34 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 15544 | If what is actual might have been impossible, we need S4 modal logic [Armstrong, by Lewis] |
| 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] |
| 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] |
| 7024 | Properties are universals, which are always instantiated [Armstrong, by Heil] |
| 9478 | Even if all properties are categorical, they may be denoted by dispositional predicates [Armstrong, by Bird] |
| 10729 | Universals explain resemblance and causal power [Armstrong, by Oliver] |
| 4031 | It doesn't follow that because there is a predicate there must therefore exist a property [Armstrong] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 10024 | The type-token distinction is the universal-particular distinction [Armstrong, by Hodes] |
| 10728 | A thing's self-identity can't be a universal, since we can know it a priori [Armstrong, by Oliver] |
| 22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
| 22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
| 22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
| 22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |
| 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] |