34 ideas
| 16477 | Asserting not-p is saying p is false [Russell] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 16486 | The physical world doesn't need logic, but the mental world does [Russell] |
| 2947 | Questions wouldn't lead anywhere without the law of excluded middle [Russell] |
| 16480 | A disjunction expresses indecision [Russell] |
| 16479 | 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell] |
| 16481 | 'Or' expresses a mental state, not something about the world [Russell] |
| 16487 | Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell] |
| 16483 | Disjunction may also arise in practice if there is imperfect memory. [Russell] |
| 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] |
| 16475 | A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell] |
| 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] |
| 16482 | All our knowledge (if verbal) is general, because all sentences contain general words [Russell] |
| 4758 | Naďve realism leads to physics, but physics then shows that naďve realism is false [Russell] |
| 16476 | For simple words, a single experience can show that they are true [Russell] |
| 16485 | Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 18006 | Chomsky's 'interpretative semantics' says syntax comes first, and is then interpreted [Chomsky, by Magidor] |
| 16478 | A mother cat is paralysed if equidistant between two needy kittens [Russell] |