Concept

What the Tortoise Said to Achilles

Summary
"What the Tortoise Said to Achilles", written by Lewis Carroll in 1895 for the philosophical journal Mind, is a brief allegorical dialogue on the foundations of logic. The title alludes to one of Zeno's paradoxes of motion, in which Achilles could never overtake the tortoise in a race. In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument. Ultimately, Achilles fails, because the clever tortoise leads him into an infinite regression. Summary of the dialogue The discussion begins by considering the following logical argument:
  • A: "Things that are equal to the same are equal to each other" (a Euclidean relation)
  • B: "The two sides of this triangle are things that are equal to the same"
  • Therefore, Z: "The two sides of this triangle are equal to each other"
The Tortoise asks Achilles whether the conclusion logically follows from the premises, and Achilles grants that it obviously do
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