Some Personal Remarks on Formal Systems:

In this context, the most important aspect of a "Formal System" is concidered to be the explicit nature of its defining structure.

In practice, this is generally expressed in terms of a set of rules.

Presumably it is a dislike by many people of the dictatorial (and perhaps unthinking, automatic, and therefore inflexible) way that some rule-based systems are implemented that makes Formal Systems so unpopular.

However, on reflection, perhaps it becomes clear that the "rules" or "axioms" which define the system are a consequence of the explict nature of the description of the system and not the main aim. Presumably, there would be little point in explicitly defining anything -if this description was not subsequently applied. So an element of enforced or voluntary acceptance is unavoidable -but this should not be seen as representing the essence of the system.

Unfortunately, formal systems are sometimes implemented (as a form of psychological defence system) or imposed (as a form of bullying) without any explit explanation of the reason behind the rules involved. Indeed, within the current context, such a use of formal systems could only be seen as an abuse -because the arbitrary imposition of rules without a full explanation would be contrary to the nature of "formality" which requires the system to be made explicit -in order for it to be fully investigated, understood and discussed.

Exploiting the Explicit:

An explicitely described system can be investigated through experimentation -including explicitly changing the rules (or axioms) that define the system in order to see how these changes affect the behaviour of the system. Because the internal structure is known -the behaviour of the system should also be consistent over time -as the system should also react in predictable ways when activated by those who understand the implications of the rules. This consistency (and fairness) is why formal systems are also used for recreational purposes in the form of games, puzzels and sports events.

Synthetic Models:

Clearly, the more complex a system is, the more difficult it is to describe all the details in fully explicit ways. On the other hand, this problem is easier for the person who designs the system. Others (observers) are forced to try and imagine how the system (not created by themselves) might be (explicitly) defined.

The difficulty in explicitely describing observed (and not self-constructed) systems also creates an epistemological problem:

Presumably, if we wish to survive in the world, then it would be an advantage if we understood the world around us (which we are forced to participate in, on some level). However, probably, the "process of understanding" involves the creation of an explicit model of the world (or the bit of it which interests us at that moment).

In order to avoid the problem of explicitly describing (modeling) a system that we do not fully understand -perhaps it would be easier to "invent" a simple set of rules which we suspect might be congruent with the way the system actually works -so that we can subsequently experiment with the model to see how closely the behaviour of the model mimics that which is being modelled. Unfortunately, the observance of any deviation between the model and that which is being modelled will not be able to explain the reason for the deviation - it can only warn us that the model is not consistant with that which it is supposed to be modeling.

Perhaps the only way to solve this problem is to "invent" a whole range of (arbitrary) different systems (based on arbitrary differences in the systems of rules) -that initially are not intended to model any particular system -but can be investigated to see if (by any chance) they behave in ways that might be congruent with one of the systems that one might wish to model.

Note that (with reference to earlier remarks) -the "arbitrary invention" of rules (which might allows the invention of seemingly bizarre and useless rules) is not the same as the "arbitrary implementation" of rules (which results in the "incorect" application of existing rules (however they might have been derived).

Formal and Semi-Formal:

Because of the difficulty of explicitly decribing all the rules in comples situations and systems -we might concider that "explicit" is not a binary term (which only allows for two values). Presumably, making things explicit is a gradual process -and involves a sliding scale which ranges from completely explicit to completely uncharted.

In this context, one might perhaps concider that "art" is a semi-formal system: Presumably, the artist tries to explore and make increasingly specific through their work what exactly their view of art is.