this series, 111-1/9 yards. To prove this is an _ignoratio elenchi_;
what the Sophist undertakes to prove is that Achilles will never
overtake it, and he really proves that Achilles passes it between the
111th and 112th yards.

The exposure of this sophism is an example also of the value of a
technical term. All attempts to expose it without using the term
_Ignoratio Elenchi_ or something equivalent to it, succeed only in
bewildering the student. It is customary to say that the root of the
fallacy lies in assuming that the sum of an infinite series is equal
to infinity. This profound error may be implied: but if any assumption
so hard to understand were really required, the fallacy would have
little force with the generality.

It has often been argued that the Syllogism involves a _petitio
principii_, because the Major Premiss contains the Conclusion, and
would not be true unless the Conclusion were true. But this is really
an _Ignoratio Elenchi_. The fact adduced, that the Major Premiss
contains the Conclusion, is indisputable; but this does not prove the
Syllogism guilty of Petitio. _Petitio principii_ is an argumentative
trick, a conscious or unconscious act of deception, a covert
assumption, and the Syllogism, so far from favouring this, is an
_expositio principii_, an explicit statement of premisses such that,
if they are true, the conclusion is true. The Syllogism merely shows
the interdependence of premisses and conclusion; its only tacit
assumption is the _Dictum de Omni_.

If, indeed, an opponent challenges the truth of the conclusion, and
you adduce premisses necessarily containing it as a refutation, that
is an _ignoratio elenchi_ unless your opponent admits those premisses.
If he admits them and denies the conclusion, you convict him of
inconsistency, but you do not prove the truth of the conclusion.
Suppose a man to take up the position: "I am not mortal, for I have
procured the _elixir vitae_". You do not disprove this by saying, "All
men are mortal, and you are a man". In denying that he is mortal, he
denies that all men are mortal. Whatever is sufficient evidence that
he is not mortal, is sufficient evidence that all men are not mortal.
Perhaps it might be said that in arguing, "All men are mortal, and
you are a man," it is not so much _ignoratio elenchi_ as _petitio
principii_ that you commit. But be it always remembered that you may
commit both fallacies at once. You may both argue beside the point