25 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] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
23429 | The environment needs localised politics, with its care for the land [Dobson] |
23424 | An ideology judges things now, and offers an ideal, with a strategy for reaching it [Dobson] |
23426 | Ecologism is often non-liberal, by claiming to know other people's best interests [Dobson] |
23427 | Socialism can be productive and centralised, or less productive and decentralised [Dobson] |
23428 | Difference feminists say women differ fundamentally from men [Dobson] |
23422 | For the environment, affluence and technology matter as much as population size [Dobson] |
23425 | Ecologism says growth must be reduced, and efficiency is not enough [Dobson] |
23430 | A million years is a proper unit of political time [Dobson] |
23423 | We currently value the present fourteen times more highly than the future [Dobson] |