35 ideas
5035 | The two basics of reasoning are contradiction and sufficient reason [Leibniz] |
21122 | Liberal Nationalism says welfare states and democracy needed a shared sense of nationality [Shorten] |
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] |
5038 | Assume that mind and body follow their own laws, but God has harmonised them [Leibniz] |
21136 | Utilitarians conflate acts and omissions; causing to drown and failing to save are the same [Shorten] |
21135 | There are eight different ways in which groups of people can be oppressed [Shorten, by PG] |
21118 | Constitutional Patriotism unites around political values (rather than national identity) [Shorten] |
21129 | Democracy is a method of selection, or it involves participation, or it concerns public discussion [Shorten] |
21130 | Some say democracy is intrinsically valuable, others that it delivers good outcomes [Shorten] |
21126 | Representative should be either obedient, or sensible, or typical [Shorten] |
21128 | There is 'mirror representation' when the institution statistically reflects the population [Shorten] |
21127 | In a changed situation a Mandated Representative can't keep promises and fight for constituents [Shorten] |
21117 | Liberal citizens have a moral requirement to respect freedom and equality [Shorten] |
21134 | Maybe the rational autonomous liberal individual is merely the result of domination [Shorten] |
21113 | Liberal equality concerns rights, and liberal freedom concerns choice of ends [Shorten] |
21121 | Liberal Nationalism encourages the promotion of nationalistic values [Shorten] |
21115 | Liberalism should not make assumptions such as the value of choosing your own life plan [Shorten] |
21114 | Liberals treat individuals as mutual strangers, rather than as social beings [Shorten] |
21123 | Liberal Nationalism is more communitarian, and Constitutional Patriotism more cosmopolitan [Shorten] |
21124 | Religious toleration has been institutionalised by the separation of church and state [Shorten] |
5037 | God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz] |