## Icon Index Symbol • 8

### Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List Discussion • Helmut Raulien

The difference between the two definitions of a $k$-place relation in the previous post is sometimes described as decontextualized versus contextualized or, in computer science lingo, weak typing versus strong typing.  The second definition is typically expressed in a peculiar mathematical idiom that starts out as follows:

A $k$-place relation is a $(k\!+\!1)$-tuple $(X_1, \ldots, X_k, L)$

That way of defining relations is a natural generalization of the way functions are defined in the mathematical subject of category theory, where the domain $X$ and the codomain $Y$ share in defining the type $X \to Y$ of the function $f : X \to Y.$

The threshold between arbitrary, artificial, or random kinds of relations and those selected for due consideration as reasonable, proper, or natural kinds tends to shift from context to context.  We usually have in mind some property or quality that marks the latter class as proper objects of contemplation relative to the end in view, and so this relates to both the intensional and the intentional views of subject matters.

To be continued …