31 ideas
| 11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
| 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] |
| 11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
| 11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
| 11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
| 11096 | Discourse generally departmentalizes itself to some degree [Quine] |
| 11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
| 11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
| 11097 | Red is the largest red thing in the universe [Quine] |
| 17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
| 11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
| 7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 11104 | Concepts are language [Quine] |
| 11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |