ACHILLES AND THE TORTOISE.
(Vol. ii., p. 154.)

This paradox, whilst one of the oldest on record (being attributed by
Aristotle to Zeus Eleates, B.C. 500), is one of the most perplexing,
upon first presentation to the mind, that can be selected {186} from the
most ample list. Its professed object was to disprove the phenomenon of
motion; but its real one, to embarrass an opponent. It has always
attracted the attention of logicians; and even to them it has often
proved embarrassing enough. The difficulty does not lie in proving that
the conclusion is absurd, but in _showing where the fallacy lies_. From
not knowing the precise kind of information required by [Greek:
Idiotaes], I am unwilling to trespass on your valuable space by any
irrelevant discussion, and confine myself to copying a very judicious
note from Dr. Whateley's _Logic_, 9th edit. p. 373.

"This is one of the sophistical puzzles noticed by Aldrich, but
he is not happy in his attempt at a solution. He proposes to
remove the difficulty by demonstrating that in a certain given
time, Achilles _would_ overtake the tortoise; as if any one had
ever doubted _that_. The very problem proposed, is to surmount
the difficulty of a seeming demonstration of a thing palpably
impossible; to show that _it is_ palpably impossible, is no
solution of the problem.

"I have heard the present example adduced as a proof that the
pretensions of logic are futile, since (it was said) the most
perfect logical demonstration may lead from true premises to an
absurd conclusion. The reverse is the truth; the example before