45 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] |
17699 | Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel] |
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] |
17611 | We want the essence of continuity, by showing its origin in arithmetic [Dedekind] |
10572 | A cut between rational numbers creates and defines an irrational number [Dedekind] |
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] |
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
18087 | If x changes by less and less, it must approach a limit [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] |
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] |
20289 | Ethics is universalisable - it must involve an impartial and universal view of things [Singer] |
20286 | Following an inner voice for morality is irresponsible in a rational agent [Singer] |
20282 | The sanctity of a human life depends either on being of our species, or on being a person [Singer] |
20278 | 'Marginal utility' says something is more useful if it is in short supply [Singer] |
20281 | Why should I do anything for posterity? What has posterity ever done for me? [Singer] |
20276 | Conflict of rules might be avoided by greater complexity, or by a hierarchy of rules [Singer] |
20290 | Psychopaths may just be bored, because they cannot participate in normal emotional life [Singer] |
20288 | You can't condemn violent revolution without assessing the evils it prevents [Singer] |
21997 | In Marxism the state will be superseded [Singer] |
20287 | If 49% of the population can be wrong, so can 51% [Singer] |
21993 | Materialist history says we are subject to incomprehensible forces [Singer] |
20277 | Equality of interests is a minimal principle, not implying equal treatment [Singer] |
20279 | Equality of opportunity unfairly rewards those lucky enough to have great ability [Singer] |
20285 | If a right entails having the relevant desire, many creatures might have no right to life [Singer] |
20284 | Why should a potential person have the rights of an actual person? [Singer] |
20283 | Killing a chimp is worse than killing a human too defective to be a person [Singer] |