error, just as our senses are fascinated
by an expert juggler. We have seen how plausibly Zeno's argument
against the possibility of motion hides a Petitio: the Fatalist
Dilemma is another example of the same sort.

If it is fated that you die, you will die whether you call in
a doctor or not, and if it is fated that you will recover, you
will recover whether you call in a doctor or not. But it must
be fated either that you die or that you recover. _Therefore_,
you will either die or recover whether you call in a doctor or
not.

Here it is tacitly assumed in the Major Premiss that the calling in
of a doctor cannot be a link in the fated chain of events. In the
statement of both the alternative conditions, it is assumed that
Fate does not act through doctors, and the conclusion is merely a
repetition of this assumption, a verbal proposition after an imposing
show of argument. "If Fate does not act through doctors, you will die
whether you call in a doctor or not."

The fallacy in this case is probably aided by our veneration for the
grand abstraction of Fate and the awful idea of Death, which absorbs
our attention and takes it away from the artful _Petitio_.

The Sophism of Achilles and the Tortoise is the most triumphant of
examples of _Ignoratio Elenchi_.

The point that the Sophism undertakes to prove is that Achilles can
never overtake a Tortoise once it has a certain start: what it really
proves, and proves indisputably, is that he cannot overtake the
Tortoise within a certain space or time.

For simplicity of exposition, let us assume that the Tortoise has 100
yards start and that Achilles runs ten times as fast. Then, clearly,
Achilles will not come up with it at the end of 100 yards, for while
he has run 100, the Tortoise has run 10; nor at the end of 110, for
then the Tortoise has run 1 more; nor at the end of 111, for then the
Tortoise has run 1/10 more; nor at the end of 111--1/10, for then the
Tortoise has gained 1/100 more. So while Achilles runs this 1/100, the
Tortoise runs 1/1000; while he runs the 1/1000, it runs 1/10000. Thus
it would seem that the Tortoise must always keep ahead: he can never
overtake it.

But the conclusion is only a confusion of ideas: all that is really
proved is that Achilles will not overtake the Tortoise while running

100 + 10 + 1 + 1/10 + 1/100 + 1/1000 + 1/10000, etc.

That is, that he will not overtake it till he has completed the sum of