8 ideas
| 10247 | We have no adequate logic at the moment, so mathematicians must create one [Veblen] |
| Full Idea: Formal logic has to be taken over by mathematicians. The fact is that there does not exist an adequate logic at the present time, and unless the mathematicians create one, no one else is likely to do so. | |
| From: Oswald Veblen (Presidential Address of Am. Math. Soc [1924], 141), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This remark was made well after Frege, but before the advent of Gödel and Tarski. That implies that he was really thinking of meta-logic. |
| 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'. |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| Full Idea: Prodicus insists that contradiction is impossible, since if two people are contradicting each other, they cannot both be speaking of the same fact. Only the one who is speaking the truth is speaking of facts as they are; the other does not speak facts. | |
| From: report of Prodicus (fragments/reports [c.423 BCE]) by Didymus the Blind - Commentary on Ecclesiastes (frags) | |
| A reaction: cf. Kant's 100 thalers example |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| Full Idea: In the old days people regarded the sun, the moon, rivers, springs, and everything else which is helpful for life as gods, because we are helped by them, just as the Egyptians regard the Nile as a god. | |
| From: Prodicus (fragments/reports [c.423 BCE], B05), quoted by Sextus Empiricus - Against the Professors (six books) 9.18 |
| 535 | The gods are just personified human benefits [Prodicus] |
| Full Idea: Things from which benefits to human life have been derived have come to be considered deities, such as Demeter and Dionysus. | |
| From: Prodicus (fragments/reports [c.423 BCE], B5), quoted by (who?) - where? |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
| Full Idea: He says that the gods worshipped by men neither exist nor have knowledge, but that the ancients exalted crops and everything else which is useful for life. | |
| From: Prodicus (fragments/reports [c.423 BCE]), quoted by Anon (Herc) - fragments 1428 19.12 |