50 ideas
| 24146 | All the major problems were formulated before Socrates [Nietzsche] |
| 24142 | What matters is how humans can be developed [Nietzsche] |
| 24143 | Thinkers might agree some provisional truths, as methodological assumptions [Nietzsche] |
| 24125 | Aristotle enjoyed the sham generalities of a system, as the peak of happiness! [Nietzsche] |
| 24147 | Thoughts are uncertain, and are just occasions for interpretation [Nietzsche] |
| 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] |
| 24137 | Mathematics is just accurate inferences from definitions, and doesn't involve objects [Nietzsche] |
| 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] |
| 24131 | There is no 'being'; it is just the opposition to nothingness [Nietzsche] |
| 24151 | I only want thinking that is anchored in body, senses and earth [Nietzsche] |
| 24150 | We can only understand through concepts, which subsume particulars in generalities [Nietzsche] |
| 24138 | Strongly believed a priori is not certain; it may just be a feature of our existence [Nietzsche] |
| 24130 | An affirmative belief is present in every basic sense impression [Nietzsche] |
| 24124 | We now have innumerable perspectives to draw on [Nietzsche] |
| 24145 | Mind is a mechanism of abstraction and simplification, aimed at control [Nietzsche] |
| 24144 | A cognitive mechanism wanting to know itself is absurd! [Nietzsche] |
| 24139 | A 'person' is just one possible abstraction from a bundle of qualities [Nietzsche] |
| 24133 | I have perfected fatalism, as recurrence and denial of the will [Nietzsche] |
| 24152 | Fate is inspiring, if you understand you are part of it [Nietzsche] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 24129 | We start with images, then words, and then concepts, to which emotions attach [Nietzsche] |
| 24127 | Judging actions by intentions - like judging painters by their thoughts! [Nietzsche] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 24149 | Values need a perspective, of preserving some aspect of life [Nietzsche] |
| 24148 | If you love something, it is connected with everything, so all must be affirmed as good [Nietzsche] |
| 24135 | Egoism should not assume that all egos are equal [Nietzsche] |
| 24132 | After Socrates virtue is misunderstood, as good for all, not for individuals [Nietzsche] |
| 24126 | We contain multitudes of characters, which can brought into the open [Nietzsche] |
| 24136 | Who can endure the thought of eternal recurrence? [Nietzsche] |
| 24154 | If you want one experience repeated, you must want all of them [Nietzsche] |
| 24153 | Humans are determined by community, so its preservation is their most valued drive [Nietzsche] |
| 24134 | There is always slavery, whether we like it or not [Nietzsche] |
| 24128 | After history following God, or a people, or an idea, we now see it in terms of animals [Nietzsche] |
| 24140 | Cause and effect is a hypothesis, based on our supposed willing of actions [Nietzsche] |
| 24141 | Having a sense of time presupposes absolute time [Nietzsche] |