46 ideas
5333 | Philosophy needs wisdom about who we are, as well as how we ought to be [Flanagan] |
5334 | We resist science partly because it can't provide ethical wisdom [Flanagan] |
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] |
10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
5340 | Explanation does not entail prediction [Flanagan] |
6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
5346 | In the 17th century a collisionlike view of causation made mental causation implausible [Flanagan] |
5341 | Only you can have your subjective experiences because only you are hooked up to your nervous system [Flanagan] |
5351 | We only have a sense of our self as continuous, not as exactly the same [Flanagan] |
5353 | The self is an abstraction which magnifies important aspects of autobiography [Flanagan] |
5354 | We are not born with a self; we develop a self through living [Flanagan] |
5349 | For Buddhists a fixed self is a morally dangerous illusion [Flanagan] |
5338 | Normal free will claims control of what I do, but a stronger view claims control of thought and feeling [Flanagan] |
5344 | Free will is held to give us a whole list of desirable capacities for living [Flanagan] |
5332 | People believe they have free will that circumvents natural law, but only an incorporeal mind could do this [Flanagan] |
5345 | We only think of ourselves as having free will because we first thought of God that way [Flanagan] |
5343 | People largely came to believe in dualism because it made human agents free [Flanagan] |
5347 | Behaviourism notoriously has nothing to say about mental causation [Flanagan] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
5339 | Cars and bodies obey principles of causation, without us knowing any 'strict laws' about them [Flanagan] |
5342 | Physicalism doesn't deny that the essence of an experience is more than its neural realiser [Flanagan] |
5335 | Emotions are usually very apt, rather than being non-rational and fickle [Flanagan] |
5348 | Intellectualism admires the 'principled actor', non-intellectualism admires the 'good character' [Flanagan] |
5355 | Cognitivists think morals are discovered by reason [Flanagan] |
5336 | Ethics is the science of the conditions that lead to human flourishing [Flanagan] |
9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |
5350 | The Hindu doctrine of reincarnation only appeared in the eighth century CE [Flanagan] |
5352 | The idea of the soul gets some support from the scientific belief in essential 'natural kinds' [Flanagan] |