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] |
| 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] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 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] |
| 3509 | Externalism may be the key idea in philosophical naturalism [Papineau] |
| 19489 | For me, fictions are internally true, without a significant internal or external truth-value [Yablo] |
| 19490 | Make-believe can help us to reason about facts and scientific procedures [Yablo] |
| 19491 | 'The clouds are angry' can only mean '...if one were attributing emotions to clouds' [Yablo] |
| 3513 | How does a dualist mind represent, exist outside space, and be transparent to itself? [Papineau] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 3514 | Functionalism needs causation and intentionality to explain actions [Papineau] |
| 3510 | Epiphenomenalism is supervenience without physicalism [Papineau] |
| 3511 | Supervenience requires all mental events to have physical effects [Papineau] |
| 3515 | Knowing what it is like to be something only involves being (physically) that thing [Papineau] |
| 3512 | If a mental state is multiply realisable, why does it lead to similar behaviour? [Papineau] |
| 3516 | The Private Language argument only means people may misjudge their experiences [Papineau] |