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] |
17486 | Supervenience is simply modally robust property co-variance [Hendry] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
17481 | Nuclear charge (plus laws) explains electron structure and spectrum, but not vice versa [Hendry] |
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] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
17478 | Maybe two kinds are the same if there is no change of entropy on isothermal mixing [Hendry] |
17484 | Maybe the nature of water is macroscopic, and not in the microstructure [Hendry] |
17479 | The nature of an element must survive chemical change, so it is the nucleus, not the electrons [Hendry] |
17485 | Maybe water is the smallest part of it that still counts as water (which is H2O molecules) [Hendry] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
17482 | Compounds can differ with the same collection of atoms, so structure matters too [Hendry] |
17483 | Water continuously changes, with new groupings of molecules [Hendry] |
17476 | Elements survive chemical change, and are tracked to explain direction and properties [Hendry] |
17477 | Defining elements by atomic number allowed atoms of an element to have different masses [Hendry] |
17480 | Generally it is nuclear charge (not nuclear mass) which determines behaviour [Hendry] |