A ~ B.
We may now represent the same judgment by the assertion that A agrees with those things which differ from B, or that A agrees with the not-B’s. Using our notation for negative terms (see p. [14]), we obtain
A = Ab
as the expression of the ordinary negative proposition. Thus if we take A to mean quicksilver, and B solid, then we have the following proposition:—
Quicksilver = Quicksilver not-solid.
There may also be several other classes of negative propositions, of which no notice was taken in the old logic. We may have cases where all A’s are not-B’s, and at the same time all not-B’s are A’s; there may, in short, be a simple identity between A and not-B, which may be expressed in the form
A = b.
An example of this form would be
Conductors of electricity = non-electrics.
We shall also frequently have to deal as results of deduction, with simple, partial, or limited identities between negative terms, as in the forms