28 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] |
| 7621 | Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein] |
| 23829 | National leaders want to preserve necessary order - but always the existing order [Weil] |
| 23828 | National prestige consists of behaving as if you could beat the others in a war [Weil] |
| 23827 | Modern wars are fought in the name of empty words which are given capital letters [Weil] |
| 22955 | Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield] |
| 20638 | General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close] |
| 20636 | Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close] |
| 21230 | The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo] |
| 21231 | Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo] |
| 20634 | General Relativity says there is no absolute force or acceleration [Einstein, by Close] |
| 20648 | Mass is a measure of energy content [Einstein] |
| 21232 | Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo] |
| 7626 | I do not believe in a personal God [Einstein] |