35 ideas
| 3972 | Truth and objectivity depend on a community of speakers to interpret what they mean [Davidson] |
| 3969 | There are no ultimate standards of rationality, since we only assess others by our own standard [Davidson] |
| 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] |
| 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] |
| 3960 | There are no such things as minds, but people have mental properties [Davidson] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 3964 | If the mind is an anomaly, this makes reduction of the mental to the physical impossible [Davidson] |
| 3961 | Obviously all mental events are causally related to physical events [Davidson] |
| 3963 | There are no strict psychophysical laws connecting mental and physical events [Davidson] |
| 3965 | Mental entities do not add to the physical furniture of the world [Davidson] |
| 3966 | The correct conclusion is ontological monism combined with conceptual dualism [Davidson] |
| 3967 | Absence of all rationality would be absence of thought [Davidson] |
| 3974 | Our meanings are partly fixed by events of which we may be ignorant [Davidson] |
| 3968 | Propositions explain nothing without an explanation of how sentences manage to name them [Davidson] |
| 3970 | Thought is only fully developed if we communicate with others [Davidson] |
| 3971 | There is simply no alternative to the 'principle of charity' in interpreting what others do [Davidson] |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| 3973 | Without a teacher, the concept of 'getting things right or wrong' is meaningless [Davidson] |
| 3962 | Cause and effect relations between events must follow strict laws [Davidson] |