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degening t1_jeb177b wrote

Like all paradoxes it is only a problem because when proposed there was a lack of mathematics knowledge. Lets look at the paradox in a different way:

How long does it take Achilles to reach the tortoise?

One way to solve this is to just add up all the time intervals for each step. So it takes Achiiles some time, t^1 to get to point A, t^2 to get to point B and so on. Our total time, T, is then:

T= t^1 + t^2 + t^3 .... for an infinite number of intervals.

So how do we get a finite number from adding an infinite number of positive values together? Without calculus we can't solve this and hence the paradox.

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Emyrssentry t1_jeb2raq wrote

Not all paradoxes can be solved with mathematics.

This sentence is false. That's a paradox as well. It cannot be true nor false. No amount of mathematics can make it true or false, it is a logical impossibility.

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degening t1_jebeeps wrote

This is not a paradox for 2 reasons:

  1. You are assuming language is logically consistent, it is not.

  2. You are assuming logically consistent systems are also complete, they are not.

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urzu_seven t1_jedo7ql wrote

>You are assuming language is logically consistent, it is not.

You declaring something to be true (or not true) does not make it so.

Nor does the paradox (it is a paradox btw, you don't get to unilaterally define what a paradox is or is not and the above is definitely accepted as a valid paradox) depending ALL language being logically consistent, it is, in fact that language can express logically inconsistent statements that allows paradoxes.

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>You are assuming logically consistent systems are also complete, they are not.

This has literally nothing to do with the original statement OR the comment you are replying to.

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pjspui t1_jeb8yiz wrote

But there remains the problem of whether, and if so how, the hare actually does move through an infinite number of states in reality, which is why you still see some people arguing that the paradox is unresolved, or at least that it requires a more elaborate solution than pointing out that an infinite geometric series can have a finite sum (which doesn't actually need calculus, and I think was known by some Greeks slightly less Ancient than Zeno).

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