5 ideas
| 17744 | De Morgan started the study of relations and their properties [De Morgan, by Walicki] |
| Full Idea: De Morgan started the sustained interest in the study of relations and their properties. | |
| From: report of Augustus De Morgan (On the Syllogism IV [1859]) by Michal Walicki - Introduction to Mathematical Logic History D.1.1 |
| 13501 | De Morgan found inferences involving relations, which eluded Aristotle's syllogistic [De Morgan, by Hart,WD] |
| Full Idea: There was a prejudice against relations (in favour of properties) but De Morgan and others that impeccable inferences turn on relations and elude Aristotle's syllogistic. Thus: All horses are animals. Hence, all heads of horses are heads of animals. | |
| From: report of Augustus De Morgan (On the Syllogism IV [1859]) by William D. Hart - The Evolution of Logic 4 | |
| A reaction: This is actually an early example of modern analytic philosophy in action. You start with the inferences, and then work back to the ontology and the definition of concepts. But in pinning down such concepts, do we miss their full meaning? |
| 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'. |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| Full Idea: Hermarchus said that animal killing is justified by considerations of human safety and nourishment and by animals' inability to form contractual relations of justice with us. | |
| From: report of Hermarchus (fragments/reports [c.270 BCE]) by David A. Sedley - Hermarchus | |
| A reaction: Could the last argument be used to justify torturing animals? Or could we eat a human who was too brain-damaged to form contracts? |
| 6011 | There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara] |
| Full Idea: Numenius argues that material reality depends on intelligible being, which depends on a first god - the Good - which is difficult to grasp, but which inspires a second god to imitate it, turning to matter and organizing it as the world. | |
| From: report of Numenius (fragments/reports [c.160]) by Dominic J. O'Meara - Numenius | |
| A reaction: The interaction problem comes either between the two gods, or between the second god and the world. The argument may have failed to catch on for long when people scented an infinite regress lurking in the middle of it. |