8 ideas
| 8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
| Full Idea: It is the quest for system and simplicity that has kept driving the scientist to posit further entities as values of his variables. By positing molecules, Boyles' law of gases could be assimilated into a general theory of bodies in motion. | |
| From: Willard Quine (On Multiplying Entities [1974], p.262) | |
| A reaction: Interesting that a desire for simplicity might lead to multiplications of entities. In fact, I presume molecules had been proposed elsewhere in science, and were adopted in gas-theory because they were thought to exist, not because simplicity is nice. |
| 8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
| Full Idea: In classical arithmetic, ratios were posited to make division generally applicable, negative numbers to make subtraction generally applicable, and irrationals and finally imaginaries to make exponentiation generally applicable. | |
| From: Willard Quine (On Multiplying Entities [1974], p.263) | |
| A reaction: This is part of Quine's proposal (c.f. Idea 8207) that entities have to be multiplied in order to produce simplicity. He is speculating. Maybe they are proposed because they are just obvious, and the generality is a nice side-effect. |
| 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. |
| 8205 | Explaining events just by bodies can't explain two events identical in space-time [Quine] |
| Full Idea: An account of events just in terms of physical bodies does not distinguish between events that happen to take up just the same portion of space-time. A man's whistling and walking would be identified with the same temporal segment of the man. | |
| From: Willard Quine (On Multiplying Entities [1974], p.260) | |
| A reaction: We wouldn't want to make his 'walking' and his 'strolling' two events. Whistling and walking are different because different objects are involved (lips and legs). Hence a man is not (ontologically) a single object. |
| 8206 | Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine] |
| Full Idea: The need to add a note of necessity to 'all black crows are black' could be met by a generalisation over classes (what belongs to sets x and y belongs to y), or maybe be quantifying over possible particulars. | |
| From: Willard Quine (On Multiplying Entities [1974], p.262) | |
| A reaction: He dislikes the second strategy because 'unactualized particulars are an obscure and troublesome lot'. The second is the strategy of Lewis. I think necessity starts to creep back in as soon as you ask WHY a generalisation holds true. |
| 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. |