59 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] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
4417 | Only that which has no history is definable [Nietzsche] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
23715 | Psychologists should be brave and proud, and prefer truth to desires, even when it is ugly [Nietzsche] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
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] |
18033 | The meaning of a representation is its role in thought, perception or decisions [Block] |
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] |