29 ideas
| 13560 | A wise man is not subservient to anything [Seneca] |
| 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] |
| 14919 | Empiricists deny what is unobservable, and reject objective modality [Fraassen] |
| 6783 | To 'accept' a theory is not to believe it, but to believe it empirically adequate [Fraassen, by Bird] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 14917 | To accept a scientific theory, we only need to believe that it is empirically adequate [Fraassen] |
| 6784 | Why should the true explanation be one of the few we have actually thought of? [Fraassen, by Bird] |
| 13066 | An explanation is just descriptive information answering a particular question [Fraassen, by Salmon] |
| 13558 | The supreme good is harmony of spirit [Seneca] |
| 13559 | I seek virtue, because it is its own reward [Seneca] |
| 13561 | Virtue is always moderate, so excess need not be feared [Seneca] |
| 13562 | It is shameful to not even recognise your own slaves [Seneca] |
| 13563 | Why does your wife wear in her ears the income of a wealthy house? [Seneca] |
| 13565 | If wealth was a good, it would make men good [Seneca] |
| 13564 | There is far more scope for virtue if you are wealthy; poverty only allows endurance [Seneca] |
| 13557 | Unfortunately the majority do not tend to favour what is best [Seneca] |