27 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] |
21740 | I doubt whether ethics is part of philosophy [Russell] |
21741 | 'You ought to do p' primarily has emotional content, expressing approval [Russell] |
1477 | Being manly and brave is the result of convention, not of human nature [Plutarch] |
21746 | Unlike hate, all desires can be satisfied by love [Russell] |
21747 | Goodness is a combination of love and knowledge [Russell] |
21743 | In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell] |
1478 | Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch] |
21742 | Originally virtue was obedience, to gods, government, or custom [Russell] |
21745 | Act so as to produce harmonious rather than discordant desires [Russell] |
21744 | Legally curbing people's desires is inferior to improving their desires [Russell] |
1479 | Animals have not been led into homosexuality, because they value pleasure very little [Plutarch] |
22891 | We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon] |