94 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] |
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] |
22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
23283 | Necessity implies possibility, but in experience it matters which comes first [Williams,B] |
4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [Williams,B] |
3238 | 'Dead person' isn't a contradiction, so 'person' is somewhat vague [Williams,B] |
3239 | You can only really love a person as a token, not as a type [Williams,B] |
7946 | The memory criterion has a problem when one thing branches into two things [Williams,B, by Macdonald,C] |
2181 | It is an absurd Kantian idea that at the limit rationality and freedom coincide [Williams,B] |
2176 | There is only a problem of free will if you think the notion of 'voluntary' can be metaphysically deepened [Williams,B] |
24008 | Reference to a person's emotions is often essential to understanding their actions [Williams,B] |
24009 | Moral education must involve learning about various types of feeling towards things [Williams,B] |
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] |
4317 | We judge weakness of will by an assessment after the event is concluded [Williams,B, by Cottingham] |
9284 | Reasons are 'internal' if they give a person a motive to act, but 'external' otherwise [Williams,B] |
2174 | Responsibility involves cause, intention, state of mind, and response after the event [Williams,B] |
22455 | Many ethical theories neglect the power of regretting the ought not acted upon [Williams,B] |
4114 | Philosophers try to produce ethical theories because they falsely assume that ethics can be simple [Williams,B] |
22453 | Moral conflicts have a different feeling and structure from belief conflicts [Williams,B, by Foot] |
22454 | We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot] |
22450 | If moral systems can't judge other moral systems, then moral relativism is true [Williams,B, by Foot] |
2178 | In bad actions, guilt points towards victims, and shame to the agent [Williams,B] |
20168 | Blame usually has no effect if the recipient thinks it unjustified [Williams,B] |
20167 | Blame partly rests on the fiction that blamed agents always know their obligations [Williams,B] |
4128 | Intuitionism has been demolished by critics, and no longer looks interesting [Williams,B] |
4366 | We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse] |
4132 | The category of person is a weak basis for ethics, because it is not fixed but comes in degrees [Williams,B] |
24007 | Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B] |
4134 | The weakness of prescriptivism is shown by "I simply don't like staying at good hotels" [Williams,B] |
4135 | Some ethical ideas, such as 'treachery' and 'promise', seem to express a union of facts and values [Williams,B] |
22410 | Maybe the unthinkable is a moral category, and considering some options is dishonourable or absurd [Williams,B] |
22408 | Consequentialism assumes that situations can be compared [Williams,B] |
22411 | For a consequentialist massacring 7 million must be better than massacring 7 million and one [Williams,B] |
4120 | It is an error of consequentialism to think we just aim at certain states of affairs; we also want to act [Williams,B] |
23282 | If all that matters in morality is motive and intention, that makes moral luck irrelevant [Williams,B] |
4252 | Promise keeping increases reliability, by making deliberation focus on something which would be overlooked [Williams,B] |
4116 | A weakness of contractual theories is the position of a person of superior ability and power [Williams,B] |
2169 | Greek moral progress came when 'virtue' was freed from social status [Williams,B] |
4112 | A crucial feature of moral thought is second-order desire - the desire to have certain desires [Williams,B] |
24010 | An admirable human being should have certain kinds of emotional responses [Williams,B] |
23279 | It is important that a person can change their character, and not just be successive 'selves' [Williams,B] |
23280 | Kantians have an poor account of individuals, and insist on impartiality, because they ignore character [Williams,B] |
3236 | Equality of opportunity without equality of respect would create a very inhuman society [Williams,B] |
4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
4249 | "Ought implies can" is a famous formula in connection with moral obligation [Williams,B] |
2172 | The modern idea of duty is unknown in archaic Greece [Williams,B] |
4121 | Why should I think of myself as both the legislator and the citizen who follows the laws? [Williams,B] |
22409 | We don't have a duty to ensure that others do their duty [Williams,B] |
4122 | If the self becomes completely impartial, it no longer has enough identity to worry about its interests [Williams,B] |
2180 | If reason cannot lead people to good, we must hope they have an internal voice [Williams,B] |
24012 | Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B] |
2179 | If the moral self is seen as characterless, then other people have a very limited role in our moral lives [Williams,B] |
22407 | Utilitarianism cannot make any serious sense of integrity [Williams,B] |
23278 | For utilitarians states of affairs are what have value, not matter who produced them [Williams,B] |
4124 | Utilitarian benevolence involves no particular attachments, and is immune to the inverse square law [Williams,B] |
4245 | Ethical conviction must be to some extent passive, and can't just depend on the will and decisions [Williams,B] |
4246 | Taking responsibility won't cure ethical uncertainty by; we are uncertain what to decide [Williams,B] |
3233 | Equality implies that people are alike in potential as well as in needs [Williams,B] |
3234 | Equality seems to require that each person be acknowledged as having a significant point of view [Williams,B] |
3235 | It is a mark of extreme exploitation that the sufferers do not realise their plight [Williams,B] |
4247 | It is a mark of our having ethical values that we aim to reproduce them in our children [Williams,B] |
4131 | Most women see an early miscarriage and a late stillbirth as being very different in character [Williams,B] |
4133 | Speciesism isn't like racism, because the former implies a viewpoint which belongs to no one [Williams,B] |
2175 | There is a problem of evil only if you expect the world to be good [Williams,B] |