42 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] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [Nietzsche] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
4421 | Philosophers have never asked why there is a will to truth in the first place [Nietzsche] |
7628 | Broad rejects the inferential component of the representative theory [Broad, by Maund] |
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] |