Editing Zeno of Elea (section)

== Philosophy ==
{{Main|Zeno's paradoxes}}
Zeno is one of three major philosophers in the Eleatic school, along with Parmenides and [[Melissus of Samos]].{{Sfn|Vamvacas|2009|p=137}} This school of philosophy was a form of [[monism]], following Parmenides' belief that all of reality is one single indivisible object.{{Sfn|Vamvacas|2009|p=152}}{{Sfn|McGreal|2000}} Both Zeno and Melissus engaged in philosophy to support the ideas of Parmenides. While Melissus sought to build on them, Zeno instead argued against opposing ideas.{{Sfn|Vamvacas|2009|p=150}} Such arguments would have been constructed to challenge the ideas of [[Pluralism (philosophy)|pluralism]], particularly those of the [[Pythagoreans]].{{Sfn|McGreal|2000}}

Zeno was the first philosopher to use argumentative rather than descriptive language in his philosophy. Previous philosophers had explained their worldview, but Zeno was the first one to create explicit arguments that were meant to be used for debate. Aristotle described Zeno as the "inventor of [[dialectic]]".{{Sfn|Vlastos|1995|p=260}} To disprove opposing views about reality, he wrote a series of paradoxes that used ''[[reductio ad absurdum]]'' arguments, or arguments that disprove an idea by showing how it leads to illogical conclusions.{{Sfn|Vamvacas|2009|p=150}} Furthermore, Zeno's philosophy makes use of [[infinitesimal]]s, or quantities that are infinitely small while still being greater than zero.{{Sfn|Vamvacas|2009|p=156}}

Criticism of Zeno's ideas may accuse him with using [[Rhetoric|rhetorical tricks]] and [[sophistry]] rather than cogent arguments.{{Sfn|Sanday|2009|p=209}}{{Sfn|Rossetti|1988|pp=146–147}} Critics point to how Zeno describes the attributes of different ideas as absolutes when they may be contextual.{{Sfn|Sanday|2009|p=209}} He may be accused of comparing similarities between concepts, such as attributes that physical space shared with physical objects, and then assuming that they be identical in other ways.{{Sfn|Rossetti|1988|p=148}}

=== 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}}

=== Motion and time ===
Zeno's arguments against motion contrast the actual phenomena of happenings and experience with the way that they are described and perceived.{{Sfn|Sanday|2009|p=211}} The exact wording of these arguments has been lost, but descriptions of them survive through [[Aristotle]] in his ''[[Physics (Aristotle)|Physics]]''.{{Sfn|Vlastos|1995|p=248}} Aristotle identified four paradoxes of motion as the most important.{{Sfn|Vamvacas|2009|p=153}} Each paradox has multiple names that it is known by.{{Sfn|Strobach|2013|p=31}}

* ''The dichotomy'', ''the racetrack'', or ''the stadium''{{Sfn|Strobach|2013|p=30}} argues that no distance can be traveled. To cross a certain distance, one must first cross half of that distance, and to cross that distance, one must first cross half of that distance, and so on. This appears to make crossing any distance impossible, as an infinite number of acts are required to do it.{{Sfn|Vamvacas|2009|p=153}} The argument contends that any appearance of movement is simply an illusion.{{Sfn|Strobach|2013|p=34}} It is unknown whether Zeno intended for it to be impossible to start or finish crossing a certain distance.{{Sfn|Palmer|2021}}
* ''Achilles and the tortoise'', or simply ''Achilles'',{{Sfn|Strobach|2013|p=30}} argues that a swift runner such as [[Achilles]] can never catch up to a slow runner, such as a tortoise. Every time Achilles goes to where the tortoise was, the tortoise will have moved ahead, and when Achilles reaches that next point, then the tortoise will have moved ahead again, and so on. This makes it seem that Achilles can never reach the tortoise.{{Sfn|Vamvacas|2009|p=154}} ''The dichotomy'' and ''Achilles'' are two variations of the same argument, and they effectively come to the same conclusions.{{Sfn|Strobach|2013|p=31}}
* ''The flying arrow'', or simply ''the arrow'',{{Sfn|Strobach|2013|p=30}} argues that all objects must be motionless in space. If an arrow is in the air, it is stationary at any given instant by occupying a specific area in space.{{Sfn|Vamvacas|2009|p=154}}
* ''The moving rows'', also sometimes called ''the stadium'',{{Sfn|Strobach|2013|p=30}} argues that periods of time can be both halved and doubled simultaneously. It describes a row of objects passing beside other rows of objects in a stadium. If one of the opposing rows is stationary and the other is moving, then it will take a different amount of time to pass them.{{Sfn|Vamvacas|2009|p=155}}

<gallery mode="packed">
Zeno Dichotomy Paradox alt.png|The dichotomy
Zeno Achilles Paradox.png|Achilles and the tortoise
Zeno Arrow Paradox.png|The flying arrow
Zeno Moving Rows Paradox.png|The moving rows
</gallery>