41 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] |
| 10653 | Maybe set theory need not be well-founded [Varzi] |
| 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] |
| 10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
| 10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
| 10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
| 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] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |
| 10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
| 10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
| 10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
| 10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
| 10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| 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] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| 7607 | Nagarjuna and others pronounced the world of experience to be an illusion [Nagarjuna, by Armstrong,K] |