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The philosophers of the Eleatic school, analyzing the nature of the movement, came to this paradox: in order for the body to move, it needs emptiness. But what is emptiness? This is what exists, but has no properties and doesn't manifest itself in any way. If emptiness exists, then it can not be known, because it is nothing and doesn't contain any being in itself. Hence, emptiness is something existing and at the same time, not existing. Thus, the assumption of the existence of motion leads to a logical contradiction. Where is the error in this reasoning?

  • Emptiness is the lack of "properties"; it is (?) what remains when the (existing) body is removed. – Mauro ALLEGRANZA Nov 4 '17 at 17:54
  • According to the Eleatics it required void; Aristotle argued against this in a sequence of five arguments and refined that concept to the notion of place. – Mozibur Ullah Nov 5 '17 at 1:36
  • Physics-ly, you're talking about a vacuum. A (non-physics) solution is to imagine the universe is filled with ether, so motion just moves around objects and ether (just like dropping a heavy rock into a pond displaces water)-- objects don't have to move through empty space. – barrycarter Nov 5 '17 at 12:30
  • As history shows, for as long as we reify the things that move this paradox will not go away. . – PeterJ Nov 7 '17 at 14:16
  • Looking at the answers, it may help to add an explaination of what "emptiness" means to a philosopher of the Eleatic school. While it would be nice if the only answers given were from people who knew this, it looks like you may get better answers if you provide people this detail (disclaimer: I don't know what it means to them either). From my little reading on them, it looks like their school (which included the famous Zeno from Zeno's paradox) focused on challenging others' assumptions rather than providing new models. Zeno's work wasn't really put to rest until Calculus. – Cort Ammon - Reinstate Monica Nov 8 '17 at 0:48
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The paradox comes about because there are several statements that are not true. Lets start by examining each, one at a time:
1- In order to move, a body needs emptiness (void, space); true.
2- Emptiness (void, space) is what "exists," that has no properties and doesn't manifest itself in any way; false, (it has length, we can see and feel emptiness (void,space).
3- If emptiness exists, then it can not be known; false, (it can be seen and felt).
4- Because it is nothing; false, it is something, it contains (itself, void, space).
5- Hence, emptiness is something existing, and at the same time not existing; false, second part of statement is false.
Thus, the assumption that a body needs emptiness (void,space) to move, does not lead to a paradox.

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An emptiness clearly has a size. The degree to which something can move obviously depends upon the size of the emptiness into which it will be moving.

So it is not devoid of properties, and has some aspects of being. Thus it is not an example of being and not being at the same time.

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If emptiness exists, then it can not be known, because it is nothing and doesn't contain any being in itself.

It is possible to define an empty set and know that it has no content.

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    The empty set, however has nothing to do with movement. – user9166 Nov 7 '17 at 20:42
  • I was replying to the quoted sentence. The broad wording covers a lot more territory than is needed to reveal an error in reasoning. The wording addresses issues unrelated to movement. – Mark Andrews Nov 8 '17 at 5:25
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I agree with jobermark you cannot have a definition of emptiness without a definition of fullness and there is no definition without it. Everything else is a degree of these extremes. Cannot imagine movement in either extremety only the degrees in between.

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Let me take a different tack than other respondents.

What is emptiness? It is the metaphorical space in a container.

In fact, motion through space is understood by a conceptual metaphor called Containment which is a hint at how neurons organize themselves at the neurocomputational level. In essence, metaphysical presuppositions that lead to these contradictions you state (and Zeno gave at length), are actually properties of how the brain constructs experience. What does it mean for something to "exist"? Did the atom "exist" before the mind conceived it? These require you to adequately disambiguate whether you are referring to an "atom" or an atom, the former a representation within our heads and the latter to das Ding an sich.

The questions you are asking are answered in different ways depending on your metaphysics which might be naive realism, transcendental idealism, or philosophical realism. As you begin to piece together a collection of propositions that satisfy your biases, you'll have a theory, and if that theory is both rational and empirical, you'll graduate to analytical philosopher!

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