5 ideas
| 11074 | 'It is true that this follows' means simply: this follows [Wittgenstein] |
| Full Idea: The proposition: "It is true that this follows from that" means simply: this follows from that. | |
| From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6 | |
| A reaction: Presumably this remark is simply expressing Wittgenstein's later agreement with the well-known view of Ramsey. Early Wittgenstein had endorsed a correspondence view of truth. |
| 11073 | Two and one making three has the necessity of logical inference [Wittgenstein] |
| Full Idea: "But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference? - Yes! it is the same. | |
| From: Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6 | |
| A reaction: This need not be a full commitment to logicism - only to the fact that the inferential procedures in mathematics are the same as those of logic. Mathematics could still have further non-logical ingredients. Indeed, I think it probably does. |
| 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. |
| 5470 | The idea of laws of nature arose in the Middle Ages [Hall,AR, by Ellis] |
| Full Idea: According to A.R. Hall, the idea that nature is governed by laws does not appear to have existed in the ancient Greek, Roman or Far Eastern traditions of science, but arose from religious, philosophical and legal ideas in medieval Europe. | |
| From: report of A.R. Hall (The Scientific Revolution 1500-1800 [1954]) by Brian Ellis - The Philosophy of Nature: new essentialism Ch.5 | |
| A reaction: This is a very illuminating point, which gives good circumstantial support for questioning the existence of external laws which are imposed on a passive nature. Modern essentialism suggest the 'laws' are the intrinsic results of properties. |
| 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. |