30 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] |
| 6685 | 'Subjectivism' is an extension of relativism from the social group to the individual [Graham] |
| 15282 | Facts should be deducible from the theory and initial conditions, and prefer the simpler theory [Osiander, by Harré/Madden] |
| 6699 | The chain of consequences may not be the same as the chain of responsibility [Graham] |
| 6698 | Negative consequences are very hard (and possibly impossible) to assess [Graham] |
| 6700 | We can't criticise people because of unforeseeable consequences [Graham] |
| 6704 | Egoism submits to desires, but cannot help form them [Graham] |
| 6701 | Rescue operations need spontaneous benevolence, not careful thought [Graham] |
| 6693 | 'What if everybody did that?' rather misses the point as an objection to cheating [Graham] |
| 6691 | It is more plausible to say people can choose between values, than that they can create them [Graham] |
| 6688 | Life is only absurd if you expected an explanation and none turns up [Graham] |
| 6705 | Existentialism may transcend our nature, unlike eudaimonism [Graham] |
| 6690 | A standard problem for existentialism is the 'sincere Nazi' [Graham] |
| 6689 | The key to existentialism: the way you make choices is more important than what you choose [Graham] |
| 6706 | The great religions are much more concerned with the religious life than with ethics [Graham] |
| 6709 | Western religion saves us from death; Eastern religion saves us from immortality [Graham] |