more from this thinker | more from this text
Full Idea
That complete space …has three dimensions, and that space in general cannot have more, is built on the proposition that not more than three lines can intersect at right angles in a point.
Gist of Idea
Space must have three dimensions, because only three lines can meet at right angles
Source
Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 285)
Book Ref
Kant,Immanuel: 'Prolegomena to Any Future Metaphysic', ed/tr. Lucas,Peter G. [Manchester UP 1971], p.40
A Reaction
Modern geometry seems to move, via the algebra, to more than three dimensions, and then battles for an intuition of how that can be. I don't know how they would respond to Kant's challenge here.
| 13180 | Space is the order of coexisting possibles [Leibniz] |
| 17736 | We can't learn of space through experience; experience of space needs its representation [Kant] |
| 5531 | Space is an a priori necessary basic intuition, as we cannot imagine its absence [Kant] |
| 16922 | Space must have three dimensions, because only three lines can meet at right angles [Kant] |
| 24096 | Unlike time, space is subjective. Empty space was assumed, but it doesn't exist [Nietzsche] |
| 6468 | There is 'private space', and there is also the 'space of perspectives' [Russell] |
| 7552 | Six dimensions are needed for a particular, three within its own space, and three to locate that space [Russell] |
| 15321 | Space can't be an individual (in space), but it is present in all places [Harré/Madden] |
| 21112 | Empty space contains a continual flux of brief virtual particles [Krauss] |
| 9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |
| 10683 | We could ignore space, and just talk of the shape of matter [Hossack] |
| 19947 | Hilbert Space is an abstraction representing all possible states of a quantum system [New Sci.] |