These considerations indicate the method by which the deductive movement is guided. Deduction requires a system of allied ideas which may be translated into one another by regular or graded steps. The question is whether the facts that confront us can be identified as typhoid fever. To all appearances, there is a great gap between them and typhoid. But if we can, by some method of substitutions, go through a series of intermediary terms (see p. 72), the gap may, after all, be easily bridged. Typhoid may mean _p_ which in turn means _o_, which means _n_ which means _m_, which is very similar to the data selected as the key to the problem. [Sidenote: or definition and classification] One of the chief objects of science is to provide for every typical branch of subject-matter a set of meanings and principles so closely interknit that any one implies some other according to definite conditions, which under certain other conditions implies another, and so on. In this way, various substitutions of equivalents are possible, and reasoning can trace out, without having recourse to specific observations, very remote consequences of any suggested principle. Definition, general formulæ, and classification are the devices by which the fixation and elaboration of a meaning into its detailed ramifications are carried on. They are not ends in themselves--as they are frequently regarded even in elementary education--but instrumentalities for facilitating the development of a conception into the form where its applicability to given facts may best be tested.[17] [17] These processes are further discussed in Chapter IX. [Sidenote: The final control of deduction] The final test of deduction lies in experimental observation. Elaboration by reasoning may make a suggested idea very rich and very plausible, but it will not settle the validity of that idea. Only if facts can be observed (by methods either of collection or of experimentation), that agree in detail and without exception with the deduced results, are we justified in accepting the deduction as giving a valid conclusion. Thinking, in short, must end as well as begin in the domain of concrete observations, if it is to be complete thinking. And the ultimate educative value of all deductive processes is measured by the degree to which they become working tools in the creation and development of new experiences. § 5. _Some Educational Bearings of the Discussion_ [Sidenote: Educational counterparts of false logical theories] [Sidenote: Isolation of "facts"]