46 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] |
3005 | 'Jocasta' needs to be distinguished from 'Oedipus's mother' because they are connected by different properties [Fodor] |
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] |
7014 | A particle and a coin heads-or-tails pick out to perfectly well-defined predicates and properties [Fodor] |
3008 | Evolution suggests that innate knowledge of human psychology would be beneficial [Fodor] |
2990 | Contrary to commonsense, most of what is in the mind seems to be unlearned [Fodor] |
3009 | Sticklebacks have an innate idea that red things are rivals [Fodor] |
2994 | In CRTT thought may be represented, content must be [Fodor] |
15494 | We can't use propositions to explain intentional attitudes, because they would need explaining [Fodor] |
7326 | Intentionality doesn't go deep enough to appear on the physicists' ultimate list of things [Fodor] |
3001 | Behaviourism has no theory of mental causation [Fodor] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
2993 | Any piece of software can always be hard-wired [Fodor] |
3011 | Causal powers must be a crucial feature of mental states [Fodor] |
5498 | Mind is a set of hierarchical 'homunculi', which are made up in turn from subcomponents [Fodor, by Lycan] |
2995 | Supervenience gives good support for mental causation [Fodor] |
2991 | Hume's associationism offers no explanation at all of rational thought [Fodor] |
3002 | If mind is just physical, how can it follow the rules required for intelligent thought? [Fodor] |
2992 | We may be able to explain rationality mechanically [Fodor] |
2988 | Folk psychology is the only explanation of behaviour we have [Fodor] |
3010 | Belief and desire are structured states, which need mentalese [Fodor] |
2999 | Obsession with narrow content leads to various sorts of hopeless anti-realism [Fodor] |
3012 | Do identical thoughts have identical causal roles? [Fodor] |
2998 | Grice thinks meaning is inherited from the propositional attitudes which sentences express [Fodor] |
3006 | Whatever in the mind delivers falsehood is parasitic on what delivers truth [Fodor] |
3007 | Many different verification procedures can reach 'star', but it only has one semantic value [Fodor] |
3004 | The meaning of a sentence derives from its use in expressing an attitude [Fodor] |
3000 | Meaning holism is a crazy doctrine [Fodor] |
3003 | Very different mental states can share their contents, so content doesn't seem to be constructed from functional role [Fodor] |
2996 | Mental states may have the same content but different extensions [Fodor] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |