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Full Idea
If the midpoint on a line between the chair and the window is five feet from the end of the bookcase. This can be true, but if no object occupies that midpoint, then unoccupied points exist
Gist of Idea
We can identify unoccupied points in space, so they must exist
Source
Robin Le Poidevin (Travels in Four Dimensions [2003], 03 'Lessons')
Book Ref
Le Poidevin,Robin: 'Travels in Four Dimensions' [OUP 2003], p.40
A Reaction
We can also locate perfect circles (running through fairy rings, or the rings of Saturn), so they must also exist. But then we can also locate the Loch Ness monster. Hm.
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| 16962 | Whitehead replaced points with extended regions [Whitehead, by Quine] |
| 14160 | Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell] |
| 18970 | The concept of a 'point' makes no sense without the idea of absolute position [Quine] |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| 17707 | We should regard space as made up of many tiny pieces [Feynman, by Mares] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| 3334 | Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA] |
| 22922 | We can identify unoccupied points in space, so they must exist [Le Poidevin] |
| 22924 | If spatial points exist, then they must be stationary, by definition [Le Poidevin] |
| 8269 | Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe] |
| 4227 | Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe] |
| 17708 | Maybe space has points, but processes always need regions with a size [Mares] |