33 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 18696 | The vagueness of truthmaker claims makes it easier to run anti-realist arguments [Button] |
| 18701 | The coherence theory says truth is coherence of thoughts, and not about objects [Button] |
| 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] |
| 18694 | Permutation Theorem: any theory with a decent model has lots of models [Button] |
| 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] |
| 18692 | Realists believe in independent objects, correspondence, and fallibility of all theories [Button] |
| 18693 | Indeterminacy arguments say if a theory can be made true, it has multiple versions [Button] |
| 18695 | An ideal theory can't be wholly false, because its consistency implies a true model [Button] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 17555 | 'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas] |
| 18700 | Cartesian scepticism doubts what is true; Kantian scepticism doubts that it is sayable [Button] |
| 18698 | Predictions give the 'content' of theories, which can then be 'equivalent' or 'adequate' [Button] |
| 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] |
| 18697 | A sentence's truth conditions are all the situations where it would be true [Button] |