4 ideas
10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
22001 | The real will of the cooperative will replace the 'will of the people' [Marx] |
Full Idea: Under collective property, the so called will of the people disappears in order to make way for the real will of the cooperative. | |
From: Karl Marx (Grundrisse [1876], p.563), quoted by Peter Singer - Marx 10 | |
A reaction: [from an 1874 note on Bakunin's 'Statism and Anarchy'] So how do you settle on the 'real' will of a cooperative? The travesty is when a ruling elite decide that, without consultation. An institution is needed. This is still a social contract. |
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. |