25 ideas
20771 | Six parts: dialectic, rhetoric, ethics, politics, physics, theology [Cleanthes, by Diog. Laertius] |
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] |
6028 | Bodies interact with other bodies, and cuts cause pain, and shame causes blushing, so the soul is a body [Cleanthes, by Nemesius] |
20831 | The soul suffers when the body hurts, creates redness from shame, and pallor from fear [Cleanthes] |
2848 | Two people might agree in their emotional moral attitude while disagreeing in their judgement [Brink] |
2851 | Emotivists find it hard to analyse assertions of moral principles, rather than actual judgements [Brink] |
2853 | Emotivists claim to explain moral motivation by basing morality on non-cognitive attitudes [Brink] |
2852 | Emotivists tend to favour a redundancy theory of truth, making moral judgement meaningless [Brink] |
2849 | Emotivism implies relativism about moral meanings, but critics say disagreements are about moral reference [Brink] |
2850 | How can emotivists explain someone who recognises morality but is indifferent to it? [Brink] |
5993 | The ascending scale of living creatures requires a perfect being [Cleanthes, by Tieleman] |