30 ideas
22496 | Wisdom only implies the knowledge achievable in any normal lifetime [Foot] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
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] |
23694 | All criterions of practical rationality derive from goodness of will [Foot] |
23686 | Moral reason is not just neutral, because morality is part of the standard of rationality [Foot, by Hacker-Wright] |
23693 | Practical rationality must weigh both what is morally and what is non-morally required [Foot] |
23687 | Moral virtues arise from human nature, as part of what makes us good human beings [Foot, by Hacker-Wright] |
22492 | Virtues are as necessary to humans as stings are to bees [Foot] |
22493 | Sterility is a human defect, but the choice to be childless is not [Foot] |
22491 | Moral evaluations are not separate from facts, but concern particular facts about functioning [Foot] |
22497 | Deep happiness usually comes from the basic things in life [Foot] |
22498 | Happiness is enjoying the pursuit and attainment of right ends [Foot] |
23695 | Good actions can never be justified by the good they brings to their agent [Foot] |
22499 | We all know that just pretending to be someone's friend is not the good life [Foot] |
22495 | Someone is a good person because of their rational will, not their body or memory [Foot] |
22502 | Refraining from murder is not made good by authenticity or self-fulfilment [Foot] |