29 ideas
21495 | Theoretical and practical politics are both concerned with the best lives for individuals [Russell] |
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] |
21517 | Individuals need creativity, reverence for others, and self-respect [Russell] |
21523 | We would not want UK affairs to be settled by a world parliament [Russell] |
21522 | Democracy is inadequate without a great deal of devolution [Russell] |
21521 | Anarchy does not maximise liberty [Russell] |
21528 | Groups should be autonomous, with a neutral authority as arbitrator [Russell] |
21527 | On every new question the majority is always wrong at first [Russell] |
21526 | Unfortunately ordinary voters can't detect insincerity [Russell] |
21525 | When the state is the only employer, there is no refuge from the prejudices of other people [Russell] |
21518 | Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell] |
21519 | We need security and liberty, and then encouragement of creativity [Russell] |
21524 | The right to own land gives a legal right to a permanent income [Russell] |
17366 | Virtually all modern views of speciation rest on relational rather than intrinsic features [Okasha] |
21520 | That our heaven is a dull place reflects the misery of excessive work in life [Russell] |