Written by Lewis Caroll in 1895.
Summary

The Tortoise assumes a proposition $p$ and a material conditional $p⟹q$.
 The exact $p$ and $q$ aren’t important to the moral of the story, though it’s something like “If $A=B$ and $B=C$ ($p$), then $A=C$ ($q$)”
 The Tortoise is playing a game: I’ll do anything you tell me to do, so long as you make explicit the rule you’re asking me to follow.

Achilles tries to convince the Tortoise to accept $q$.
 He says that logic obliges you to acknowledge $q$ in this case.

The Tortoise is willing to go along with this but demands that this rule be made explicit:
 Achilles adds an extra axiom: $p∧(p⟹q)⟹q$.

Achilles says that, now, you really have to accept $q$, given that you’re committed to:
 $p$
 $p⟹q$
 $p∧(p⟹q)⟹q$.

But the Tortoise notes that, if taking those three propositions and concluding $q$ is really something logic obliges one to do, then it bears writing down:
 $p∧(p⟹q)∧(p∧(p⟹q))⟹q$

This can go ad infinitum; the Tortoise wins.
Brandom commentary

The most influential pragmatist work in the philosophy of logic.

The lesson:
 in any particular case, you can substitute a rule (that tells you you can go from this to that) with an axiom.
 But there have got to be some moves you can make without having to explicitly license them by a principle.
 I.e. you’ve got to distinguish between 1.) premises from which to reason 2.) principles in accordance with which to reason.

This teaches an ungetoverable lesson about the necessity for an implicit practical background of making some moves that are just okay. Things that would be put in a logical system, not in the forms of axioms, but in the form of rules.
(This is from one of Brandom’s lectures on Sellars)