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Full Idea
Points are limits of parts of space, in which case parts of space cannot be aggregates of them.
Gist of Idea
Points are limits of parts of space, so parts of space cannot be aggregates of them
Source
E.J. Lowe (The Possibility of Metaphysics [1998], 3.9)
Book Ref
Lowe,E.J.: 'The Possibility of Metaphysics' [OUP 2001], p.75
A Reaction
To try to build space out of points (how many per cc?) is fairly obviously asking for trouble, but Lowe articulates nicely why it is a non-starter.
| 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] |