Pivotal moments in one’s intellectual development come unexpectedly. For me the key moment arrived in 9th grade English class when Miss Blumenstock gave a brief run-down of Zeno’s “theory of motion” [see footnote] and asked us to write a paper supporting or refuting him. Never could I have guessed it would lead to atheism.
That is exactly where it led, though it would take 5 1/2 years to get there.
Zeno’s “theory”, as she presented it, was that motion was not continuous but rather consisted of discrete segments. The path of an arrow shot across the horizon would actually, according to Zeno, not be smooth (although it might appear so to our eyes) but would in fact jump from segment to segment.
Why didn’t Zeno think motion was smooth and continuous? The answer is mathematics. Zeno realized there could not be an actual infinity of numbers between point a and point b on a numberline: numbers by their nature were inherently finite and countable, and therefore the path of an arrow across the sky had to consist of finite, countable steps.
If we think about it, we realize Zeno’s arrow was an early call for the Cosmological argument, which hinges on the assertion that there cannot be an actual infinity. There can’t be, per the Cosmological argument, an infinite regress of physical causes and there can’t be, per Zeno, an infinite number of steps in the motion of any object.
Just as there are two types of infinity — the macro infinity of going on and on to higher numbers and the micro infinity of more numbers between any two numbers on a number line — so there are two types of physical infinities which one can deny in the world. Zeno denied one, the Cosmological argument denies the other. Continue reading