52 ideas
20121 | Grammar only reveals popular metaphysics [Nietzsche] |
24082 | Is the will to truth the desire to avoid deception? [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] |
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] |
20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
18436 | Entities are truthmakers for their resemblances, so no extra entities or 'resemblances' are needed [Rodriquez-Pereyra] |
24077 | Necessity is thought to require an event, but is only an after-effect of the event [Nietzsche] |
20126 | The strength of knowledge is not its truth, but its entrenchment in our culture [Nietzsche] |
20119 | We became increasingly conscious of our sense impressions in order to communicate them [Nietzsche] |
20122 | We have no organ for knowledge or truth; we only 'know' what is useful to the human herd [Nietzsche] |
4423 | We assume causes, geometry, motion, bodies etc to live, but they haven't been proved [Nietzsche] |
6579 | Nietzsche's perspectivism says our worldview depends on our personality [Nietzsche, by Fogelin] |
24083 | It would be absurd to say we are only permitted our own single perspective [Nietzsche] |
20115 | All of our normal mental life could be conducted without consciousness [Nietzsche] |
20117 | Only the need for communication has led to consciousness developing [Nietzsche] |
20118 | Only our conscious thought is verbal, and this shows the origin of consciousness [Nietzsche] |
20116 | Most of our lives, even the important parts, take place outside of consciousness [Nietzsche] |
20120 | Whatever moves into consciousness becomes thereby much more superficial [Nietzsche] |
2932 | 'Know thyself' is impossible and ridiculous [Nietzsche] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
24078 | Thoughts cannot be fully reproduced in words [Nietzsche] |
24081 | Most of our intellectual activity is unconscious [Nietzsche] |
2933 | Why do you listen to the voice of your conscience? [Nietzsche] |
20141 | Higher human beings see and hear far more than others, and do it more thoughtfully [Nietzsche] |
24076 | A morality ranks human drives and actions, for the sake of the herd, and subordinating individuals [Nietzsche] |
22471 | Nietzsche thought it 'childish' to say morality isn't binding because it varies between cultures [Nietzsche, by Foot] |
2935 | No two actions are the same [Nietzsche] |
20198 | Many virtues are harmful traps, but that is why other people praise them [Nietzsche] |
4275 | You cannot advocate joyful wisdom while rejecting pity, because the two are complementary [Scruton on Nietzsche] |
2934 | To see one's own judgement as a universal law is selfish [Nietzsche] |
24080 | We should give style to our character - by applying an artistic plan to its strengths and weaknesses [Nietzsche] |
20125 | The ethical teacher exists to give purpose to what happens necessarily and without purpose [Nietzsche] |
9306 | To ward off boredom at any cost is vulgar [Nietzsche] |
24079 | The best life is the dangerous life [Nietzsche] |
2936 | Imagine if before each of your actions you had to accept repeating the action over and over again [Nietzsche] |
6842 | Nietzsche says facing up to the eternal return of meaninglessness is the response to nihilism [Nietzsche, by Critchley] |
2931 | God is dead, and we have killed him [Nietzsche] |