metaTao: the Tao of Tao

In common speaking a usual situation is the one when a descriptive/application term (called subject term) is applied to another term (object) within its scope of definition/application to form a predicate.
For example, the subject term "production" may be applied after the object "apple" getting the term "apple production", a well-formed predicate with meaning.
A special case is when the subject term and the object term coincide, or where the subject term is applied to himself.
In the example we get "production of productions", a term that has still meaning and could refer generally to the study of the production techniques.
When a term is applied to subject itself is of use described by the prefix meta (from the greek: μετά = "after", "beyond", "with", "self"): metaterm.
In the shown example a production of productions is called metaproduction.
Not all the words with the prefix meta naturally have this meaning, for example a metaphor is not exactly a "phor of phor" while Metaphysics is not properly physics applied to physics.
In metadescriptions it is crucial to distinguish between the two levels of discourse, the level of the object elements and that relative to the metaelements which describe them. Born here a further distinction between levels, the logical one in addition to the hierarchical.
The logic levels can be organized hierarchically, and hierarchical levels can also be logical levels.
The fundamental distinction between logical and hierarchical levels is that the classes that represent the first are one another self-contained but are always on the same logical plane: each class is an extension of the previous but still at the same logical level, such as biology contains the chemistry, chemistry include physics, etc. while the classes corresponding to logic levels are not on the same plane, between the there is a logical gap and not just an extension of new elements: a metaclass is not simply an extension of the classes that compose it but a new class with characteristics and logical/functional properties entirely new and different from those of the classes that compose it.

In the figure we have a class C2 with C1 elements, mapped to a metaclass C4 that contains as elements some class C3, of which C2 is an element,; this is further mapped to a meta-meta-upper class etc.. At each class corresponds a logic level 1, 2 etc.

Some examples of metaterms are metadata, data that organize data, metatheories, a theory on another theory, as metamathematics, where one can define metatheorems - for example on the proof theory of theorems in mathematics, or metalogic, a metatheory study of logic, especially mathematical logic.

One description area where the distinction between logical levels is essential is in the field of linguistics, the study of natural languages (such English, Italian, et.) and artificial languages, such programming languages (C, LISP, HTML, etc.). In fact, if a book on C is written in english there is no possibility of confusion between the natural language narrative subject (english) and the described object language (C), but when an english book speaks about english, such as a book of english linguistics , several problems of confusion may arise when an english word is used as a metaterm of the metalanguage subject and when instead is a term of the object language described. In this case the use of metaterms between language and metalanguage and the distinction between logical levels of discourse is essential.

In system theory a system is commonly composed of elements, but more generally may include other systems, and in this case is a metasystem, as well as a system process may be composed of other processes, and in this case is a metaprocess. The distinction between logic levels which operates the description of system/process is essential in order not to create confusion or paradoxes.