It is easier to explain what these fallacies consist in than to illustrate them convincingly. It is chiefly in long arguments that the mischief is done. "A Fallacy," says Whately, "which when stated barely in a few sentences would not deceive a child, may deceive half the world if diluted in a quarto volume." Very rarely is a series of propositions put before us in regular form and order, all bearing on a definite point. A certain conclusion is in dispute, not very definitely formulated perhaps, and a mixed host of considerations are tumbled out before us. If we were perfectly clear-headed persons, capable of protracted concentration of attention, incapable of bewilderment, always on the alert, never in a hurry, never over-excited, absolutely without prejudice, we should keep our attention fixed upon two things while listening to an argument, the point to be proved, and the necessary premisses. We should hold the point clearly in our minds, and watch indefatigably for the corroborating propositions. But none of us being capable of this, all of us being subject to bewilderment by a rapid whirl of statements, and all of us biased more or less for or against a conclusion, the sophist has facilities for doing two things--taking for granted that he has stated the required premisses (_petitio principii_), and proving to perfect demonstration something which is not the point in dispute, but which we are willing to mistake for it (_ignoratio elenchi_). It is chiefly in the heat of argument that either Petitio or Ignoratio succeeds. When a fallacy continues to perplex us in cold blood, it must have in its favour either some deeply-rooted prejudice or some peculiar intricacy in the language used, or some abstruseness in the matter. If we are not familiar with the matter of the argument, and have but a vague hold of the words employed, we are, of course, much more easily imposed upon. The famous Sophisms of antiquity show the fascination exercised over us by proving something, no matter how irrelevant. If certain steps in an argument are sound, we seem to be fascinated by them so that we cannot apply our minds to the 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.