more from this thinker | more from this text
Full Idea
Infinitesimals do not stand in a determinate order relation to zero: we cannot say an infinitesimal is either less than zero, identical to zero, or greater than zero. ….Infinitesimals are so close to zero as to be theoretically indiscriminable from it.
Gist of Idea
Infinitesimals do not stand in a determinate order relation to zero
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 7.4)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.215
| 21382 | Things get smaller without end [Anaxagoras] |
| 18081 | Nature uses the infinite everywhere [Leibniz] |
| 18080 | A tangent is a line connecting two points on a curve that are infinitely close together [Leibniz] |
| 18091 | Infinitesimals are ghosts of departed quantities [Berkeley] |
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| 18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 18834 | Infinitesimals do not stand in a determinate order relation to zero [Rumfitt] |