When Lewis Carroll discusses a similar logical problem in &quot;What the Tortoise Said to Achilles&quot; it comes from the perspective of a Zeno paradox which cannot be resolved in the same way.<p>Essentially, Achilles says &quot;A, therefore Z.&quot; Tortoise says, &quot;Well, suppose I don&#x27;t see the connection here, you have some symbols on this side and some symbols on that side, could you help me?&quot; So Achilles modifies this to, &quot;A, and A implies Z, therefore Z.&quot; And the Tortoise says, &quot;well, that sounds very good and I trust your proof that A implies Z but I&#x27;m still not seeing the connection here. Could you help me connect those left hand things to the right hand thing?&quot; So Achilles modifies this to &quot;A, and A implies Z, and (A and A implies Z) implies Z, therefore Z.&quot; And the Tortoise says, &quot;aha, of course &#x27;(A and A implies Z) implies Z&#x27; ... but wait, now that I&#x27;ve written that down, I again don&#x27;t see the connection here...&quot;. Essentially the point is that our generic rule that replaces &quot;x and x implies y&quot; with &quot;x and y&quot; 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  <i>process</i> 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.)<p>(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&#x2F;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.)