The science of chemistry now depends to a great extent on a correct classification of the elements, as will be learnt by consulting the able article on Classification by Professor G. C. Foster in Watts’ Dictionary of Chemistry. But the present system of chemical classification was not reached until at least three previous false systems had been long entertained. And though there is much reason to believe that the present mode of classification according to atomicity is substantially correct, errors may yet be discovered in the details of the grouping.
Symbolic Statement of the Theory of Classification.
The theory of classification can be explained in the most complete and general manner, by reverting for a time to the use of the Logical Alphabet, which was found to be of supreme importance in Formal Logic. That form expresses the necessary classification of all objects and ideas as depending on the laws of thought, and there is no point concerning the purpose and methods of classification which may not be stated precisely by the use of letter combinations, the only inconvenience being the abstract form in which the subject is thus represented.
If we pay regard only to three qualities in which things may resemble each other, namely, the qualities A, B, C, there are according to the laws of thought eight possible classes of objects, shown in the fourth column of the Logical Alphabet (p. [94]). If there exist objects belonging to all these eight classes, it follows that the qualities A, B, C, are subject to no conditions except the primary laws of thought and things (p. [5]). There is then no special law of nature to discover, and, if we arrange the objects in any one order rather than another, it must be for the purpose of showing that the combinations are logically complete.
Suppose, however, that there are but four kinds of objects possessing the qualities A, B, C, and that these kinds are represented by the combinations ABC, AbC, aBc, abc. The order of arrangement will now be of importance; for if we place them in the order
| ABC |
| AbC |
| aBc | abc |
placing the B’s first and those which are b’s last, we shall perhaps overlook the law of correlation of properties involved. But if we arrange the combinations as follows
| ABC |
| aBc |
| AbC | abc |
it becomes apparent at once that where A is, and only where A is, the property C is to be found, B being indifferently present and absent. The second arrangement then would be called a natural one, as rendering manifest the conditions under which the combinations exist.
As a further instance, let us suppose that eight objects are presented to us for classification, which exhibit combinations of the five properties, A, B, C, D, E, in the following manner:—