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Single Idea 14160
[filed under theme 27. Natural Reality / C. Space / 3. Points in Space
]
Full Idea
I won't discuss whether points are unities or simple terms, but whether space is an aggregate of them. ..There is no geometry without points, nothing against them, and logical reasons in their favour. Space is the extension of the concept 'point'.
Gist of Idea
Space is the extension of 'point', and aggregates of points seem necessary for geometry
Source
Bertrand Russell (The Principles of Mathematics [1903], §423)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.445
The
13 ideas
with the same theme
[minimal units that make up space]:
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10863
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Cantor proved that three dimensions have the same number of points as one dimension
[Cantor, by Clegg]
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16962
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Whitehead replaced points with extended regions
[Whitehead, by Quine]
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14160
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Space is the extension of 'point', and aggregates of points seem necessary for geometry
[Russell]
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18970
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The concept of a 'point' makes no sense without the idea of absolute position
[Quine]
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17811
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The natural conception of points ducks the problem of naming or constructing each point
[Kreisel]
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17707
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We should regard space as made up of many tiny pieces
[Feynman, by Mares]
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18257
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Why should the limit of measurement be points, not intervals?
[Dummett]
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3334
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Rationalists see points as fundamental, but empiricists prefer regions
[Benardete,JA]
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22922
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We can identify unoccupied points in space, so they must exist
[Le Poidevin]
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22924
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If spatial points exist, then they must be stationary, by definition
[Le Poidevin]
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8269
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Points are limits of parts of space, so parts of space cannot be aggregates of them
[Lowe]
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4227
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Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract
[Lowe]
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17708
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Maybe space has points, but processes always need regions with a size
[Mares]
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