Quotes from book
What the Tortoise Said to Achilles

Name: What the Tortoise Said to Achilles
Author: Lewis Carroll

"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.

“And at last we've got to the end of this ideal racecourse! Now that you accept A and B and C and D, of course you accept Z."
"Do I?" said the Tortoise innocently. "Let's make that quite clear. I accept A and B and C and D. Suppose I still refused to accept Z?"
"Then Logic would take you by the throat, and force you to do it!" Achilles triumphantly replied. "Logic would tell you, 'You can't help yourself. Now that you've accepted A and B and C and D, you must accept Z!' So you've no choice, you see."
"Whatever Logic is good enough to tell me is worth writing down," said the Tortoise. "So enter it in your notebook, please. We will call it
(E) If A and B and C and D are true, Z must be true.
Until I've granted that, of course I needn't grant Z. So it's quite a necessary step, you see?”

Lewis Carroll book What the Tortoise Said to Achilles

"I see," said Achilles; and there was a touch of sadness in his tone.
"What the Tortoise Said to Achilles", Mind, n.s., 4 (1895), pp. 278–80