73 ideas
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| 13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
| 13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
| 9912 | There are no such things as numbers [Benacerraf] |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| 13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| 13415 | An adequate account of a number must relate it to its series [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| 17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
| 9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 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] |
| 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] |
| 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] |
| 22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
| 5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |