Questions Concerning Certain Faculties Claimed For Signs
Given that sign relations are special cases of triadic relations, we can get significant insight into the structures of both cases by examining a few simple examples of triadic relations, without getting distracted by all the extra features that come into play with sign relations.
When I’m talking about a -place relation I’ll always be thinking about a set of -tuples. Each -tuple has the form:
or, as Peirce often wrote them:
Of course, could be a set of one -tuple but that would be counted a trivial case.
That sums up the extensional view of -place relations, so far as we need it for now.
Using a single letter like to refer to a set of -tuples is already the genesis of an intensional view, since we now think of the elements of as having some property in common, even if it’s only their membership in When we turn to devising some sort of formalism for working with relations in general, whether it’s an algebra, logical calculus, or graph-theoretic notation, it’s in the nature of the task to “unify the manifold”, to represent a many as a one, to express a set of many tuples by means of a single sign. That can be a great convenience, producing formalisms of significant power, but failing to discern the many in the one can lead to no end of confusion.
To be continued …