59 ideas
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 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] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 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] |