34 ideas
7578 | I conceived it my task to create difficulties everywhere [Kierkegaard] |
22047 | Wherever there is painless contradiction there is also comedy [Kierkegaard] |
22092 | Kierkegaard's truth draws on authenticity, fidelity and honesty [Kierkegaard, by Carlisle] |
15999 | Pure truth is for infinite beings only; I prefer endless striving for truth [Kierkegaard] |
20313 | The highest truth we can get is uncertainty held fast by an inward passion [Kierkegaard] |
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] |
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] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
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] |
20742 | The real subject is ethical, not cognitive [Kierkegaard] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
7579 | While big metaphysics is complete without ethics, personal philosophy emphasises ethics [Kierkegaard] |
7581 | Speculative philosophy loses the individual in a vast vision of humanity [Kierkegaard] |
20314 | People want to lose themselves in movements and history, instead of being individuals [Kierkegaard] |
7582 | Becoming what one is is a huge difficulty, because we strongly aspire to be something else [Kierkegaard] |
7586 | God does not think or exist; God creates, and is eternal [Kierkegaard] |
20312 | God cannot be demonstrated objectively, because God is a subject, only existing inwardly [Kierkegaard] |
7580 | Pantheism destroys the distinction between good and evil [Kierkegaard] |
7584 | Without risk there is no faith [Kierkegaard] |
7583 | Faith is the highest passion in the sphere of human subjectivity [Kierkegaard] |