31 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] |
12708 | The soul is not a substance but a substantial form, the first active faculty [Leibniz] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
22673 | Wherever there is a small community, the association of the people is natural [Tocqueville] |
22676 | The people are just individuals, and only present themselves as united to foreigners [Tocqueville] |
22679 | Vast empires are bad for well-being and freedom, though they may promote glory [Tocqueville] |
22680 | People would be much happier and freer in small nations [Tocqueville] |
22675 | In American judges rule according to the Constitution, not the law [Tocqueville] |
22677 | A monarchical family is always deeply concerned with the interests of the state [Tocqueville] |
22683 | Despots like to see their own regulations ignored, by themselves and their agents [Tocqueville] |
22669 | Aristocracy is constituted by inherited landed property [Tocqueville] |
22674 | In Europe it is thought that local government is best handled centrally [Tocqueville] |
22678 | An election, and its lead up time, are always a national crisis [Tocqueville] |
22682 | Universal suffrage is no guarantee of wise choices [Tocqueville] |
22670 | Slavery undermines the morals and energy of a society [Tocqueville] |
22681 | The liberty of the press is more valuable for what it prevents than what it promotes [Tocqueville] |
22672 | It is admirable to elevate the humble to the level of the great, but the opposite is depraved [Tocqueville] |
22671 | Equality can only be established by equal rights for all (or no rights for anyone) [Tocqueville] |