"What the Tortoise Said to Achilles", written by Lewis Carroll in 1895 for the philosophical journal Mind, 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.
- 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 accepts premises A and B as true but not the hypothetical:
- C: "If A and B are true, Z must be true" later reworked in more sober philosophical terms by W.V.O. Quine.
Editions
Reprinted:
- in the New Series of the same journal, a century later:
- in
- on a number of websites, including "What the Tortoise Said to Achilles" at Digital Text International, and "What the Tortoise Said to Achilles" at Fair Use Repository.
- on Wikisource: .
- in Reprinted as the second dialogue, entitled "Two-Part Invention – or What the Tortoise Said to Achilles", between chapters 1 and 2. Hofstadter appropriated the characters of Achilles and the Tortoise for other, original, dialogues in the book which alternate contrapuntally with prose chapters.
As audio:
See also
- Deduction theorem
- Homunculus argument
- Münchhausen trilemma
- Paradox
- Regress argument
- Rule of inference
Other works
- Gödel, Escher, Bach, a book by Douglas Hofstadter which includes this story (though retitled as "Two-Part Invention"), and original stories with the Tortoise and Achilles characters
References
Further reading
- Moktefi, Amirouche & Abeles, Francine F. (eds.). “‘What the Tortoise Said to Achilles’: Lewis Carroll's Paradox of Inference.” The Carrollian: The Lewis Carroll Journal, No. 28, November 2016. [Special issue.]