33 ideas
9376 | A sentence may simultaneously define a term, and also assert a fact [Boghossian] |
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] |
9375 | Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian] |
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] |
9369 | 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian] |
9367 | The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian] |
9373 | That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian] |
9380 | We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian] |
9384 | We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian] |
9374 | If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
9378 | If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian] |
9377 | 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian] |
9372 | Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian] |
17721 | There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins] |
9368 | Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |