29 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 7096 | We may still admire a person's character even if the traits are involuntary [Statman] |
| 7098 | There is a new sort of moral scepticism, about the possibility of moral theories [Statman] |
| 7099 | With a broad concept of flourishing, it might be possible without the virtues [Statman] |
| 7100 | Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman] |
| 7102 | Promises create moral duties that have nothing to do with character [Statman] |
| 7095 | Moral education is better by concrete example than abstract principle [Statman] |
| 7094 | Friends express friendship even when no utility is involved [Statman] |
| 7093 | Behaviour may be disgusting or inhumane, but violate no duty [Statman] |
| 7104 | The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman] |
| 7103 | Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman] |
| 5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |