Tortoise Quotes
I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Bertrand Russell
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