31 ideas
7990 | Serene wisdom is freedom from ties, and indifference to fortune [Anon (Bhag)] |
7989 | Seek salvation in the wisdom of reason [Anon (Bhag)] |
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] |
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] |
7996 | I am all the beauty and goodness of things, says Krishna [Anon (Bhag)] |
16650 | 'Unity' is a particularly difficult word, because things can have hidden unity [Duns Scotus] |
7995 | In all living beings I am the light of consciousness, says Krishna [Anon (Bhag)] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
7999 | All actions come from: body, lower self, perception, means of action, or Fate [Anon (Bhag)] |
7991 | Hate and lust have their roots in man's lower nature [Anon (Bhag)] |
7988 | There is no greater good for a warrior than to fight in a just war [Anon (Bhag)] |
7992 | The visible forms of nature are earth, water, fire, air, ether; mind, reason, and the sense of 'I' [Anon (Bhag)] |
7994 | Everything, including the gods, comes from me, says Krishna [Anon (Bhag)] |
7993 | Brahman is supreme, Atman his spirit in man, and Karma is the force of creation [Anon (Bhag)] |
7997 | Only by love can men see me, know me, and come to me, says Krishna [Anon (Bhag)] |
7998 | The three gates of hell are lust, anger and greed [Anon (Bhag)] |