On Norm Commitment and Rule-Following

In thinking about Wittgenstein's Philosophical Investigations, is it useful to think further about commitment to norms?

Norm Collapse

Under which conditions do norms lose their "power"? We might better articulate this question in the following ways:

1. When do norms cease being norms?
2. When do norms lose their enforceability?
3. When do norms stop being rules that are followed?

Consider, for example, laws that no one enforces or follows.

Consider languages that are in complete disuse, each of their grammatical rules abandoned (though they exist in ancient textbooks).

Below, we will consider these questions through the lens of Norm Commitment and attempt to define this more robustly.

Norm Commitment

Given the following kind of expression in a Deontic Modal Logic:

• ◊□A (e.g. - "It is possibly obligatory that A.")

We might append a number Φ ∈ [0,1] representing degree of commitment to that moral expression. For example:

1. At 1, the expression is thoroughly determinate, perfectly clear, perfectly consistent in being obeyed and enforced.
2. At .5, the expression is subject to intentional linguistic ambiguity and vagueness.
3. At 0, the expression is contradicted (or ¬◊□A), treated as if it were false, subject to extremely vagueness and intentional ambiguity, etc.

I don't think this is merely a mathematical construction, we see varying degrees of commitment to norms all the time. Whether in law, religion, or elsewhere.

This small technical extension added to the basic edifice Deontic Modal Logic gives us the ability to understand norms more fully.

Motivation and Norm Commitment

I think this technical edifice can be used to supplement certain applied considerations in the sub-discipline called Practical Philosophy (which is primarily interested in modelling instrumental reasoning and theories of motivation backed by science).

Motivation, at least with respect to norm commitment, can be partly modelled using these simple techniques and linked to the perhaps more interesting theories of motivation elsewhere.

It's particularly interesting to think about motivation but coming at it from the other angle:

If there were perfect norm commitment, would we be concerned with motivation at all?