Written by Lewis Caroll in 1895.


  • The Tortoise assumes a proposition and a material conditional .

    • The exact and aren’t important to the moral of the story, though it’s something like “If and (), then ()”
    • 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 .

    • He says that logic obliges you to acknowledge 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: .
  • Achilles says that, now, you really have to accept , given that you’re committed to:

    • .
  • But the Tortoise notes that, if taking those three propositions and concluding is really something logic obliges one to do, then it bears writing down:

  • 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 un-get-over-able 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)