Page:The kernel and the husk (Abbott, 1886).djvu/72

56 connected in such a way that a conclusion can be drawn from them. But even here Imagination plays a part: for the conclusion of every syllogism (roughly speaking) depends upon the following axiom: "If a is included in b, and b is included in c, then a is included in c; in other words, if a watch is in a box, and the box is in a room, then the watch is in the room." Now this general proposition, like all general propositions, is arrived at with the aid of the Imagination, so that we may fairly say that the Imagination, helps to lay the foundation of the Syllogism. When therefore you bear in mind that in every Syllogism the Premises are often the result of an Induction in which Imagination has played a part, and that the conclusion always depends upon an axiom of the Imagination, you must admit that even Deductive Reasoning by no means excludes the Imagination.

(iii) Practically, errors seldom arise, and truth is seldom discovered, from mere Deductive Reasoning. Any one can see his way through a logical Syllogism, and almost any one can lay his finger on the weak point in an illogical one. But the difficulty is to start the Reasoning in the right direction and to begin the Logical Chain with an appropriate Syllogism.

For example, suppose we wish to prove that "every triangle which has two angles equal, has two sides opposite to them equal": how can our Reason, our discriminative faculty, help us here? At present, not at all. We must first call to our aid the Imagination, which says to us, "Imagine the triangle with two equal angles to have two unequal sides opposite to them, and see what follows." And every one who has done a geometrical Deduction knows that we frequently start by "imagining" the conclusion to be already proved, or the problem to be already performed, and then endeavouring to realise, among the many consequences that would follow, which of those