term by striking out their indifferent part. It is really a process of substitution which enables us to do this; for having any proposition of the form
A = ABC ꖌ AB c , (1)
we know by the Law of Duality that
AB = ABC ꖌ AB c . (2)
As the second member of this is identical with the second member of (1) we may substitute, obtaining
This process of reducing useless alternatives may be applied again and again; for it is plain that
communicates no more information than that A is B. Abstraction of indifferent terms is in fact the converse process to that of development described in p. 89; and it is one of the most important operations in the whole sphere of reasoning.
The reader should observe that in the proposition
we cannot abstract C and infer
but from
we may abstract all reference to the term C.
It ought to be carefully remarked, however, that alternatives which seem to be without meaning often imply important knowledge. Thus if I say that “a triangle is a three-sided rectilinear figure, with or without three equal angles,” the last alternatives really express a property of triangles, namely, that some triangles have three equal angles, and some do not have them. If we