What the Tortoise Said to Achilles

Answers

• Q10JUDGMENT

  Can a fixed procedure for reasoning settle a disagreement when the participants accept the same premises?

  No. shared premises do not compel. Shows in dialogue that a party who accepts the premises can still refuse the conclusion, because each rule of inference added as a new premise demands another rule to apply it.

  "You might," the candid hero admitted; "though such obtuseness would certainly be phenomenal. Still, the event is possible . So I must ask you to grant one more Hypothetical." "Very good. I'm quite willing to grant it, as soon as you've written it down. We will call it ( D ) If A and B and C are true, then Z must be true. "I have !" Achilles joyfully exclaimed, as he ran the pencil into its sheath. "And at last we've got to the end of this ideal race-course! 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 book, 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 .

  Mind n.s. 4, no. 14 (April 1895), pp. 278-280; Wikisource page opened, full text.