Submitted by PerfectSociety in Philosophy

What the paradox is trying to communicate is that at any particular instant in time the arrow does not traverse any distance. The problem uncovered by the paradox of the arrow in this case is quite simple: Because there are an infinite number of instances where at each instant distance traversed=0...how can it be that taking the sum of distances traversed at each instant results in some quantity of traversed distance other than 0? Adding 0 to itself an infinite number of times should still equal 0 right?

In math, we can prove that a line segment is comprised of infinite points (each point has a length of 0). Is this type of proof able to resolve Zeno's Paradox of the Arrow?

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surreal wrote

tell me more, i've only started reading about dialetheism and stuff.

isn't the sum of infinite zeros still zero? Why is the length zero if we split it in infinite segments and not just infinitely small length? maybe the length of each segment is zero and not zero at the same time?

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PerfectSociety OP wrote

tell me more, i've only started reading about dialetheism and stuff.

Same.

isn't the sum of infinite zeros still zero?

So that's the question at hand. The Arrow Paradox involves looking at instants of time, i.e. when the interval of time is 0 rather than some incredibly small number like Planck time. At a particular instant in time, the Arrow does not traverse any distance. So the problem that the paradox brings forth is that if at each instant in time the distance traversed is 0, then how can it be that when you add the distances traversed from all the instants together you get some non-zero answer? (This is basically your question.)

I've been told by another person that measure theory resolves this, because we can prove in math that a line segment is comprised of an infinite number of points and each point has 0 length and 0 width. If this is the case - that an infinite number of points each with 0 length can, when added together, create a non-zero length (the length of the line segment) - then the same kind of logic could apply to the Arrow Paradox thus resolving it.

I don't find this particularly intuitive, but that's why I'm asking about it here to see if others can take a crack at it.

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