35 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)] |
| 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)] |
| 5078 | Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R] |
| 5067 | Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R] |
| 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)] |
| 5079 | Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R] |
| 5068 | 'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R] |
| 5076 | To Greeks it seemed obvious that the virtue of anything is the perfection of its function [Taylor,R] |
| 5077 | The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R] |
| 5066 | If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R] |
| 5065 | The ethics of duty requires a religious framework [Taylor,R] |
| 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)] |