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.
The most influential pragmatist work in the philosophy of logic.
- 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)