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Full Idea
Surfaces, lines and points are not, strictly speaking, parts of space at all, but just 'limits' of certain kinds, and as such 'abstract' entities.
Gist of Idea
Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract
Source
E.J. Lowe (A Survey of Metaphysics [2002], p.254)
Book Ref
Lowe,E.J.: 'A Survey of Metaphysics' [OUP 2002], p.254
A Reaction
This is fairly crucial when dealing with Zeno's paradoxes. How many points in a line? How long to get through a point?
| 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] |