26 ideas
19579 | The history of philosophy is just experiments in how to do philosophy [Novalis] |
19583 | Philosophy only begins when it studies itself [Novalis] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
19581 | A problem is a solid mass, which the mind must break up [Novalis] |
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] |
19584 | Whoever first counted to two must have seen the possibility of infinite counting [Novalis] |
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] |
22025 | Novalis thought self-consciousness cannot disclose 'being', because we are temporal creatures [Novalis, by Pinkard] |
22067 | Poetry is true idealism, and the self-consciousness of the universe [Novalis] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19585 | Every person has his own language [Novalis] |
19582 | Morality and philosophy are mutually dependent [Novalis] |
22027 | Life isn't given to us like a novel - we write the novel [Novalis] |
19580 | If the pupil really yearns for the truth, they only need a hint [Novalis] |
17009 | I won't object if someone shows that gravity consistently arises from the action of matter [Newton] |