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 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.