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] |
| 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] |
| 11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
| 11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
| 11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
| 11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
| 11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
| 11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
| 11886 | There are problems both with individual essences and without them [Mackie,P] |
| 11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
| 11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
| 11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
| 11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
| 11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
| 11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
| 11892 | Things may only be counterparts under some particular relation [Mackie,P] |
| 11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
| 11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
| 21513 | We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing] |
| 21497 | If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing] |
| 11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |