Correct and accurate conclusions may be arrived at if we carefully observe the relation of the spheres of concepts, and only conclude that one sphere is contained in a third sphere, when we have clearly seen that this first sphere is contained in a second, which in its turn is contained in the third. On the other hand, the art of sophistry lies in casting only a superficial glance at the relations of the spheres of the concepts, and then manipulating these relations to suit our purposes, generally in the following way:—When the sphere of an observed concept lies partly within that of another concept, and partly within a third altogether different sphere, we treat it as if it lay entirely within the one or the other, as may suit our purpose. For example, in speaking of passion, we may subsume it under the concept of the greatest force, the mightiest agency in the world, or under the concept of the irrational, and this again under the concept of impotency or weakness. We may then repeat the process, and start anew with each concept to which the argument leads us. A concept has almost always several others, which partially come under it, and each of these contains part of the sphere of the first, but also includes in its own sphere something more, which is not in the first. But we draw attention only to that one of these latter concepts, under which we wish to subsume the first, and let the others remain unobserved, or keep them concealed. On the possession of this skill depends the whole art of sophistry and all finer fallacies; for logical fallacies such as mentiens, velatus, cornatus, &c., are clearly too clumsy for actual use. I am not aware that hitherto any one has traced the nature of all sophistry and persuasion back to this last [pg 064] possible ground of its existence, and referred it to the peculiar character of concepts, i.e., to the procedure of reason itself. Therefore, as my exposition has led me to it, though it is very easily understood, I will illustrate it in the following table by means of a schema. This table is intended to show how the spheres of concepts overlap each other at many points, and so leave room for a passage from each concept to whichever one we please of several other concepts. I hope, however, that no one will be led by this table to attach more importance to this little explanation, which I have merely given in passing, than ought to belong to it, from the nature of the subject. I have chosen as an illustration the concept of travelling. Its sphere partially includes four others, to any of which the sophist may pass at will; these again partly include other spheres, several of them two or more at once, and through these the sophist takes whichever way he chooses, always as if it were the only way, till at last he reaches, in good or evil, whatever end he may have in view. In passing from one sphere to another, it is only necessary always to follow the direction from the centre (the given chief concept) to the circumference, and never to reverse this process. Such a piece of sophistry may be either an unbroken speech, or it may assume the strict syllogistic form, according to what is the weak side of the hearer. Most scientific arguments, and especially philosophical demonstrations, are at bottom not much more than this, for how else would it be possible, that so much, in different ages, has not only been falsely apprehended (for error itself has a different source), but demonstrated and proved, and has yet afterwards been found to be fundamentally wrong, for example, the Leibnitz-Wolfian Philosophy, Ptolemaic Astronomy, Stahl's Chemistry, Newton's Theory of Colours, &c.[15]