81 ideas
| 18330 | Judging by the positive forces, the Renaissance was the last great age [Nietzsche] |
| 2900 | I revere Heraclitus [Nietzsche] |
| 2913 | Thucydides was the perfect anti-platonist sophist [Nietzsche] |
| 2909 | Thinking has to be learned in the way dancing has to be learned [Nietzsche] |
| 2892 | Wanting a system in philosophy is a lack of integrity [Nietzsche] |
| 2896 | I want to understand the Socratic idea that 'reason equals virtue equals happiness' [Nietzsche] |
| 2897 | With dialectics the rabble gets on top [Nietzsche] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 2898 | Anything which must first be proved is of little value [Nietzsche] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [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] |
| 18317 | The 'real being' of things is a nothingness constructed from contradictions in the actual world [Nietzsche] |
| 18315 | We get the concept of 'being' from the concept of the 'ego' [Nietzsche] |
| 18316 | The grounds for an assertion that the world is only apparent actually establish its reality [Nietzsche] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 18314 | In language we treat 'ego' as a substance, and it is thus that we create the concept 'thing' [Nietzsche] |
| 21971 | Transcendental philosophy is the subject becoming the originator of unified reality [Kant] |
| 18309 | The evidence of the senses is falsified by reason [Nietzsche] |
| 18323 | Any explanation will be accepted as true if it gives pleasure and a feeling of power [Nietzsche] |
| 18310 | The 'highest' concepts are the most general and empty concepts [Nietzsche] |
| 20368 | There are no 'individual' persons; we are each the sum of humanity up to this moment [Nietzsche] |
| 2899 | The fanatical rationality of Greek philosophy shows that they were in a state of emergency [Nietzsche] |
| 18313 | The big error is to think the will is a faculty producing effects; in fact, it is just a word [Nietzsche] |
| 20133 | The 'motive' is superficial, and may even hide the antecedents of a deed [Nietzsche] |
| 18326 | The beautiful never stands alone; it derives from man's pleasure in man [Nietzsche] |
| 20101 | Without music life would be a mistake [Nietzsche] |
| 2902 | Healthy morality is dominated by an instinct for life [Nietzsche] |
| 18311 | Philosophers hate values having an origin, and want values to be self-sufficient [Nietzsche] |
| 18324 | There are no moral facts, and moralists believe in realities which do not exist [Nietzsche] |
| 2904 | The doctrine of free will has been invented essentially in order to blame and punish people [Nietzsche] |
| 18321 | To evaluate life one must know it, but also be situated outside of it [Nietzsche] |
| 2893 | In every age the wisest people have judged life to be worthless [Nietzsche] |
| 2894 | Value judgements about life can never be true [Nietzsche] |
| 18322 | When we establish values, that is life itself establishing them, through us [Nietzsche] |
| 2895 | The value of life cannot be estimated [Nietzsche] |
| 18308 | A philosopher fails in wisdom if he thinks the value of life is a problem [Nietzsche] |
| 18319 | Love is the spiritualisation of sensuality [Nietzsche] |
| 2903 | A good human will be virtuous because they are happy [Nietzsche] |
| 2891 | Only the English actually strive after happiness [Nietzsche] |
| 18327 | A wholly altruistic morality, with no egoism, is a thoroughly bad thing [Nietzsche] |
| 15606 | Military idea: what does not kill me makes me stronger [Nietzsche] |
| 18328 | Invalids are parasites [Nietzsche] |
| 18331 | Democracy is organisational power in decline [Nietzsche] |
| 18332 | The creation of institutions needs a determination which is necessarily anti-liberal [Nietzsche] |
| 2911 | True justice is equality for equals and inequality for unequals [Nietzsche] |
| 18320 | To renounce war is to renounce the grand life [Nietzsche] |
| 2908 | There is a need for educators who are themselves educated [Nietzsche] |
| 18329 | Sometimes it is an error to have been born - but we can rectify it [Nietzsche] |
| 2905 | 'Purpose' is just a human fiction [Nietzsche] |
| 18312 | The supreme general but empty concepts must be compatible, and hence we get 'God' [Nietzsche] |
| 2906 | By denying God we deny human accountability, and thus we redeem the world [Nietzsche] |
| 18325 | Christians believe that only God can know what is good for man [Nietzsche] |
| 2901 | How could the Church intelligently fight against passion if it preferred poorness of spirit to intelligence? [Nietzsche] |
| 18318 | People who disparage actual life avenge themselves by imagining a better one [Nietzsche] |