One more point remains to be considered to complete our outline of the Aristotelian theory of knowledge. The sciences have "principles" which are discerned to be true by immediate inspection. But what if one man professes to see the self-evident truth of such an alleged principle, while another is doubtful of its truth, or even denies it? There can be no question of silencing the objector by a demonstration, since no genuine simple principle admits of demonstration. All that can be done, _e.g._ if a man doubts whether things equal to the same thing are equal to one another, or whether the law of contradiction is true, is to examine the consequences of a denial of the axiom and to show that they include some which are false, or which your antagonist at least considers false. In this way, by showing the falsity of consequences which follow from the denial of a given "principle," you indirectly establish its truth. Now reasoning of this kind differs from "science" precisely in the point that you take as your major premiss, not what you regard as true, but the opposite thesis of your antagonist, which you regard as false. Your object is not to prove a true conclusion but to show your opponent that _his_ premisses lead to false conclusions. This is "dialectical" reasoning in Aristotle’s sense of the word, _i.e._ reasoning not from your own but from some one else’s premisses. Hence the chief philosophical importance which Aristotle ascribes to "dialectic" is that it provides a method of defending the undemonstrable axioms against objections. Dialectic of this kind became highly important in the mediæval Aristotelianism of the schoolmen, with whom it became a regular method, as may be seen _e.g._ in the _Summa_ of St. Thomas, to begin their consideration of a doctrine by a preliminary rehearsal of all the arguments they could find or devise against the conclusion they meant to adopt. Thus the first division of any article in the _Summa Theologiæ_ of Thomas is regularly constituted by arguments based on the premisses of actual or possible antagonists, and is strictly dialectical. (To be quite accurate Aristotle should, of course, have observed that this dialectical method of defending a principle becomes useless in the case of a logical axiom which is presupposed by all deduction. For this reason Aristotle falls into fallacy when he tries to defend the law of contradiction by dialectic. It is true that if the law be denied, then any and every predicate may be indifferently ascribed to any subject. But until the law of contradiction has been admitted, you have no right to regard it as absurd to ascribe all predicates indiscriminately to all subjects. Thus, it is only assumed laws which are _not_ ultimate laws of logic that admit of dialectical justification. If a truth is so ultimate that it has either to be recognised by direct inspection or not at all, there can be no arguing at all with one who cannot or will not see it.)