3 ideas
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| Full Idea: In 1846 De Morgan introduced the enormously influential notion of a possibly arbitrary and stipulated 'universe of discourse'. It replaced Boole's original - and metaphysically a bit suspect - universe of 'all things'. | |
| From: report of Augustus De Morgan (works [1846]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 | |
| A reaction: This not only brings formal logic under control, but also reflects normal talk, because there is always an explicit or implicit domain of discourse when we talk. Of virtually any conversation, you can say what it is 'about'. |
| 1490 | You would have to be very morally lazy to ignore criticisms of your own culture [Nagel] |
| Full Idea: One would have to be very morally lazy to be unconcerned with the possibility that the prevailing morality of one's culture had something fundamentally wrong with it. | |
| From: Thomas Nagel (MacIntyre versus the Enlightenment [1988], 203) |
| 17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
| Full Idea: Principles must be judged from the point of view of science, and not science from the point of view of principles fixed once and for all. Geometry existed before Euclid's 'Elements', just as arithmetic and set theory did before Peano's 'Formulaire'. | |
| From: Ernst Zermelo (New Proof of Possibility of Well-Ordering [1908], §2a) | |
| A reaction: This shows why the axiomatisation of set theory is an ongoing and much-debated activity. |