41 ideas
18290 | But what is the reasoning of the body, that it requires the wisdom you seek? [Nietzsche] |
18303 | Reject wisdom that lacks laughter [Nietzsche] |
18305 | To love truth, you must know how to lie [Nietzsche] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
16634 | I can't be unaware of anything which is in me [Descartes] |
20757 | The powerful self behind your thoughts and feelings is your body [Nietzsche] |
18289 | Forget the word 'I'; 'I' is performed by the intelligence of your body [Nietzsche] |
18299 | The will is constantly frustrated by the past [Nietzsche] |
18297 | We created meanings, to maintain ourselves [Nietzsche] |
18293 | The noble man wants new virtues; the good man preserves what is old [Nietzsche] |
18301 | We only really love children and work [Nietzsche] |
18307 | I want my work, not happiness! [Nietzsche] |
18291 | Virtues can destroy one another, through jealousy [Nietzsche] |
18287 | People now find both wealth and poverty too much of a burden [Nietzsche] |
18295 | If you want friends, you must be a fighter [Nietzsche] |
18286 | The greatest experience possible is contempt for your own happiness, reason and virtue [Nietzsche] |
3635 | Essence must be known before we discuss existence [Descartes] |
18296 | An enduring people needs its own individual values [Nietzsche] |
18294 | The state coldly claims that it is the people, but that is a lie [Nietzsche] |
18304 | Saints want to live as they desire, or not to live at all [Nietzsche] |
18300 | Whenever we have seen suffering, we have wanted the revenge of punishment [Nietzsche] |
18302 | Man and woman are deeply strange to one another! [Nietzsche] |
18292 | I can only believe in a God who can dance [Nietzsche] |
3634 | We can't prove a first cause from our inability to grasp infinity [Descartes] |
18298 | Not being a god is insupportable, so there are no gods! [Nietzsche] |
18288 | Heaven was invented by the sick and the dying [Nietzsche] |
18306 | We don't want heaven; now that we are men, we want the kingdom of earth [Nietzsche] |