Re: Ontolog Forum
Artem Kaznatcheev posted an interesting discussion on his blog under the title “Models as Maps and Maps as Interfaces” that I saw as fitting under this head. A reader of Peirce may recognize critical insights of pragmatic thought cropping up toward the end of his analysis, prompting me to add the following comment:
Map and “mirror of nature” metaphors take us a good distance in understanding how creatures represent their worlds to themselves and others. But from a pragmatic semiotic point of view we can see how these metaphors lock us into iconic forms of representation, overstretching dyadic relations, and thus falling short of the full power of triadic symbolic relations that support practical interaction with the world.
to a binary value in 
that is, a characteristic function or indicator function 
and 
the fiber of 
under 
is the set of elements denoted or indicated by the predicate. That is the semantics, anyway. As far as syntax goes, there are many formal languages whose syntactic expressions serve as names for those functions and nominally speaking one may call those names predicates.
where 
is the object domain (think universe of discourse) and 
and 
are domains of signs (think channels or languages) being used to talk and think about 
is most often applied in one of two ways.
In cases where 
we are often concerned with transformations taking place within a single set of signals and we may write 
to signify our focus on sign relational triples of the form 
where 
is a sign that follows 
in a logical or temporal sequence, in short, where 
