56 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] |
| 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] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 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] |
| 22849 | Rawls's theory cannot justify liberalism, since it presupposes free and equal participants [Charvet] |
| 22848 | People with strong prior beliefs would have nothing to do with a veil of ignorance [Charvet] |
| 22838 | Societies need shared values, so conservatism is right if rational discussion of values is impossible [Charvet] |
| 22846 | The universalism of utilitarianism implies a world state [Charvet] |
| 22835 | Liberals value freedom and equality, but the society itself must decide on its values [Charvet] |
| 22831 | Modern libertarian societies still provide education and some housing [Charvet] |
| 22839 | Liberalism needs people to either have equal autonomy, or everyone to have enough autonomy [Charvet] |
| 22847 | Kant places a higher value on the universal rational will than on the people asserting it [Charvet] |
| 22821 | Liberalism asserts maximum freedom, but that must be equal for all participants [Charvet] |
| 22834 | Egalitarian liberals prefer equality (either of input or outcome) to liberty [Charvet] |
| 22822 | Liberals promote community and well-being - because all good societies need them [Charvet] |
| 22841 | Identity multiculturalism emerges from communitarianism, preferring community to humanity [Charvet] |
| 22842 | For communitarians it seems that you must accept the culture you are born into [Charvet] |
| 22830 | Give by ability and receive by need, rather than a free labour market [Charvet] |
| 22829 | Allowing defamatory speech is against society's interests, by blurring which people are trustworthy [Charvet] |
| 22836 | 'Freedom from' is an empty idea, if the freedom is not from impediments to my desires [Charvet] |
| 22837 | Positive freedom can lead to coercion, if you are forced to do what you chose to do [Charvet] |
| 22844 | First level autonomy is application of personal values; second level is criticising them [Charvet] |
| 22840 | Mere equality, as in two trees being the same height, has no value at all [Charvet] |
| 22843 | Inequalities are worse if they seem to be your fault, rather than social facts [Charvet] |
| 22845 | Money allows unlimited inequalities, and we obviously all agree to money [Charvet] |
| 22828 | The rule of law mainly benefits those with property and liberties [Charvet] |
| 22825 | The 1689 Bill of Rights denied the monarch new courts, or the right to sit as judge [Charvet] |
| 22823 | The rule of law is mainly to restrict governments [Charvet] |
| 22827 | Justice superior to the rule of law is claimed on behalf of the workers, or the will of the nation [Charvet] |
| 22826 | From 1701 only parliament could remove judges, whose decisions could not be discussed [Charvet] |
| 22832 | Welfare is needed if citizens are to accept the obligations of a liberal state [Charvet] |