57 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] |
| 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] |
| 9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
| 579 | Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle] |
| 578 | Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle] |
| 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] |
| 20489 | Human beings can never really flourish in a long-term state of nature [Wolff,J] |
| 20483 | Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J] |
| 20532 | Should love be the first virtue of a society, as it is of the family? [Wolff,J] |
| 20490 | For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J] |
| 20493 | Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J] |
| 20494 | Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J] |
| 20500 | We can see the 'general will' as what is in the general interest [Wolff,J] |
| 20497 | How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J] |
| 20506 | 'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J] |
| 20530 | Political choice can be by utility, or maximin, or maximax [Wolff,J] |
| 20487 | A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J] |
| 20488 | It is hard for anarchists to deny that we need experts [Wolff,J] |
| 20529 | Utilitarianism probably implies a free market plus welfare [Wolff,J] |
| 20510 | A system of democracy which includes both freedom and equality is almost impossible [Wolff,J] |
| 20511 | Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J] |
| 20502 | Democracy has been seen as consistent with many types of inequality [Wolff,J] |
| 20496 | A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J] |
| 20498 | We should decide whether voting is for self-interests, or for the common good [Wolff,J] |
| 20499 | Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J] |
| 20509 | Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J] |
| 20524 | Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J] |
| 20518 | Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J] |
| 20531 | Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J] |
| 20526 | Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J] |
| 20528 | Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J] |
| 20503 | Political equality is not much use without social equality [Wolff,J] |
| 20513 | If natural rights are axiomatic, there is then no way we can defend them [Wolff,J] |
| 20512 | Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J] |
| 20514 | If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J] |
| 20522 | Utilitarians might say property ownership encourages the best use of the land [Wolff,J] |
| 20534 | Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J] |
| 20492 | Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J] |