7 ideas
| 21546 | We can't sharply distinguish variables, domains and values, if symbols frighten us [Russell] |
| Full Idea: Whoever is afraid of symbols can hardly hope to acquire exact ideas where it is necessary to distinguish 1) the variable in itself as opposed to its value, 2) any value of the variable, 3) all values, 4) some value. | |
| From: Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905], p.84) | |
| A reaction: Not the best example, perhaps, of the need for precision, but a nice illustration of the new attitude Russell brought into philosophy. |
| 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. |
| 21531 | Common sense agrees with Meinong (rather than Russell) that 'Pegasus is a flying horse' is true [Lackey on Russell] |
| Full Idea: Meinong's theory says that 'Pegasus is a flying horse' is true, while Russell's says that this assertion is false. The average man, if he knows his mythology, would probably agree with Meinong. | |
| From: comment on Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.19 | |
| A reaction: It seems obvious that some disambiguation is needed here. Assenting to that assertion would be blatantly contextual. No one backs Pegasus at a race track. |
| 21545 | I prefer to deny round squares, and deal with the difficulties by the theory of denoting [Russell] |
| Full Idea: I should prefer to say that there is no such object as 'the round square'. The difficulties of excluding such objects can, I think, be avoided by the theory of denoting. | |
| From: Bertrand Russell (Review: Meinong 'Untersuchungen zur..' [1905], p.81) | |
| A reaction: The 'theory of denoting' is his brand new theory of definite descriptions, which makes implicit claims of existence explicit, so that they can be judged. Why can't we just say that a round square can be an intentional object, but not a real object? |
| 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. |