Proving rules

There is a saying that 'the exception proves the rule'.  I used to find this very puzzling when I was young.

It means (I think) that an exception which honours the purpose of the rule helps us to understand how to follow it 'properly'.

In a Dworkinesque example, the rule 'do not walk on the grass' is made intelligible by the exception of the gardener's behaviour.  Because the gardener can walk on the grass, we understand the rule as having the purpose of preserving the lawn, and this helps us to follow it:  it makes it more intelligible even though (apparently) less universal - less mechanical.

If we want to construct a machine, however, we do not need intelligible rules, we need reliable rules.  We need to be able to use the rules to predict the behaviour of the machine.  Production line manufacturing, particularly in it's earliest manifestations, increased control and predictability, as well as efficiency (although efficiency dominated the PR).  A human production line worker is expected to behave in a machine-like way.

I expect that the tacit negotiations of just how machine-like would reflect important aspects of the power structures of particular institutions.

A  syntactical, mathematical, or 'physical' rule can look machine-like.  It operates over a restricted domain, and has explicit outcomes for all the possibilities within that domain.  It is 'embedded' in the description of the domain.  When we explain 'mass', we also explain 'acceleration' and 'force'.  We can write down some equations which exhaust these concepts and their interactions.

There are appropriate and inappropriate ways of applying this 'formalism' to the 'real world', of course, and the rules for doing this have to be intelligible rather than computationally reliable.