?Interrobang! · Track 3 · middle

Ode to What the Tortoise Said to Achilles

Lewis Carroll's 1895 dialogue: Achilles asks the Tortoise to accept modus ponens. The Tortoise agrees to the premises but demands each hypothetical as a new premise first — infinitely. An ode to the infinite regress at the bottom of logic itself — the rules of inference that cannot justify their own use without using them.

Lyrics

The race is over.
The dust has settled on the road.
Achilles, you caught him.
Or so you thought.
There you sit, on a plank.
Winner and loser.

You lay out your victory.
So simple. So clean.
Two things we know are true.
Call them A. Call them B.
And from them, a third thing, Z, must follow.
Euclid said so.
The lines are drawn. The case is closed.
You lean back, hero of the swift foot.

But he just smiles that slow smile.
And asks about the space between.
"That 'must follow' part... write it down for me.
Call it C.
If A and B are true, Z must be.
A lovely thought.
But is it true?"

So you take out your notebook.
Charles Dodgson's own pen, scratching in the April quiet of 1895.
You write it down. Premise C.
Now look. A, B, and C.
The whole logical chain.
There's nowhere left to run.
The conclusion is Z. It must be.
You can feel the heat rising from the road.

But he just taps his shell.
And asks about the space between.
"That new step... write it down for me.
Call it D.
If A and B and C are true, Z must be.
A handsome rule.
But will you grant me that?"

And the page fills up.
And the sun gets low.
And you're still writing down the rules for the rules.
For the rules.
Every time you build the ladder,
he asks you to justify the rung you're standing on.
And the ground...
the very ground...
is just another premise you haven't written down yet.

Premise E.
Premise F.
The list will outlive the road.
The list will outlive your name.
He's still sitting there.
Still smiling.
And you are still writing.