27 ideas
7426 | Critical philosophy is what questions domination at every level [Foucault] |
7423 | Philosophy and politics are fundamentally linked [Foucault] |
7420 | When logos controls our desires, we have actually become the logos [Foucault] |
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] |
7424 | Saying games of truth were merely power relations would be a horrible exaggeration [Foucault] |
7422 | A subject is a form which can change, in (say) political or sexual situations [Foucault] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
7419 | Ethics is the conscious practice of freedom [Foucault] |
7425 | The aim is not to eliminate power relations, but to reduce domination [Foucault] |
7418 | The idea of liberation suggests there is a human nature which has been repressed [Foucault] |
15313 | By 'force' I mean the sources of all actions - sometimes called 'powers' by their outcomes [Breheny] |