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Single Idea 10863
[filed under theme 27. Natural Reality / C. Space / 3. Points in Space
]
Full Idea
Cantor proved that one-dimensional space has exactly the same number of points as does two dimensions, or our familiar three-dimensional space.
Gist of Idea
Cantor proved that three dimensions have the same number of points as one dimension
Source
report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14
Book Ref
Clegg,Brian: 'Infinity' [Robinson 2003], p.183
The
13 ideas
with the same theme
[minimal units that make up space]:
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]
|