The principles of the author's theory of classification are summarized, and the necessity of expressing true relations between concepts in a classification is stressed. The logical faults in existing classifications (especially U.D.C., Bliss, and Colon) are discussed in comparison. The psychological and logical bases of the author's theory are considered in greater detail than before, especially as regards the derivation of the operators. In this connexion a change has been found necessary in the writing of the reaction operator, being A/—B, for B acts on A (instead of A—/B). Four new operators are introduced, being ‘dimensional’ (time and space, &c.), ‘comparison’, ‘association’, and ‘concurrence’, the last three on a basis of learning theory and work on conditioned responses in psychology. Examples are given of their uses. Operators represent logical relations, and their meanings, in everyday language, are discussed. The selection of a preferred order for the construction of a classification is shown to be possible on a logical basis, being the fully deductive order. The problem of notation is then dealt with in detail. It is shown that a fully elastic ‘deductive’ notation, allowing extrapolation and interpolation in all ways, not achieved in other classifications, is possible, but still does not meet the requirements of inductive classification. A notation is developed which provides arbitrary symbols for isolates, connected by operator symbols, and this is shown to be the only solution which meets all the requirements for expressing an inductive classification according to the author's theory.
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