51 ideas
| 17651 | Without words or other symbols, we have no world [Goodman] |
| 22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
| 17652 | Truth is irrelevant if no statements are involved [Goodman] |
| 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] |
| 17518 | Counting 'coin in this box' may have coin as the unit, with 'in this box' merely as the scope [Ayers] |
| 17516 | If counting needs a sortal, what of things which fall under two sortals? [Ayers] |
| 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] |
| 17520 | Events do not have natural boundaries, and we have to set them [Ayers] |
| 17656 | Being primitive or prior always depends on a constructional system [Goodman] |
| 17661 | We don't recognise patterns - we invent them [Goodman] |
| 17659 | Reality is largely a matter of habit [Goodman] |
| 17657 | We build our world, and ignore anything that won't fit [Goodman] |
| 17654 | A world can be full of variety or not, depending on how we sort it [Goodman] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 17519 | To express borderline cases of objects, you need the concept of an 'object' [Ayers] |
| 17510 | Speakers need the very general category of a thing, if they are to think about it [Ayers] |
| 17522 | We use sortals to classify physical objects by the nature and origin of their unity [Ayers] |
| 17515 | Seeing caterpillar and moth as the same needs continuity, not identity of sortal concepts [Ayers] |
| 17511 | Recognising continuity is separate from sortals, and must precede their use [Ayers] |
| 17517 | Could the same matter have more than one form or principle of unity? [Ayers] |
| 17513 | If there are two objects, then 'that marble, man-shaped object' is ambiguous [Ayers] |
| 17523 | Sortals basically apply to individuals [Ayers] |
| 17521 | You can't have the concept of a 'stage' if you lack the concept of an object [Ayers] |
| 17514 | Temporal 'parts' cannot be separated or rearranged [Ayers] |
| 17509 | Some say a 'covering concept' completes identity; others place the concept in the reference [Ayers] |
| 17653 | Things can only be judged the 'same' by citing some respect of sameness [Goodman] |
| 17512 | If diachronic identities need covering concepts, why not synchronic identities too? [Ayers] |
| 17660 | Discovery is often just finding a fit, like a jigsaw puzzle [Goodman] |
| 17658 | Users of digital thermometers recognise no temperatures in the gaps [Goodman] |
| 17650 | We lack frames of reference to transform physics, biology and psychology into one another [Goodman] |
| 17655 | Grue and green won't be in the same world, as that would block induction entirely [Goodman] |
| 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] |
| 17649 | If the world is one it has many aspects, and if there are many worlds they will collect into one [Goodman] |