42 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] |
| 10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
| 4568 | If 'Queen of England' does not refer if there is no queen, its meaning can't refer if there is one [Cooper,DE] |
| 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] |
| 4574 | If some peoples do not have categories like time or cause, they can't be essential features of rationality [Cooper,DE] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 4573 | If it is claimed that language correlates with culture, we must be able to identify the two independently [Cooper,DE] |
| 4575 | A person's language doesn't prove their concepts, but how are concepts deduced apart from language? [Cooper,DE] |
| 4561 | Many sentences set up dispositions which are irrelevant to the meanings of the sentences [Cooper,DE] |
| 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] |
| 4564 | I can meaningfully speculate that humans may have experiences currently impossible for us [Cooper,DE] |
| 4565 | The verification principle itself seems neither analytic nor verifiable [Cooper,DE] |
| 4562 | Most people know how to use the word "Amen", but they do not know what it means [Cooper,DE] |
| 4563 | 'How now brown cow?' is used for elocution, but this says nothing about its meaning [Cooper,DE] |
| 4571 | Reference need not be a hit-or-miss affair [Cooper,DE] |
| 4566 | Any thesis about reference is also a thesis about what exists to be referred to [Cooper,DE] |
| 4572 | If predicates name things, that reduces every sentence to a mere list of names [Cooper,DE] |
| 4576 | An analytic truth is one which becomes a logical truth when some synonyms have been replaced [Cooper,DE] |
| 5064 | Rights are moral significance, or liberty, or right not to be restrained, or entitlement [Mawson] |