| ---------------- | | Resistant Not-resistant (Matter) (Space) | ------------------- | | Gravitating Not-gravitating | ----------- | | Simple Compound

Having subdivided ‘Simple’ by all possible characters, we must then go back and similarly subdivide Not-phenomenal, Unextended, Not-resistant, Not-gravitating, and Compound.  Now, if we knew all possible characters, and the order of their importance, we might prepare a priori a classification of all possible things; at least, of all things that come under the principles of Contradiction and Excluded Middle.  Many of our compartments might contain nothing actual; there may, for example, be nothing that is not phenomenal to some mind, or nothing that is extended and not-resistant (no vacuum), and so forth.  This would imply a breach of the rule, that the dividing quality be not common to the whole class; but, in fact, doubts have been, and are, seriously entertained whether these compartments are filled or not.  If they are not, we have concepts representing nothing, which have been generated by the mere force of grammatical negation, or by the habit of thinking according to the principle of Excluded Middle; and, on the strength of these empty concepts, we have been misled into dividing by an attribute, which (being universal) cannot be a fundamentum divisionis.  But though in such a classification places might be empty, there would be a place for everything; for whatever did not come into some positive class (such as Gravitating) must fall under one of the negative classes (the ‘Nots’) that run down the right-hand side of the Table and of its subdivisions.

This is the ideal of classification.  Unfortunately we have to learn what characters or attributes are possible, by experience and comparison; we are far from knowing them all:  and we do not know the order of their importance; nor are we even clear what ‘important’ means in this context, whether ‘widely prevalent,’ or ‘ancient,’ or ’causally influential,’ or ‘indicative of others.’  Hence, in classifying actual things, we must follow the inductive method of beginning with particulars, and sorting them according to their likeness and difference as discovered by investigation.  The exceptional cases, in which deduction is really useful, occur where certain limits to the number and combination of qualities happen to be known, as they may be in human institutions, or where there are mathematical conditions.  Thus, we might be able to classify orders of Architecture, or the classical metres and stanzas of English poetry; though, in fact, these things are too free, subtle and complex for deductive treatment:  for do not the Arts grow like trees?  The only sure cases are mathematical; as we may show that there are possible only three kinds of plane triangles, four conic sections, five regular solids.

Sec. 5.  The rules for testing a Division are as follows: