43 ideas
| 19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
| 19583 | Philosophy only begins when it studies itself [Novalis] |
| 22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
| 19588 | The highest aim of philosophy is to combine all philosophies into a unity [Novalis] |
| 19598 | Philosophy relies on our whole system of learning, and can thus never be complete [Novalis] |
| 19586 | Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis] |
| 19587 | Philosophy aims to produce a priori an absolute and artistic world system [Novalis] |
| 19574 | If man sacrifices truth he sacrifices himself, by acting against his own convictions [Novalis] |
| 19571 | Delusion and truth differ in their life functions [Novalis] |
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
| 19581 | A problem is a solid mass, which the mind must break up [Novalis] |
| 13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| 12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
| 19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
| 18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
| 18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
| 15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| 22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
| 19575 | Refinement of senses increasingly distinguishes individuals [Novalis] |
| 22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
| 19572 | Experiences tests reason, and reason tests experience [Novalis] |
| 19590 | Empiricists are passive thinkers, given their philosophy by the external world and fate [Novalis] |
| 19594 | General statements about nature are not valid [Novalis] |
| 19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
| 19596 | The whole body is involved in the formation of thoughts [Novalis] |
| 19573 | The seat of the soul is where our inner and outer worlds interpenetrate [Novalis] |
| 19577 | Everything is a chaotic unity, then we abstract, then we reunify the world into a free alliance [Novalis] |
| 19585 | Every person has his own language [Novalis] |
| 19578 | Only self-illuminated perfect individuals are beautiful [Novalis] |
| 19582 | Morality and philosophy are mutually dependent [Novalis] |
| 22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
| 19589 | The whole point of a monarch is that we accept them as a higher-born, ideal person [Novalis] |
| 19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
| 19593 | Persons are shaped by a life history; splendid persons are shaped by world history [Novalis] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 19595 | Nature is a whole, and its individual parts cannot be wholly understood [Novalis] |
| 19592 | The basic relations of nature are musical [Novalis] |
| 19576 | Religion needs an intermediary, because none of us can connect directly to a godhead [Novalis] |