41 ideas
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
6627 | Radical pragmatists abandon the notion of truth [Stich, by Lowe] |
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] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
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] |
15200 | How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin] |
14761 | Change is not just having two different qualities at different points in some series [McTaggart] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
22628 | Substance has to exist, with no intrinsic qualities or relations [McTaggart] |
4765 | Stich accepts eliminativism (labelled 'pragmatism') about rationality and normativity [Stich, by Engel] |
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] |
2608 | For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer] |
22936 | A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin] |
4231 | Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe] |
8591 | There could be no time if nothing changed [McTaggart] |
22935 | The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin] |
7802 | A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle] |
4230 | A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe] |
15199 | The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin] |