Re: Peirce List Discussion • Helmut Raulien

The “divisor of” relation signified by is a dyadic relation on the set of positive integers so it can be understood as a subset of the cartesian product   It is an example of a partial order, whereas the “less than or equal to” relation signified by is an example of a total order relation.

The mathematics of relations can be applied most felicitously to semiotics, but here we must bump the adicity or arity up to three.  We take any sign relation to be subset of a cartesian product where is the set of objects under consideration in a given discussion, is the set of signs, and is the set of interpretant signs involved in the same discussion.

One thing we need to understand here is that the sign relation relevant to a given level of discussion can be rather more abstract than what we would call a sign process proper, that is, a structure extended through a dimension of time.  Indeed, many of the most powerful sign relations are those that generate sign processes through iteration or recursion or other operations of that sort.  When this happens, the most penetrating analysis of the sign process or semiosis in view will come through grasping the core sign relation that generates it.

Resources

• Relation Theory
• Triadic Relations
• Sign Relations
• Peirce’s 1870 Logic Of Relatives