40 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] |
23708 | Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG] |
23709 | Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye] |
23707 | Powers are properties which necessitate dispositions [Friend/Kimpton-Nye] |
23714 | Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye] |
23711 | A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye] |
23712 | Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye] |
23698 | Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye] |
23699 | 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye] |
23700 | A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye] |
23701 | A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye] |
23702 | A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye] |
23703 | Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye] |
23704 | We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
23710 | Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye] |
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] |
23706 | Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |