## Triadic Forms of Constraint, Determination, Interaction • 2

Re: Peirce List Discussion • Gary Richmond

Here’s one way of stating what I call a constraint:

• The set $L$ is constrained to a subset of the set $M.$

Here’s one way of stating a triadic constraint:

• The set $L$ is a subset of the cartesian product $X \times Y \times Z.$

So any way we define a triadic relation we are stating or imposing a triadic constraint.

In particular, any way we define a sign relation we are stating or imposing a triadic constraint of the form:

• $L \subseteq O \times S \times I.$

where:

• $O$ is the set of all objects under discussion,
• $S$ is the set of all signs under discussion, and
• $I$ is the set of all interpretant signs under discussion.

The concepts of constraint, definition, determination, lawfulness, ruliness, and so on all have their basis in the idea that one set is contained as a subset of another set.

Among the next questions that may occur to us, we might ask:

• What bearings do these types of global constraints have on various local settings we might select?

And conversely:

• To what extent do various types of local constraints combine to constrain or determine various types of global constraint?

There are by the way such things as mutual constraints, indeed, they are very common, and not just in matters of human bondage.  So, for instance, the fact that objects constrain or determine signs in a given sign relation does not exclude the possibility that signs constrain or determine objects within the same sign relation.

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