84 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] |
9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
2898 | Anything which must first be proved is of little value [Nietzsche] |
9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
9605 | If a proposition is false, then its negation is true [Brown,JR] |
9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
9630 | The most brilliant formalist was Hilbert [Brown,JR] |
9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
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] |
9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
18316 | The grounds for an assertion that the world is only apparent actually establish its reality [Nietzsche] |
18314 | In language we treat 'ego' as a substance, and it is thus that we create the concept 'thing' [Nietzsche] |
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] |
9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
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] |
2895 | The value of life cannot be estimated [Nietzsche] |
18322 | When we establish values, that is life itself establishing them, through us [Nietzsche] |
2893 | In every age the wisest people have judged life to be worthless [Nietzsche] |
18308 | A philosopher fails in wisdom if he thinks the value of life is a problem [Nietzsche] |
2894 | Value judgements about life can never be true [Nietzsche] |
18321 | To evaluate life one must know it, but also be situated outside of it [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] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
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] |
2901 | How could the Church intelligently fight against passion if it preferred poorness of spirit to intelligence? [Nietzsche] |
18325 | Christians believe that only God can know what is good for man [Nietzsche] |
5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |
18318 | People who disparage actual life avenge themselves by imagining a better one [Nietzsche] |