56 ideas
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |