# The connection between the kalam argument and Zeno's paradox doesn't hold water.

## Summary

## Quotes

“A first, fairly common reaction is to compare the problem we are dealing with with the one raised by Zeno in his famous paradox concerning the infinite divisibility of space. [...] But this is not a rigorous comparison. Let's go back to the essentials: Zeno asserts that to cross any finite distance

d, you have to cross an infinite number of segments: d/2, d/4, d/8, d/16, ... which seems impossible to him, since it's "impossible to cross infinity". Zeno is certainly wrong, because the sum in question is equal to (d - d/2n), which converges to "d" when "n" tends to infinity. What is "impossible to cross" is an infinite distance - not an infinitely divisible distance. It would therefore be wrong to assert, in order to resolve the paradox, that the existence of motion proves, by the fact, that a real infinity has indeed been crossed. We don't refute Zeno by declaring that it is possible to cross real infinity, but by distinguishing two types of infinity. Segments whose length tends towards zero do not constitute discrete "stages" for the mobile, whose crossing would take more and more time; they are the simple mental division of a finite distance, covered in a finite time. What is constructed by the potentially infinite addition of segments is not an infinite distance or time, but a finite distance and time. The mere fact that the mobile has a constant speed means that they are all swallowed up in infinite time. The infinite that Zeno deals with is potential; it exists only for the mind that indefinitely divides the abstract space of geometry. This is the difference with the case we're interested in. Whereas Zeno deals with potentially infinite intervals of decreasing length, the "kalam" argument deals with equal intervals of truly infinite number. The resolution of Zeno's paradox therefore does not apply to the "kalam" argument.”

*God exists*, p.221-222, Éditions du Cerf, Paris, 2013.