38 ideas
| 14255 | We understand things through their dependency relations [Fine,K] |
| 14250 | Metaphysics deals with the existence of things and with the nature of things [Fine,K] |
| 14259 | Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K] |
| 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] |
| 14253 | An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K] |
| 14261 | There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K] |
| 14251 | A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K] |
| 14257 | An object depends on another if the second cannot be eliminated from the first's definition [Fine,K] |
| 14254 | Dependency is the real counterpart of one term defining another [Fine,K] |
| 14252 | We should understand identity in terms of the propositions it renders true [Fine,K] |
| 14256 | How do we distinguish basic from derived esssences? [Fine,K] |
| 14258 | Maybe some things have essential relationships as well as essential properties [Fine,K] |
| 14260 | An object only essentially has a property if that property follows from every definition of the object [Fine,K] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |