31 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] |
| 16435 | Plantinga proposes necessary existent essences as surrogates for the nonexistent things [Plantinga, by Stalnaker] |
| 14655 | The 'identity criteria' of a name are a group of essential and established facts [Plantinga] |
| 14658 | 'Being Socrates' and 'being identical with Socrates' characterise Socrates, so they are among his properties [Plantinga] |
| 14656 | Does Socrates have essential properties, plus a unique essence (or 'haecceity') which entails them? [Plantinga] |
| 14654 | Properties are 'trivially essential' if they are instantiated by every object in every possible world [Plantinga] |
| 14653 | X is essentially P if it is P in every world, or in every X-world, or in the actual world (and not ¬P elsewhere) [Plantinga] |
| 14660 | If a property is ever essential, can it only ever be an essential property? [Plantinga] |
| 14661 | Essences are instantiated, and are what entails a thing's properties and lack of properties [Plantinga] |
| 14657 | Does 'being identical with Socrates' name a property? I can think of no objections to it [Plantinga] |
| 14652 | 'De re' modality is as clear as 'de dicto' modality, because they are logically equivalent [Plantinga] |
| 14659 | We can imagine being beetles or alligators, so it is possible we might have such bodies [Plantinga] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |