36 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] |
| 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] |
| 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] |
| 12312 | The real essence of a thing is its powers, or 'dispositional properties' [Copi] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 10937 | Essential properties are the 'deepest' ones which explain the others [Copi, by Rami] |
| 12308 | In modern science, nominal essence is intended to be real essence [Copi] |
| 12303 | Within the four types of change, essential attributes are those whose loss means destruction [Copi] |
| 17488 | Empiricist theories are sets of laws, which give explanations and reductions [Glennan] |
| 17493 | Modern mechanism need parts with spatial, temporal and function facts, and diagrams [Glennan] |
| 17487 | Mechanistic philosophy of science is an alternative to the empiricist law-based tradition [Glennan] |
| 17489 | Mechanisms are either systems of parts or sequences of activities [Glennan] |
| 17490 | 17th century mechanists explained everything by the kinetic physical fundamentals [Glennan] |
| 17491 | Unlike the lawlike approach, mechanistic explanation can allow for exceptions [Glennan] |
| 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] |
| 17494 | Since causal events are related by mechanisms, causation can be analysed in that way [Glennan] |
| 12307 | Modern science seeks essences, and is getting closer to them [Copi] |
| 12310 | Real essences are scientifically knowable, but so are non-essential properties [Copi] |