63 ideas
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| 17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 4669 | Persons are conscious, they relate, they think, they feel, and they are self-aware [Glover] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 4656 | A problem arises in any moral system that allows more than one absolute right [Glover] |
| 4657 | Double Effect: no bad acts with good consequences, but possibly good acts despite bad consequences [Glover] |
| 4658 | Acts and Omissions: bad consequences are morally better if they result from an omission rather than an act [Glover] |
| 4659 | It doesn't seem worse to switch off a life-support machine than to forget to switch it on [Glover] |
| 4660 | Harmful omissions are unavoidable, while most harmful acts can be avoided [Glover] |
| 4661 | What matters is not intrinsic value of life or rights, but worthwhile and desired life, and avoidance of pain [Glover] |
| 4648 | 'Death' is best seen as irreversible loss of consciousness, since this is why we care about brain function [Glover] |
| 3785 | You can't separate acts from the people performing them [Glover] |
| 3786 | Aggression in defence may be beneficial but morally corrupting [Glover] |
| 4650 | The quality of a life is not altogether independent of its length [Glover] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 3784 | Duty prohibits some acts, whatever their consequences [Glover] |
| 3782 | Satisfaction of desires is not at all the same as achieving happiness [Glover, by PG] |
| 3787 | Rule-utilitarianism is either act-utilitarianism, or not really utilitarian [Glover] |
| 3783 | How can utilitarianism decide the ideal population size? [Glover] |
| 4675 | The sanctity of life doctrine implies a serious increase of abnormality among the population [Glover] |
| 4654 | Autonomy favours present opinions over future ones, and says nothing about the interests of potential people [Glover] |
| 4655 | If a whole community did not mind death, respect for autonomy suggests that you could kill them all [Glover] |
| 4680 | Autonomy seems to acquire greater weight when the decision is more important to a person [Glover] |
| 4670 | Being alive is not intrinsically good, and there is no 'right to life' [Glover] |
| 4668 | You can't have a right to something you can't desire, so a foetus has no 'right' to life [Glover] |
| 4649 | If someone's life is 'worth living', that gives one direct reason not to kill him [Glover] |
| 4651 | Utilitarians object to killing directly (pain, and lost happiness), and to side-effects (loss to others, and precedents) [Glover] |
| 4671 | What is wrong with killing someone, if another equally worthwhile life is substituted? [Glover] |
| 4676 | The 'no trade-off' position: killing is only justified if it prevents other deaths [Glover] |
| 4685 | Societies spend a lot to save known persons, but very little to reduce fatal accidents [Glover] |
| 4683 | Involuntary euthanasia is wrong because it violates autonomy, and it has appalling side-effects [Glover] |
| 4682 | Euthanasia is voluntary (patient's wish), or involuntary (ignore wish), or non-voluntary (no wish possible) [Glover] |
| 4684 | Maybe extreme treatment is not saving life, but prolonging the act of dying [Glover] |
| 4681 | The Nazi mass murders seem to have originated in their euthanasia programme [Glover] |
| 4667 | How would we judge abortion if mothers had transparent wombs? [Glover] |
| 4665 | Conception isn't the fixed boundary for a person's beginning, because twins are possible within two weeks [Glover] |
| 4652 | If killing is wrong because it destroys future happiness, not conceiving a happy child is also wrong [Glover] |
| 4662 | Defenders of abortion focus on early pregnancy, while opponents focus on later stages [Glover] |
| 4663 | If abortion is wrong, it is because a foetus is a human being or a person (or potentially so) [Glover] |
| 4664 | If abortion is wrong because of the 'potential' person, that makes contraception wrong too [Glover] |
| 4673 | Abortion differs morally from deliberate non-conception only in its side-effects [Glover] |
| 4666 | If viability is a test or boundary at the beginning of life, it should also be so for frail old people [Glover] |
| 4672 | Apart from side effects, it seems best to replace an inadequate foetus with one which has a better chance [Glover] |
| 4674 | It is always right for a qualified person to perform an abortion when requested by the mother [Glover] |
| 4679 | One test for a worthwhile life is to assess the amount of life for which you would rather be unconscious [Glover] |