38 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] |
| 23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
| 23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
| 7631 | Sensation is not committed to any external object, but perception is [Reid] |
| 23637 | Primary qualities are the object of mathematics [Reid] |
| 23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
| 23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
| 6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
| 23641 | People dislike believing without evidence, and try to avoid it [Reid] |
| 23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 23640 | Only mature minds can distinguish the qualities of a body [Reid] |
| 21075 | The state of nature always involves the threat of war [Kant] |
| 20569 | Kant made the social contract international and cosmopolitan [Kant, by Oksala] |
| 21079 | The a priori general will of a people shows what is right [Kant] |
| 21077 | Each nation should, from self-interest, join an international security constitution [Kant] |
| 21078 | A constitution must always be improved when necessary [Kant] |
| 21076 | Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant] |
| 20570 | There is now a growing universal community, and violations of rights are felt everywhere [Kant] |
| 20571 | There are political and inter-national rights, but also universal cosmopolitan rights [Kant] |
| 21073 | Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant] |
| 21074 | Some trust in the enemy is needed during wartime, or peace would be impossible [Kant] |