The system-theoretic concept of “constraint” is one that unifies a manifold of other notions — definition, determination, habit, information, law, predicate, regularity, and so on. Indeed, it is often the best way to understand those concepts.
Something in what you wrote brought this little essay of mine to mind:
Here I am thinking of the concept of constraint that constitutes one of the fundamental ideas of classical cybernetics and mathematical systems theory.
For example, here is the way Ashby introduces the concept of constraint in his Introduction to Cybernetics (1956).
A most important concept, with which we shall be much concerned later, is that of constraint. It is a relation between two sets, and occurs when the variety that exists under one condition is less than the variety that exists under another. Thus, the variety of the human sexes is 1 bit; if a certain school takes only boys, the variety in the sexes within the school is zero; so as 0 is less than 1, constraint exists. (1964 ed., p. 127).
At its simplest, then, constraint is just an aspect of the subset relation.
The objective of an agent, organism, or similar regulator is to keep within its viable region, a particular subset of its possible state space. That is the constraint of primary interest to the agent.
Incidentally, Ashby’s book, in my estimation still the best introduction to classical cybernetics going, is available online in PDF form:
- Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK. Online.