We may sum up this discussion by saying that mathematical inference consists in attaching the same reactions to two different groups of signs, whose meanings are fixed by convention in relation to their constituent parts, whereas induction consists, first, in taking something as a sign of something else, and later, when we have learned to take A as a sign of B, in taking A as also a sign of C. Thus the usual cases of induction and deduction are distinguished by the fact that, in the former, the inference consists in taking one sign as a sign of two different things, while in the latter the inference consists in taking two different signs as signs of the same thing. This statement is a little too antithetical to be taken as an exact expression of the whole truth in the matter. What is true, however, is that both kinds of inferences are concerned with the relation of a sign to what it signifies, and therefore come within the scope of the law of association. CHAPTER VIII KNOWLEDGE BEHAVIOURISTICALLY CONSIDERED The word “knowledge”, like the word “memory”, is avoided by the behaviourist. Nevertheless there is a phenomenon commonly called “knowledge”, which is tested behaviouristically in examinations. I want to consider this phenomenon in this chapter, with a view to deciding whether there is anything in it that the behaviourist cannot deal with adequately. It will be remembered that, in Chapter II, we were led to the view that knowledge is a characteristic of the complete process from stimulus to reaction, or even, in the cases of sight and hearing, from an external object to a reaction, the external object being connected with the stimulus by a chain of physical causation in the outer world. Let us, for the moment, leave on one side such cases as sight and hearing, and confine ourselves, for the sake of definiteness, to knowledge derived from touch.