26 ideas
21677 | How can the not-true fail to be false, or the not-false fail to be true? [Cicero] |
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] |
21667 | Oratory and philosophy are closely allied; orators borrow from philosophy, and ornament it [Cicero] |
21678 | If desire is not in our power then neither are choices, so we should not be praised or punished [Cicero] |
22809 | The social contract sees society as constituted by and for individuals [Taylor,C] |
22811 | Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C] |
22815 | If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C] |
22814 | Our reliance on other people close to us does not imply any political obligations [Taylor,C] |
22810 | A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C] |
22812 | For most people the primacy of rights mainly concerns freedom [Taylor,C] |
22813 | Property is not essential for life, but it may be essential for independence [Taylor,C] |
23417 | If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka] |