32 ideas
15557 | Verisimilitude has proved hard to analyse, and seems to have several components [Lewis] |
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] |
15554 | A disposition needs a causal basis, a property in a certain causal role. Could the disposition be the property? [Lewis] |
15560 | We can explain a chance event, but can never show why some other outcome did not occur [Lewis] |
15559 | Does a good explanation produce understanding? That claim is just empty [Lewis] |
15556 | Science may well pursue generalised explanation, rather than laws [Lewis] |
15558 | A good explanation is supposed to show that the event had to happen [Lewis] |
4809 | Lewis endorses the thesis that all explanation of singular events is causal explanation [Lewis, by Psillos] |
14321 | To explain an event is to provide some information about its causal history [Lewis] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
15555 | Explaining match lighting in general is like explaining one lighting of a match [Lewis] |
15551 | Ways of carving causes may be natural, but never 'right' [Lewis] |
15552 | We only pick 'the' cause for the purposes of some particular enquiry. [Lewis] |
15553 | Causal dependence is counterfactual dependence between events [Lewis] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |