59 ideas
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
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] |
10662 | Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole') [Inwagen, by Varzi] |
17587 | The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen] |
17558 | Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen] |
17583 | There are no heaps [Inwagen] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, 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] |
17578 | I reject talk of 'stuff', and treat it in terms of particles [Inwagen] |
17582 | Singular terms can be vague, because they can contain predicates, which can be vague [Inwagen] |
17556 | Material objects are in space and time, move, have a surface and mass, and are made of some stuff [Inwagen] |
8264 | Maybe table-shaped particles exist, but not tables [Inwagen, by Lowe] |
17565 | Nihilism says composition between single things is impossible [Inwagen] |
14228 | If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction [Liggins on Inwagen] |
14468 | Actions by artefacts and natural bodies are disguised cooperations, so we don't need them [Inwagen] |
17571 | Every physical thing is either a living organism or a simple [Inwagen] |
17562 | The statue and lump seem to share parts, but the statue is not part of the lump [Inwagen] |
17574 | If you knead clay you make an infinite series of objects, but they are rearrangements, not creations [Inwagen] |
17531 | I assume matter is particulate, made up of 'simples' [Inwagen] |
17560 | If contact causes composition, do two colliding balls briefly make one object? [Inwagen] |
17561 | If bricks compose a house, that is at least one thing, but it might be many things [Inwagen] |
17566 | I think parthood involves causation, and not just a reasonably stable spatial relationship [Inwagen] |
14230 | We can deny whole objects but accept parts, by referring to them as plurals within things [Inwagen, by Liggins] |
17557 | Special Composition Question: when is a thing part of something? [Inwagen] |
17564 | The essence of a star includes the released binding energy which keeps it from collapse [Inwagen] |
17575 | The persistence of artifacts always covertly involves intelligent beings [Inwagen] |
17577 | When an electron 'leaps' to another orbit, is the new one the same electron? [Inwagen] |
17589 | If you reject transitivity of vague identity, there is no Ship of Theseus problem [Inwagen] |
17588 | We should talk of the transitivity of 'identity', and of 'definite identity' [Inwagen] |
17572 | Actuality proves possibility, but that doesn't explain how it is possible [Inwagen] |
17579 | Counterparts reduce counterfactual identity to problems about similarity relations [Inwagen] |
17590 | A merely possible object clearly isn't there, so that is a defective notion [Inwagen] |
17591 | Merely possible objects must be consistent properties, or haecceities [Inwagen] |
17563 | The strong force pulls, but also pushes apart if nucleons get too close together [Inwagen] |
17559 | Is one atom a piece of gold, or is a sizable group of atoms required? [Inwagen] |
17586 | At the lower level, life trails off into mere molecular interaction [Inwagen] |
17568 | A tumour may spread a sort of life, but it is not a life, or an organism [Inwagen] |
17581 | Being part of an organism's life is a matter of degree, and vague [Inwagen] |
17584 | Some events are only borderline cases of lives [Inwagen] |
17569 | Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap [Inwagen] |
17580 | One's mental and other life is centred on the brain, unlike any other part of the body [Inwagen] |
17570 | The chemical reactions in a human life involve about sixteen elements [Inwagen] |
17585 | Life is vague at both ends, but could it be totally vague? [Inwagen] |
17567 | A flame is like a life, but not nearly so well individuated [Inwagen] |
17576 | If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me [Inwagen] |
17573 | There is no reason to think that mere existence is a valuable thing [Inwagen] |