62 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] |
| 5937 | The goodness of opinions depends on their grounds, and corresponding degrees of conviction [Ross] |
| 5936 | Knowledge is superior to opinion because it is certain [Ross] |
| 5927 | I prefer the causal theory to sense data, because sensations are events, not apprehensions [Ross] |
| 5940 | Two goods may be comparable, although they are not commensurable [Ross] |
| 5924 | Identical objects must have identical value [Ross] |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| 5933 | Aesthetic enjoyment combines pleasure with insight [Ross] |
| 5928 | Beauty is neither objective nor subjective, but a power of producing certain mental events [Ross] |
| 5911 | Moral duties are as fundamental to the universe as the axioms of mathematics [Ross] |
| 5926 | The beauty of a patch of colour might be the most important fact about it [Ross] |
| 7259 | Ross said moral principles are self-evident from the facts, but not from pure thought [Ross, by Dancy,J] |
| 5913 | The moral convictions of thoughtful educated people are the raw data of ethics [Ross] |
| 5920 | Value is held to be either a quality, or a relation (usually between a thing and a mind) [Ross] |
| 5923 | The arguments for value being an objective or a relation fail, so it appears to be a quality [Ross] |
| 5918 | The thing is intrinsically good if it would be good when nothing else existed [Ross] |
| 5930 | All things being equal, we all prefer the virtuous to be happy, not the vicious [Ross] |
| 5922 | An instrumentally good thing might stay the same, but change its value because of circumstances [Ross] |
| 5921 | We can ask of pleasure or beauty whether they are valuable, but not of goodness [Ross] |
| 5932 | The four goods are: virtue, pleasure, just allocation of pleasure, and knowledge [Ross] |
| 5910 | The three intrinsic goods are virtue, knowledge and pleasure [Ross] |
| 5898 | 'Right' and 'good' differ in meaning, as in a 'right action' and a 'good man' [Ross] |
| 5899 | If there are two equally good acts, they may both be right, but neither a duty [Ross] |
| 5904 | In the past 'right' just meant what is conventionally accepted [Ross] |
| 5919 | Goodness is a wider concept than just correct ethical conduct [Ross] |
| 5941 | Motives decide whether an action is good, and what is done decides whether it was right [Ross] |
| 5938 | Virtue is superior to pleasure, as pleasure is never a duty, but goodness is [Ross] |
| 5931 | All other things being equal, a universe with more understanding is better [Ross] |
| 5939 | Morality is not entirely social; a good moral character should love truth [Ross] |
| 5905 | We clearly value good character or understanding, as well as pleasure [Ross] |
| 5929 | No one thinks it doesn't matter whether pleasure is virtuously or viciously acquired [Ross] |
| 5906 | Promise-keeping is bound by the past, and is not concerned with consequences [Ross] |
| 18622 | Promises create a new duty to a particular person; they aren't just a strategy to achieve well-being [Ross] |
| 5908 | Prima facie duties rest self-evidently on particular circumstance [Ross] |
| 5917 | People lose their rights if they do not respect the rights of others [Ross] |
| 5900 | We should do our duty, but not from a sense of duty [Ross] |
| 5942 | We like people who act from love, but admire more the people who act from duty [Ross] |
| 5909 | Be faithful, grateful, just, beneficent, non-malevolent, and improve yourself [Ross, by PG] |
| 5914 | An act may be described in innumerable ways [Ross] |
| 5912 | We should use money to pay debts before giving to charity [Ross] |
| 20751 | As a young girl assumes her status as feminine, she acts in a more fragile immobile way [Young,IM] |
| 5916 | Rights were originally legal, and broadened to include other things [Ross] |
| 5915 | Rights can be justly claimed, so animals have no rights, as they cannot claim any [Ross] |