23 ideas
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] |
22687 | Maybe literary assessment is evaluating the artist as a suitable friend [Gaut] |
22686 | Formalists say aesthetics concerns types of beauty, or unity, complexity and intensity [Gaut] |
22685 | Good art does not necessarily improve people (any more than good advice does) [Gaut] |
22690 | 'Moralism' says all aesthetic merits are moral merits [Gaut] |
22684 | Good ethics counts towards aesthetic merit, and bad ethics counts against it [Gaut] |
22689 | If we don't respond ethically in the way a work prescribes, that is an aesthetic failure [Gaut] |
20739 | Levinas took 'first philosophy' to begin with seeing the vulnerable faces of others [Levinas, by Aho] |
20445 | Levinas says Marxism is the replacement of individualist ethics, by solidarity and sociality [Levinas, by Critchley] |