Constraints and Indications

[Jon Awbrey]

Constraints and Indications • 1
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

All,

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 the entire complex of concepts.

Entwined with the concept of “constraint” is the concept of “information”,
the power signs bear to reduce uncertainty and advance inquiry. Asking what
consequences those ideas have for Peirce’s theory of triadic sign relations
led me some years ago to the thoughts recorded on the following page.

Pragmatic Semiotic Information
• https://oeis.org/wiki/Pragmatic_Semiotic_Information

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 how W. Ross 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 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.

Reference —

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

Regards,

Jon

cc: https://www.academia.edu/community/VrKv7y