We continue with §3. Application of the Algebraic Signs to Logic.
The Signs for Multiplication (cont.)
The sum generally denotes no logical term. But may be considered as denoting some two ’s.
It is natural to write:
where the dot shows that this multiplication is invertible.
We may also use the antique figures so that:
Then alone will denote some two things.
But this multiplication is not in general commutative, and only becomes so when it affects a relative which imparts a relation such that a thing only bears it to one thing, and one thing alone bears it to a thing.
For instance, the lovers of two women are not the same as two lovers of women, that is:
are unequal; but the husbands of two women are the same as two husbands of women, that is:
|and in general;|
(Peirce, CP 3.75)