54 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] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 19597 | Logic (the theory of relations) should be applied to mathematics [Novalis] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 19581 | A problem is a solid mass, which the mind must break up [Novalis] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 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] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 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] |
| 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] |
| 17593 | Always be ready to give reasons for your beliefs [Peter] |