44 ideas
| 7500 | Early Greeks cared about city and companions; later Greeks concentrated on the self [Foucault] |
| 10308 | Questions about objects are questions about certain non-vacuous singular terms [Hale] |
| 10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
| 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] |
| 10316 | We should decide whether singular terms are genuine by their usage [Hale] |
| 10312 | Often the same singular term does not ensure reliable inference [Hale] |
| 10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
| 10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
| 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] |
| 10512 | The abstract/concrete distinction is based on what is perceivable, causal and located [Hale] |
| 10517 | Colours and points seem to be both concrete and abstract [Hale] |
| 10519 | The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale] |
| 10520 | Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale] |
| 10524 | There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale] |
| 10521 | If F can't have location, there is no problem of things having F in different locations [Hale] |
| 10511 | It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns [Hale] |
| 10318 | Realists take universals to be the referrents of both adjectives and of nouns [Hale] |
| 10310 | Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated [Hale] |
| 10518 | Shapes and directions are of something, but games and musical compositions are not [Hale] |
| 10513 | Many abstract objects, such as chess, seem non-spatial, but are not atemporal [Hale] |
| 10514 | If the mental is non-spatial but temporal, then it must be classified as abstract [Hale] |
| 10523 | Being abstract is based on a relation between things which are spatially separated [Hale] |
| 10307 | The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale] |
| 10315 | We can't believe in a 'whereabouts' because we ask 'what kind of object is it?' [Hale] |
| 10522 | The relations featured in criteria of identity are always equivalence relations [Hale] |
| 10321 | We sometimes apply identity without having a real criterion [Hale] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 7501 | Why couldn't a person's life become a work of art? [Foucault] |
| 7498 | Greeks and early Christians were much more concerned about food than about sex [Foucault] |