44 ideas
16943 | Philosophy is continuous with science, and has no external vantage point [Quine] |
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] |
16949 | Klein summarised geometry as grouped together by transformations [Quine] |
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] |
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] |
16939 | Mass terms just concern spread, but other terms involve both spread and individuation [Quine] |
16948 | Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine] |
16945 | We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
16944 | Science is common sense, with a sophisticated method [Quine] |
16941 | Induction relies on similar effects following from each cause [Quine] |
16940 | Induction is just more of the same: animal expectations [Quine] |
16933 | Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine] |
16934 | General terms depend on similarities among things [Quine] |
16938 | To learn yellow by observation, must we be told to look at the colour? [Quine] |
8486 | Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine] |
16947 | Similarity is just interchangeability in the cosmic machine [Quine] |
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] |
16932 | Projectible predicates can be universalised about the kind to which they refer [Quine] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
7375 | Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett] |
16935 | If similarity has no degrees, kinds cannot be contained within one another [Quine] |
16936 | Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine] |
16937 | You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine] |
16942 | It is hard to see how regularities could be explained [Quine] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |