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Peirce is here observing what we might dub a "contingent morphism" or a "skeptraphotic arrow", if you will.  Provided that a certain condition, to be named and, what is more hopeful, to be clarified in short order, happens to be satisfied, we would find it holding that the "number of" map ''v'' : ''S'' → '''R''' such that ''vs'' = [''s''] serves to preserve the multiplication of relative terms, that is as much to say, the composition of relations, in the form:  [''xy''] = [''x''][''y''].

Peirce is here observing what we might call a ''contingent morphism''.  Provided that a certain condition, to be named in short order, happens to be satisfied, we would find it holding that the "number of" map <math>v : S \to \mathbb{R}</math> such that <math>v(s) = [s]\!</math> serves to preserve the multiplication of relative terms, that is to say, the composition of relations, in the form:  <math>[xy] = [x][y].\!</math>

So let us try to uncross Peirce's manifestly chiasmatic encryption of the condition that is called on in support of this preservation.

So let us try to uncross Peirce's manifestly chiasmatic encryption of the condition that is called on in support of this preservation.