52 ideas
| 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] |
| 10405 | In the iterative conception of sets, they form a natural hierarchy [Swoyer] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 10407 | Logical Form explains differing logical behaviour of similar sentences [Swoyer] |
| 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] |
| 17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
| 10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
| 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] |
| 18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
| 9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
| 18087 | If x changes by less and less, it must approach a limit [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] |
| 14592 | Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer] |
| 10421 | Supervenience is nowadays seen as between properties, rather than linguistic [Swoyer] |
| 14594 | Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer] |
| 10410 | Anti-realists can't explain different methods to measure distance [Swoyer] |
| 10399 | If a property such as self-identity can only be in one thing, it can't be a universal [Swoyer] |
| 10416 | Can properties have parts? [Swoyer] |
| 14595 | Can properties exemplify other properties? [Swoyer] |
| 10417 | There are only first-order properties ('red'), and none of higher-order ('coloured') [Swoyer] |
| 10413 | The best-known candidate for an identity condition for properties is necessary coextensiveness [Swoyer] |
| 10402 | Various attempts are made to evade universals being wholly present in different places [Swoyer] |
| 10400 | Conceptualism says words like 'honesty' refer to concepts, not to properties [Swoyer] |
| 10403 | If properties are abstract objects, then their being abstract exemplifies being abstract [Swoyer] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 14593 | Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer] |
| 10406 | One might hope to reduce possible worlds to properties [Swoyer] |
| 10404 | Extreme empiricists can hardly explain anything [Swoyer] |
| 10408 | Intensions are functions which map possible worlds to sets of things denoted by an expression [Swoyer] |
| 10409 | Research suggests that concepts rely on typical examples [Swoyer] |
| 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] |
| 10401 | The F and G of logic cover a huge range of natural language combinations [Swoyer] |
| 10420 | Maybe a proposition is just a property with all its places filled [Swoyer] |
| 10412 | If laws are mere regularities, they give no grounds for future prediction [Swoyer] |
| 10411 | Two properties can have one power, and one property can have two powers [Swoyer] |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |