62 ideas
4588 | There is no such thing as 'science'; there are just many different sciences [Heil] |
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] |
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] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
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] |
4616 | A higher level is 'supervenient' if it is determined by lower levels, but has its own natural laws [Heil] |
4603 | Functionalists in Fodor's camp usually say that a genuine property is one that figures in some causal laws [Heil] |
4617 | A stone does not possess the property of being a stone; its other properties make it a stone [Heil] |
4612 | Complex properties are just arrangements of simple properties; they do not "emerge" as separate [Heil] |
4615 | Complex properties are not new properties, they are merely new combinations of properties [Heil] |
4587 | From the property predicates P and Q, we can get 'P or Q', but it doesn't have to designate another property [Heil] |
4611 | The supporters of 'tropes' treat objects as bundles of tropes, when I think objects 'possess' properties [Heil] |
7720 | Two things can only resemble one another in some respect, and that may reintroduce a universal [Lowe] |
7712 | On substances, Leibniz emphasises unity, Spinoza independence, Locke relations to qualities [Lowe] |
4592 | If you can have the boat without its current planks, and the planks with no boat, the planks aren't the boat [Heil] |
4586 | You can't embrace the formal apparatus of possible worlds, but reject the ontology [Heil] |
4591 | Idealism explains appearances by identifying appearances with reality [Heil] |
7710 | Perception is a mode of belief-acquisition, and does not involve sensation [Lowe] |
7711 | Science requires a causal theory - perception of an object must be an experience caused by the object [Lowe] |
4610 | Different generations focus on either the quality of mind, or its scientific standing, or the content of thought [Heil] |
4618 | If minds are realised materially, it looks as if the material laws will pre-empt any causal role for mind [Heil] |
4621 | Whatever exists has qualities, so it is no surprise that states of minds have qualities [Heil] |
4623 | Propositional attitudes are not the only intentional states; there is also mental imagery [Heil] |
4626 | The widespread externalist view says intentionality has content because of causal links of agent to world [Heil] |
4622 | Error must be possible in introspection, because error is possible in all judgements [Heil] |
7714 | Personal identity is a problem across time (diachronic) and at an instant (synchronic) [Lowe] |
4590 | If causation is just regularities in events, the interaction of mind and body is not a special problem [Heil] |
4614 | Disposition is a fundamental feature of reality, since basic particles are capable of endless possible interactions [Heil] |
4595 | No mental state entails inevitable behaviour, because other beliefs or desires may intervene [Heil] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
4599 | Hearts are material, but functionalism says the property of being a heart is not a material property [Heil] |
4624 | If you are a functionalist, there appears to be no room for qualia [Heil] |
4601 | Higher-level sciences cannot be reduced, because their concepts mark boundaries invisible at lower levels [Heil] |
4602 | Higher-level sciences designate real properties of objects, which are not reducible to lower levels [Heil] |
4593 | 'Property dualism' says mind and body are not substances, but distinct families of properties [Heil] |
4597 | Early identity theory talked of mind and brain 'processes', but now the focus is properties [Heil] |
4609 | It seems contradictory to be asked to believe that we can be eliminativist about beliefs [Heil] |
4596 | The appeal of the identity theory is its simplicity, and its solution to the mental causation problem [Heil] |
4598 | Functionalists emphasise that mental processes are not to be reduced to what realises them [Heil] |
4619 | 'Multiple realisability' needs to clearly distinguish low-level realisers from what is realised [Heil] |
4620 | Multiple realisability is not a relation among properties, but an application of predicates to resembling things [Heil] |
4594 | A scientist could know everything about the physiology of headaches, but never have had one [Heil] |
4625 | Is mental imagery pictorial, or is it propositional? [Heil] |
4607 | Folk psychology and neuroscience are no more competitors than cartography and geology are [Heil] |
7715 | Mentalese isn't a language, because it isn't conventional, or a means of public communication [Lowe] |
7722 | If meaning is mental pictures, explain "the cat (or dog!) is NOT on the mat" [Lowe] |
4605 | Truth-conditions correspond to the idea of 'literal meaning' [Heil] |
4606 | To understand 'birds warble' and 'tigers growl', you must also understand 'tigers warble' [Heil] |
4604 | If propositions are abstract entities, how do human beings interact with them? [Heil] |