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] |
| 10653 | Maybe set theory need not be well-founded [Varzi] |
| 10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
| 10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
| 10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
| 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] |
| 10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |
| 10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
| 10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
| 10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
| 10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
| 10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| 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] |