-Alan Watts, Way of Zen
Even when this regression is finite, it has a name: anxiety.
"How Our Brains Think Your Brain Decides Without You"
Essentially, Achilles says "A, therefore Z." Tortoise says, "Well, suppose I don't see the connection here, you have some symbols on this side and some symbols on that side, could you help me?" So Achilles modifies this to, "A, and A implies Z, therefore Z." And the Tortoise says, "well, that sounds very good and I trust your proof that A implies Z but I'm still not seeing the connection here. Could you help me connect those left hand things to the right hand thing?" So Achilles modifies this to "A, and A implies Z, and (A and A implies Z) implies Z, therefore Z." And the Tortoise says, "aha, of course '(A and A implies Z) implies Z' ... but wait, now that I've written that down, I again don't see the connection here...". Essentially the point is that our generic rule that replaces "x and x implies y" with "x and y" is a process which lives outside the declarative scope of formal logic. (In the Curry-Howard isomorphism: you can have a value of type `x` and a function which turns values of type `x` into values of type `y`, but these are definitions, and there is no way to capture the true process of applying the function to the value -- just another declaration of another function which has type `x → (x → y) → y` which is by itself never involved in a process.)
(As an amateur physicist, I hasten to remind everyone that Zeno won in the end; there is a context which Zeno could have never foreseen where a Zeno paradox makes a certain kind of motion impossible. The reason nobody can travel faster than light is that if you take your spaceship and try to race a light beam, first you throw down a beacon, and then you accelerate to speed c/2 relative to that beacon -- in your shiny new reference frame, due to the constancy of the speed of light in inertial reference frames, the light beam is still moving at speed c away from you.)