Editing Zeno of Elea (section)

=== Plurality and space ===
Zeno rejected the idea of [[Pluralism (philosophy)|plurality]], or that more than one thing can exist.{{Sfn|Vamvacas|2009|p=151}} According to [[Proclus]], Zeno had forty arguments against plurality.{{Sfn|Vlastos|1995|p=241}}

In one argument, Zeno proposed that multiple objects cannot exist, because this would require everything to be finite and infinite simultaneously.{{Sfn|Vlastos|1995|p=241}}{{Sfn|Vamvacas|2009|p=152}} He used this logic to challenge the existence of indivisible atoms.{{Sfn|Vamvacas|2009|pp=151–152}} Though the first part of this argument is lost, its main idea is recorded by Simplicius. According to him, Zeno began the argument with the idea that nothing can have size because "each of the many is self-identical and one".{{Sfn|Vlastos|1995|pp=241–242}} Zeno argued that if objects have mass, then they can be divided.{{Sfn|Vamvacas|2009|p=152}} The divisions would in turn be divisible, and so on, meaning that no object could have a finite size, as there would always be a smaller part to take from it.{{Sfn|Vlastos|1995|p=242}} Zeno also argued from the other direction: if objects do not have mass, then they cannot be combined to create something larger.{{Sfn|Vamvacas|2009|p=152}}{{Sfn|Vlastos|1995|p=242}}

In another argument, Zeno proposed that multiple objects cannot exist, because it would require an infinite number of objects to have a finite number of objects; he held that in order for there to be a finite number of objects, there must be an infinite number of objects dividing them. For two objects to exist separately, according to Zeno, there must be a third thing dividing them, otherwise they would be parts of the same thing. This dividing thing would then itself need two dividing objects to separate it from the original objects. These new dividing objects would then need dividing objects, and so on.{{Sfn|Vlastos|1995|pp=245–246}}

As with all other aspects of existence, Zeno argued that location and [[physical space]] are part of the single object that exists as reality.{{Sfn|Vamvacas|2009|p=152}} Zeno believed that for all things that exist, they must exist in a certain point in physical space. For a point in space to exist, it must exist in another point in space.{{Sfn|Vlastos|1995|p=255}} This space must in turn exist in another point in space, and so on.{{Sfn|Vamvacas|2009|p=152}} Zeno was likely the first philosopher to directly propose that being is incorporeal rather than taking up physical space.{{Sfn|Vlastos|1995|p=259}}