76 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] |
| 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] |
| 2392 | Properties supervene if you can't have one without the other [Chalmers] |
| 2393 | Logical supervenience is when one set of properties must be accompanied by another set [Chalmers] |
| 2394 | Natural supervenience is when one set of properties is always accompanied by another set [Chalmers] |
| 2398 | Reduction requires logical supervenience [Chalmers] |
| 16048 | Physicalism says in any two physically indiscernible worlds the positive facts are the same [Chalmers, by Bennett,K] |
| 2401 | All facts are either physical, experiential, laws of nature, second-order final facts, or indexical facts about me [Chalmers] |
| 16424 | Strong metaphysical necessity allows fewer possible worlds than logical necessity [Chalmers] |
| 16425 | Metaphysical necessity is a bizarre, brute and inexplicable constraint on possibilities [Chalmers] |
| 16426 | How can we know the metaphysical impossibilities; the a posteriori only concerns this world [Chalmers] |
| 13956 | Kripke is often taken to be challenging a priori insights into necessity [Chalmers] |
| 13963 | Maybe logical possibility does imply conceivability - by an ideal mind [Chalmers] |
| 2407 | One can wrongly imagine two things being non-identical even though they are the same (morning/evening star) [Chalmers] |
| 2390 | We attribute beliefs to people in order to explain their behaviour [Chalmers] |
| 2397 | 'Perception' means either an action or a mental state [Chalmers] |
| 2422 | The structure of the retina has already simplified the colour information which hits it [Chalmers] |
| 2396 | Reductive explanation is not the be-all and the end-all of explanation [Chalmers] |
| 2426 | Why are minds homogeneous and brains fine-grained? [Chalmers] |
| 2391 | Can we be aware but not conscious? [Chalmers] |
| 2412 | Can we explain behaviour without consciousness? [Chalmers] |
| 2386 | Hard Problem: why brains experience things [Chalmers] |
| 2416 | What turns awareness into consciousness? [Chalmers] |
| 2423 | Going down the scale, where would consciousness vanish? [Chalmers] |
| 2403 | Nothing in physics even suggests consciousness [Chalmers] |
| 2400 | Is intentionality just causal connections? [Chalmers] |
| 2389 | Sometimes we don't notice our pains [Chalmers] |
| 2419 | Why should qualia fade during silicon replacement? [Chalmers] |
| 2402 | It seems possible to invert qualia [Chalmers] |
| 2415 | In blindsight both qualia and intentionality are missing [Chalmers] |
| 2414 | When distracted we can totally misjudge our own experiences [Chalmers] |
| 2409 | Maybe dualist interaction is possible at the quantum level? [Chalmers] |
| 2411 | Supervenience makes interaction laws possible [Chalmers] |
| 2424 | It is odd if experience is a very recent development [Chalmers] |
| 2413 | If I can have a zombie twin, my own behaviour doesn't need consciousness [Chalmers] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 2417 | Does consciousness arise from fine-grained non-reductive functional organisation? [Chalmers] |
| 2428 | Maybe the whole Chinese Room understands Chinese, though the person doesn't [Chalmers] |
| 2418 | The Chinese Mind doesn't seem conscious, but then nor do brains from outside [Chalmers] |
| 2406 | H2O causes liquidity, but no one is a dualist about that [Chalmers] |
| 2405 | Perhaps consciousness is physically based, but not logically required by that base [Chalmers] |
| 2395 | Zombies imply natural but not logical supervenience [Chalmers] |
| 9318 | Phenomenal consciousness is fundamental, with no possible nonphenomenal explanation [Chalmers, by Kriegel/Williford] |
| 2404 | Nothing external shows whether a mouse is conscious [Chalmers] |
| 2429 | Temperature (etc.) is agreed to be reducible, but it is multiply realisable [Chalmers] |
| 12608 | Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke] |
| 18403 | Indexicals may not be objective, but they are a fact about the world as I see it [Chalmers] |
| 12605 | A sense is individuated by the conditions for reference [Peacocke] |
| 12607 | Fregean concepts have their essence fixed by reference-conditions [Peacocke] |
| 12609 | Concepts have distinctive reasons and norms [Peacocke] |
| 12604 | Any explanation of a concept must involve reference and truth [Peacocke] |
| 12610 | Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke] |
| 14708 | Rationalist 2D semantics posits necessary relations between meaning, apriority, and possibility [Chalmers, by Schroeter] |
| 13958 | The 'primary intension' is non-empirical, and fixes extensions based on the actual-world reference [Chalmers] |
| 2399 | Meaning has split into primary ("watery stuff"), and secondary counterfactual meaning ("H2O") [Chalmers] |
| 13959 | The 'secondary intension' is determined by rigidifying (as H2O) the 'water' picked out in the actual world [Chalmers] |
| 13957 | Primary and secondary intensions are the a priori (actual) and a posteriori (counterfactual) aspects of meaning [Chalmers] |
| 13961 | We have 'primary' truth-conditions for the actual world, and derived 'secondary' ones for counterfactual worlds [Chalmers] |
| 13962 | Two-dimensional semantics gives a 'primary' and 'secondary' proposition for each statement [Chalmers] |
| 13960 | In two-dimensional semantics we have two aspects to truth in virtue of meaning [Chalmers] |
| 16427 | Presumably God can do anything which is logically possible [Chalmers] |