26 ideas
| 21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
| 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] |
| 20086 | Nowadays sovereignty (once the basis of a state) has become relative [Reybrouck] |
| 20090 | Today it seems almost impossible to learn the will of the people [Reybrouck] |
| 20087 | There are no united monolothic 'peoples', and no 'national gut feelings' [Reybrouck] |
| 20089 | Technocrats may be efficient, but they lose legitimacy as soon as they do unpopular things [Reybrouck] |
| 20088 | Technocrats are expert managers, who replace politicians, and can be long-term and unpopular [Reybrouck] |
| 20085 | Democracy is the best compromise between legitimacy and efficiency [Reybrouck] |
| 20095 | A referendum result arises largely from ignorance [Reybrouck] |
| 20094 | You don't really govern people if you don't involve them [Reybrouck] |
| 20093 | In the 18th century democratic lots lost out to elections, that gave us a non-hereditary aristocracy [Reybrouck] |
| 20091 | Representative elections were developed in order to avoid democracy [Reybrouck] |