Psychology Dictionary of Arguments

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Space, philosophy: various discussions deal, among others, with the question whether the space is absolute or whether empty space is possible. In different sciences, multi-dimensional spaces with certain properties are used to better calculate like Hilbert spaces in the theory of relativity or multidimensional spaces in mathematical nodal theory. No ontological assumptions are made. See also substantivalism, relativism, movement, absoluteness, compactness, conceptual space, dimensions, logical space, four-dimensionalism.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Concept Summary/Quotes Sources

Zeno on Space - Dictionary of Arguments

Sainsbury V 19
Space/divisibility/Zenon: the advocate of infinite divisibility must show that he has no physical but a spiritual division in mind.
Problem: now one can assume that the parts shrink to zero, but then they cannot put together any space at all!

Division/Sainsbury: the argument of infinitely growing space (if it is composed of infinitely many parts, it is wrong: e.g. the sequence 1/2,1/4,1/8... does not become infinitely large!

V 21
The series x + x² + x³...with x = 1/2 is mathematically suspect! ...

Space/Zenon: it is controversial whether space has the same properties as numbers.

Divisibility/Sainsbury: for the space with infinitely many parts to become infinitely large, the parts must exceed a certain finite size!
Error: to derive from:

"Each part has a finite size"

to:

"There is a finite size that every part has". (>Everything/all/every/each
, >Distribution).

Also wrong: "The last pair of rectangles at the end of the row has a finite size and the preceding ones are larger". Because there is no last pair!

V 24
Space/Sainsbury: perhaps it is granular, as quantum theory assumes for energy. But Zenon does not lead us to this assumption.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Zeno
Sai I
R.M. Sainsbury