50 ideas
| 2930 | The main aim of philosophy must be to determine the order of rank among values [Nietzsche] |
| 20143 | Scientific knowledge is nothing without a prior philosophical 'faith' [Nietzsche] |
| 23722 | Objectivity is not disinterestedness (impossible), but the ability to switch perspectives [Nietzsche] |
| 4417 | Only that which has no history is definable [Nietzsche] |
| 23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [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] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [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] |
| 10197 | An immanent universal is wholly present in more than one place [Zimmerman,DW] |
| 10198 | If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW] |
| 10199 | Discernible differences at different times may just be in counterparts [Zimmerman,DW] |
| 4421 | Philosophers have never asked why there is a will to truth in the first place [Nietzsche] |
| 23719 | Forgetfulness is a strong positive ability, not mental laziness [Nietzsche] |
| 4420 | There is only 'perspective' seeing and knowing, and so the best objectivity is multiple points of view [Nietzsche] |
| 4414 | Philosophers invented "free will" so that our virtues would be permanently interesting to the gods [Nietzsche] |
| 4419 | People who think in words are orators rather than thinkers, and think about facts instead of thinking facts [Nietzsche] |
| 4411 | It is a delusion to separate the man from the deed, like the flash from the lightning [Nietzsche] |
| 3793 | We must question the very value of moral values [Nietzsche] |
| 4408 | The concept of 'good' was created by aristocrats to describe their own actions [Nietzsche] |
| 23716 | A strong rounded person soon forgets enemies, misfortunes, and even misdeeds [Nietzsche] |
| 20129 | All animals strive for the ideal conditions to express their power, and hate any hindrances [Nietzsche] |
| 4409 | Only the decline of aristocratic morality led to concerns about "egoism" [Nietzsche] |
| 3259 | Nietzsche rejects impersonal morality, and asserts the idea of living well [Nietzsche, by Nagel] |
| 4416 | Basic justice is the negotiation of agreement among equals, and the imposition of agreement [Nietzsche] |
| 4418 | A masterful and violent person need have nothing to do with contracts [Nietzsche] |
| 4407 | Plato, Spinoza and Kant are very different, but united in their low estimation of pity [Nietzsche] |
| 4415 | Guilt and obligation originated in the relationship of buying and selling, credit and debt [Nietzsche] |
| 23718 | If we say birds of prey could become lambs, that makes them responsible for being birds of prey [Nietzsche] |
| 23717 | Modern nihilism is now feeling tired of mankind [Nietzsche] |
| 23721 | Old tribes always felt an obligation to the earlier generations, and the founders [Nietzsche] |
| 20142 | The state begins with brutal conquest of a disorganised people, not with a 'contract' [Nietzsche] |
| 23720 | Punishment makes people harder, more alienated, and hostile [Nietzsche] |
| 4410 | The truly great haters in world history have always been priests [Nietzsche] |