54 ideas
20121 | Grammar only reveals popular metaphysics [Nietzsche] |
24082 | Is the will to truth the desire to avoid deception? [Nietzsche] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
20360 | We Germans value becoming and development more highly than mere being of what 'is' [Nietzsche] |
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] |
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] |
5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |
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] |