37 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] |
| 14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
| 14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
| 12031 | Essences are taken to be qualitative properties [Adams,RM] |
| 12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
| 14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
| 16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
| 14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
| 11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
| 16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
| 11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
| 14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
| 5662 | Maybe induction could never prove the existence of something unobservable [Ayer] |
| 5664 | Consciousness must involve a subject, and only bodies identify subjects [Ayer] |
| 5668 | People own conscious states because they are causally related to the identifying body [Ayer] |
| 5661 | We identify experiences by their owners, so we can't define owners by their experiences [Ayer] |
| 5665 | Memory is the best proposal as what unites bundles of experiences [Ayer] |
| 5666 | Not all exerience can be remembered, as this would produce an infinite regress [Ayer] |
| 5669 | Personal identity can't just be relations of experiences, because the body is needed to identify them [Ayer] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |