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. |
| 8824 | No one has defended translational phenomenalism since Ayer in 1940 [Ayer, by Kim] |
| Full Idea: I know of no serious defence of 'translational phenomenalism' since Ayer's in 1940. | |
| From: report of A.J. Ayer (The Foundations of Empirical Knowledge [1940]) by Jaegwon Kim - What is 'naturalized epistemology'? 303-4+n | |
| A reaction: We can think of Ayer as a hero who explored how far extreme empiricism would go. We still have anti-realists who are singing from a revised version of the song-sheet. Personally I am with Russell, that we must embrace the best explanation. |
| 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. |
| 15251 | The attribution of necessity to causation is either primitive animism, or confusion with logical necessity [Ayer] |
| Full Idea: How are we to explain the word 'must' [about causation]? The answer is, I think, that it is either a relic of animism, or else reveals an inclination to treat causal connexion as if it were a form of logical necessity. | |
| From: A.J. Ayer (The Foundations of Empirical Knowledge [1940], IV.18) | |
| A reaction: The animism proposal just about makes sense (as a primitive feature of minds), but why would anyone, if they had the time and understanding, dream of treating a regular connection as a 'logical' necessity? |
| 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. |