5 ideas
| 13639 | Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro] |
| Full Idea: Quine (in 1941) attacked 'Principia Mathematica' because the items in the range of higher-order variables (attributes etc) are intensional and thus do not have a clearly defined identity relation. | |
| From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Stewart Shapiro - Foundations without Foundationalism 1.3 |
| 21557 | Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey] |
| Full Idea: Quine (1941) said that Russell had confused use and mention, and thus thought he had reduced classes to linguistic entities, while in fact he reduced them only to Platonic properties. | |
| From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133 | |
| A reaction: This is cited as the 'orthodox critical interpretation' of Russell and Whitehead. Confusion of use and mention was a favourite charge of Quine's. |
| 18810 | Aristotle's proofs give understanding, so it can't be otherwise, so consequence is necessary [Smiley, by Rumfitt] |
| Full Idea: The ingredient of necessity [in Aristotle's account of consequence] is required by his demand that proof should produce 'understanding' [episteme], coupled with his claim that understanding something involves seeing that it cannot be otherwise. | |
| From: report of Timothy Smiley (Conceptions of Consequence [1998], p.599) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: An intriguing reverse of the normal order. Not 'necessity in logic delivers understanding', but 'reaching understanding shows the logic was necessary'. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |