6 ideas
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 21686 | Sense-data are dubious abstractions, with none of the plausibility of tables [Quine] |
| Full Idea: The notion of pure sense datum is a pretty tenuous abstraction, a good deal more conjectural than the notion of an external object, a table or a sheep. | |
| From: Willard Quine (On Mental Entities [1952], p.225) | |
| A reaction: This seems to sum up the view of sense-data held by the generation after Russell and Moore. Ayer still talks about them, but Russell had already given them up. The simple challenge is - what is the evidence for their existence? Cf innate ideas. |
| 21685 | Empiricism says evidence rests on the senses, but that insight is derived from science [Quine] |
| Full Idea: The crucial insight of empiricism is that any evidence for science has its end points in the senses. This insight remains valid, but it is an insight which comes after physics, physiology, and psychology, not before. | |
| From: Willard Quine (On Mental Entities [1952], p.225) | |
| A reaction: Interesting. I think Hume and co. were probably outlining essential presuppositions and contraints which must be accepted by science. Quine offers empiricism as more like a description of science (with success as its authority?). |
| 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. |