Type of Media 1
Author 1
Date 7
Type of Media
Author
Indivisible Lines, 1936
By: Nicol, A. T.
Title Indivisible Lines
Type Article
Language English
Date 1936
Journal The Classical Quarterly
Volume 30
Issue 2
Pages 120-126
Categories no categories
Author(s) Nicol, A. T.
Editor(s)
Translator(s)
To summarize, Democritus, who had moved beyond the confusion between point and atom, also avoided the notion of indivisible lines. The people who confused points and atoms probably held a similar theory of motion and space. However, it was not they but Plato who proposed the existence of indivisible lines, driven by his conception of the problem of continuity. This idea, however, was not straightforward to understand, and Plato did not explain it in detail in the dialogues. Anyone reading the Timaeus and knowing that Plato believed in indivisible lines might become confused trying to locate references to them in that dialogue. It was Xenocrates who made the theory widely known, but he further complicated the issue by introducing the concept of the ideal line, potentially adding other misunderstandings. Aristotle described this as "giving in" to a dichotomy argument, which directly suggests Zeno. All this made it easy for those who did not fully grasp the theory to conflate it with the ideas of the point-atomists. The argument is as follows: if indivisible lines exist, then there must also be surfaces that are divided by those indivisible lines, and all surfaces could be reduced to indivisible surfaces. For example, if x is the length of an indivisible line, a surface measuring x by 2x could be divided into two square surfaces with sides of length x. These squares could then be divided diagonally, but no further division would be possible, as this would require either cutting the indivisible length x or creating a line shorter than x. The same logic applies to solids divided along indivisible surfaces. In this reasoning, the indivisible surface is treated as a surface bounded by indivisible lines. This has been noted by the Oxford translator. The author of περὶ ἀτόμων γραμμῶν (Peri atomōn grammōn) either realized, or was informed, that indivisible lines were essentially points but did not recognize that indivisible surfaces were lines. If there existed, alongside Plato's theory of indivisible lines, another theory positing that matter, space, and motion were composed of tiny indivisibles, it would have been easy to conflate the two ideas. The passage quoted from Peri atomōn grammōn serves as an example of such a confusion. [conclusion p. 125-126 ]

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Indivisible Lines, 1936
By: Nicol, A. T.
Title Indivisible Lines
Type Article
Language English
Date 1936
Journal The Classical Quarterly
Volume 30
Issue 2
Pages 120-126
Categories no categories
Author(s) Nicol, A. T.
Editor(s)
Translator(s) 
To summarize, Democritus, who had moved beyond the confusion between point and atom, also avoided the notion of indivisible lines. The people who confused points and atoms probably held a similar theory of motion and space. However, it was not they but Plato who proposed the existence of indivisible lines, driven by his conception of the problem of continuity. This idea, however, was not straightforward to understand, and Plato did not explain it in detail in the dialogues.

Anyone reading the Timaeus and knowing that Plato believed in indivisible lines might become confused trying to locate references to them in that dialogue. It was Xenocrates who made the theory widely known, but he further complicated the issue by introducing the concept of the ideal line, potentially adding other misunderstandings. Aristotle described this as "giving in" to a dichotomy argument, which directly suggests Zeno. All this made it easy for those who did not fully grasp the theory to conflate it with the ideas of the point-atomists.

The argument is as follows: if indivisible lines exist, then there must also be surfaces that are divided by those indivisible lines, and all surfaces could be reduced to indivisible surfaces. For example, if x is the length of an indivisible line, a surface measuring x by 2x could be divided into two square surfaces with sides of length x. These squares could then be divided diagonally, but no further division would be possible, as this would require either cutting the indivisible length x or creating a line shorter than x. The same logic applies to solids divided along indivisible surfaces.

In this reasoning, the indivisible surface is treated as a surface bounded by indivisible lines. This has been noted by the Oxford translator. The author of περὶ ἀτόμων γραμμῶν (Peri atomōn grammōn) either realized, or was informed, that indivisible lines were essentially points but did not recognize that indivisible surfaces were lines.

If there existed, alongside Plato's theory of indivisible lines, another theory positing that matter, space, and motion were composed of tiny indivisibles, it would have been easy to conflate the two ideas. The passage quoted from Peri atomōn grammōn serves as an example of such a confusion. [conclusion p. 125-126 ]

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