false reference if the descriptions fit [Evans] |
| 9043 | We use expressions 'deferentially', to conform to the use of other people [Evans] |
| 9040 | Charity should minimize inexplicable error, rather than maximising true beliefs [Evans] |
| 20400 | Intentions either succeed or fail, so external evidence for them is always irrelevant [Wimsatt/Beardsley, by Davies,S] |
| 7266 | The author's intentions are irrelevant to the judgement of a work's success [Wimsatt/Beardsley] |
| 7267 | Poetry, unlike messages, can be successful without communicating intentions [Wimsatt/Beardsley] |
| 7268 | The thoughts of a poem should be imputed to the dramatic speaker, and hardly at all to the poet [Wimsatt/Beardsley] |
| 7269 | The intentional fallacy is a romantic one [Wimsatt/Beardsley] |
| 7271 | Biography can reveal meanings and dramatic character, as well as possible intentions [Wimsatt/Beardsley] |