39 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] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
17000 | We might fix identities for small particulars, but it is utopian to hope for such things [Kripke] |
11868 | A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke] |
17044 | A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke] |
16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
17058 | What many people consider merely physically necessary I consider completely necessary [Kripke] |
4970 | What is often held to be mere physical necessity is actually metaphysical necessity [Kripke] |
17059 | Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke] |
4950 | Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke] |
17003 | Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke] |
9221 | The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider] |
17052 | The a priori analytic truths involving fixing of reference are contingent [Kripke] |
4969 | I regard the mind-body problem as wide open, and extremely confusing [Kripke] |
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] |
4956 | A description may fix a reference even when it is not true of its object [Kripke] |
17032 | Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |