28 ideas
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
1564 | True and false statements can use exactly the same words [Anon (Diss)] |
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] |
1559 | Thracians think tattooing adds to a girl's beauty, but elsewhere it is a punishment [Anon (Diss)] |
1561 | Anything can be acceptable in some circumstances and unacceptable in others [Anon (Diss)] |
1560 | Lydians prostitute their daughters to raise a dowery, but no Greek would marry such a girl [Anon (Diss)] |
17060 | Best Explanation is the core notion of epistemology [Harman, by Smart] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
1567 | How could someone who knows everything fail to act correctly? [Anon (Diss)] |
1563 | Every apparent crime can be right in certain circumstances [Anon (Diss), by PG] |
1562 | It is right to lie to someone, to get them to take medicine they are reluctant to take [Anon (Diss)] |
1566 | The first priority in elections is to vote for people who support democracy [Anon (Diss)] |
1565 | We learn language, and we don't know who teaches us it [Anon (Diss)] |