39 ideas
19635 | Hegel produced modern optimism; he failed to grasp that consciousness never progresses [Hegel, by Cioran] |
8215 | Hegel was the last philosopher of the Book [Hegel, by Derrida] |
16011 | Hegel doesn't storm the heavens like the giants, but works his way up by syllogisms [Kierkegaard on Hegel] |
5433 | For Hegel, things are incomplete, and contain external references in their own nature [Hegel, by Russell] |
3301 | On the continent it is generally believed that metaphysics died with Hegel [Benardete,JA on Hegel] |
19661 | Making sufficient reason an absolute devalues the principle of non-contradiction [Hegel, by Meillassoux] |
20952 | Rather than in three stages, Hegel presented his dialectic as 'negation of the negation' [Hegel, by Bowie] |
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] |
21777 | Negation of negation doubles back into a self-relationship [Hegel, by Houlgate] |
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] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on 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] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
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] |
5645 | The dialectical opposition of being and nothing is resolved in passing to the concept of becoming [Hegel, by Scruton] |
5646 | Hegel gives an ontological proof of the existence of everything [Hegel, by Scruton] |
21755 | For Hegel, categories shift their form in the course of history [Hegel, by Houlgate] |
21754 | Our concepts and categories disclose the world, because we are part of the world [Hegel, by Houlgate] |
22079 | Hegel said Kant's fixed categories actually vary with culture and era [Hegel, by Houlgate] |
9225 | Hegel reputedly claimed to know a priori that there are five planets [Hegel, by Field,H] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
23221 | The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish] |
21758 | Humans have no fixed identity, but produce and reveal their shifting identity in history [Hegel, by Houlgate] |
20414 | Hegel's Absolute Spirit is the union of human rational activity at a moment, and whatever that sustains [Hegel, by Eldridge] |
3909 | Society isn’t founded on a contract, since contracts presuppose a society [Hegel, by Scruton] |
4347 | When man wills the natural, it is no longer natural [Hegel] |
4188 | Hegel's entire philosophy is nothing but a monstrous amplification of the ontological proof [Schopenhauer on Hegel] |
6686 | Hegel said he was offering an encyclopaedic rationalisation of Christianity [Hegel, by Graham] |