50 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] |
| 6548 | Physicalism requires the naturalisation or rejection of set theory [Lycan] |
| 22246 | A train of reasoning must be treated as all happening simultaneously [Recanati] |
| 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] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 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] |
| 6532 | Types cannot be reduced, but levels of reduction are varied groupings of the same tokens [Lycan] |
| 6531 | Institutions are not reducible as types, but they are as tokens [Lycan] |
| 6534 | One location may contain molecules, a metal strip, a key, an opener of doors, and a human tragedy [Lycan] |
| 6529 | I see the 'role'/'occupant' distinction as fundamental to metaphysics [Lycan] |
| 6549 | I think greenness is a complex microphysical property of green objects [Lycan] |
| 6543 | Intentionality comes in degrees [Lycan] |
| 6537 | Teleological views allow for false intentional content, unlike causal and nomological theories [Lycan] |
| 6546 | Pain is composed of urges, desires, impulses etc, at different levels of abstraction [Lycan] |
| 6547 | The right 'level' for qualia is uncertain, though top (behaviourism) and bottom (particles) are false [Lycan] |
| 6527 | If energy in the brain disappears into thin air, this breaches physical conservation laws [Lycan] |
| 6528 | In lower animals, psychology is continuous with chemistry, and humans are continuous with animals [Lycan] |
| 6554 | Two behaviourists meet. The first says,"You're fine; how am I?" [Lycan] |
| 6545 | If functionalism focuses on folk psychology, it ignores lower levels of function [Lycan] |
| 6541 | Functionalism must not be too abstract to allow inverted spectrum, or so structural that it becomes chauvinistic [Lycan] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 6539 | The distinction between software and hardware is not clear in computing [Lycan] |
| 6535 | Teleological characterisations shade off smoothly into brutely physical ones [Lycan] |
| 6533 | Mental types are a subclass of teleological types at a high level of functional abstraction [Lycan] |
| 6544 | Identity theory is functionalism, but located at the lowest level of abstraction [Lycan] |
| 6536 | Teleological functionalism helps us to understand psycho-biological laws [Lycan] |
| 6530 | We reduce the mind through homuncular groups, described abstractly by purpose [Lycan] |
| 6542 | A Martian may exhibit human-like behaviour while having very different sensations [Lycan] |
| 22247 | Indexicality is not just a feature of language; examples show it also occurs in thought [Recanati] |
| 22248 | How can we communicate indexical thoughts to people not in the right context? [Recanati] |
| 22242 | Mental files are concepts, which are either collections or (better) containers [Recanati] |
| 22243 | The Frege case of believing a thing is both F and not-F is explained by separate mental files [Recanati] |
| 22245 | A linguistic expression refers to what its associated mental file refers to [Recanati] |
| 22250 | There are speakers' thoughts and hearers' thoughts, but no further thought attached to the utterance [Recanati] |
| 22249 | The Naive view of communication is that hearers acquire exactly the thoughts of the speaker [Recanati] |
| 6538 | We need a notion of teleology that comes in degrees [Lycan] |
| 6551 | 'Physical' means either figuring in physics descriptions, or just located in space-time [Lycan] |