28 ideas
3745 | Must sentences make statements to qualify for truth? [O'Connor] |
3742 | Beliefs must match facts, but also words must match beliefs [O'Connor] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
3744 | The semantic theory requires sentences as truth-bearers, not propositions [O'Connor] |
3749 | What does 'true in English' mean? [O'Connor] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
3746 | Logic seems to work for unasserted sentences [O'Connor] |
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] |
3747 | Events are fast changes which are of interest to us [O'Connor] |
3743 | We can't contemplate our beliefs until we have expressed them [O'Connor] |
3748 | Without language our beliefs are particular and present [O'Connor] |
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] |