58 ideas
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 4748 | Anselm of Canterbury identified truth with God [Anselm, by Engel] |
| 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] |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |
| 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] |
| 12408 | Sartre to Waitress: Coffee with no cream, please... [Sommers,W] |
| 12397 | Said Plato: 'The things that we feel... [Sommers,W] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 12407 | Barman to Descartes: Would you like another drink?... [Sommers,W] |
| 12399 | There was a young student called Fred... [Sommers,W] |
| 20963 | A philosopher and his wife are out for a drive... [Sommers,W] |
| 12404 | Dear Sir, Your astonishment's odd.... [Sommers,W] |
| 12403 | There once was a man who said: 'God... [Sommers,W] |
| 12402 | ..But if he's a student of Berkeley... [Sommers,W] |
| 12409 | The philosopher Berkeley once said.. [Sommers,W] |
| 14694 | "My dog's got synaesthesia." How does he smell? ..... [Sommers,W] |
| 12401 | A toper who spies in the distance... [Sommers,W] |
| 12410 | There once was a man who said 'Damn!... [Sommers,W] |
| 9392 | How do behaviourists greet each other? [Sommers,W] |
| 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] |
| 12405 | 'If you're aristocratic,' said Nietzsche... [Sommers,W] |
| 9391 | Why do anarchists drink herbal tea? [Sommers,W] |
| 12400 | Cries the maid: 'You must marry me Hume!'... [Sommers,W] |
| 16527 | Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W] |
| 17592 | The barman called 'Time!', and Augustine said..... [Sommers,W] |
| 15208 | The past, present and future walked into a bar.... [Sommers,W] |
| 21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
| 21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
| 21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
| 21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
| 1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
| 21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
| 21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
| 21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
| 1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |