55 ideas
13395 | If an analysis shows the features of a concept, it doesn't seem to 'reduce' the concept [Jubien] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
13378 | It is a mistake to think that the logic developed for mathematics can clarify language and philosophy [Jubien] |
13402 | We only grasp a name if we know whether to apply it when the bearer changes [Jubien] |
13405 | The baptiser picks the bearer of a name, but social use decides the category [Jubien] |
13399 | Examples show that ordinary proper names are not rigid designators [Jubien] |
13398 | We could make a contingent description into a rigid and necessary one by adding 'actual' to it [Jubien] |
13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
13404 | To exist necessarily is to have an essence whose own essence must be instantiated [Jubien] |
13386 | If objects are just conventional, there is no ontological distinction between stuff and things [Jubien] |
13403 | The category of Venus is not 'object', or even 'planet', but a particular class of good-sized object [Jubien] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
13375 | The idea that every entity must have identity conditions is an unfortunate misunderstanding [Jubien] |
13393 | Any entity has the unique property of being that specific entity [Jubien] |
13388 | It is incoherent to think that a given entity depends on its kind for its existence [Jubien] |
13384 | Objects need conventions for their matter, their temporal possibility, and their spatial possibility [Jubien] |
13385 | Basically, the world doesn't have ready-made 'objects'; we carve objects any way we like [Jubien] |
13383 | If the statue is loved and the clay hated, that is about the object first qua statue, then qua clay [Jubien] |
13400 | If one entity is an object, a statue, and some clay, these come apart in at least three ways [Jubien] |
13401 | The idea of coincident objects is a last resort, as it is opposed to commonsense naturalism [Jubien] |
13380 | Parts seem to matter when it is just an object, but not matter when it is a kind of object [Jubien] |
13376 | We should not regard essentialism as just nontrivial de re necessity [Jubien] |
13381 | Thinking of them as 'ships' the repaired ship is the original, but as 'objects' the reassembly is the original [Jubien] |
13382 | Rearranging the planks as a ship is confusing; we'd say it was the same 'object' with a different arrangement [Jubien] |
13379 | If two objects are indiscernible across spacetime, how could we decide whether or not they are the same? [Jubien] |
13394 | Entailment does not result from mutual necessity; mutual necessity ensures entailment [Jubien] |
13391 | Modality concerns relations among platonic properties [Jubien] |
13374 | To analyse modality, we must give accounts of objects, properties and relations [Jubien] |
13389 | The love of possible worlds is part of the dream that technical logic solves philosophical problems [Jubien] |
13390 | Possible worlds don't explain necessity, because they are a bunch of parallel contingencies [Jubien] |
23226 | There is a single mouse neuron which has 862 inputs and 626 outputs [Cobb] |
23216 | The brain is not passive, and merely processing inputs; it is active, and intervenes in the world [Cobb] |
13396 | Analysing mental concepts points to 'inclusionism' - that mental phenomena are part of the physical [Jubien] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
13377 | First-order logic tilts in favour of the direct reference theory, in its use of constants for objects [Jubien] |