An open-and-shut system essentially works to reinforce a
pre-existing function or provide secondary rhetorical support for
a system.

It works within the assumptions already present in the system,
and returns the same argument or standards already existing
within the system.

In its archetypal form it may follow 2 - 4 steps, which adopt the
following rules:

If it follows 4 steps, the logic supports the entirety of a system
whose function is generally taken-for-granted. For example, it
may provide additional explanations of something previously
unexplained, typically through cycles such as cycles of nature.
Thus, the first of three types of open-and-shut systems is a
circular process that serves an explanatory function.

If it follows 3 steps it is often not natural, but metaphysical. One
extreme case is considered, with its natural extension, but
another opposite extreme case is introduced leading back to the
original argument. This may be seen as a dialectical argument
often with the effect of supporting the least contested system.

If it follows 2 steps it is often not natural or metaphysical, but
transcendental. The first of the two steps involves special insight
into the subject, while the second step involves its natural
conclusion, often some form of godhood or epiphany. Like the
immediately-previously mentioned type, it may serve as a more
efficient shortcut to longer-step methods.

The insight of the method is that typologically 1-category sets and
5-category sets would be considered identical, which is the
notional premise.

Open-and-shut arguments divide reality into: (1) knowledge, (2)
arguments, and (3) intelligence. And they output just these things.