A language is a convention according to which certan material objects,
to be referred to as linguistic objects, define certain actions,
which are referred to as their meanings. There are two basic types
of linguistic objects: commands and statements.
Commands are used in the context of control, where the meaning
of a command issued by the controlling system is the resulting action
of the controled system. The meaning of a statement is the piece
of knowledge (true or false), that is a hierarchical generator
Human language is a multilevel system.
On the lower levels, which are close to
our sensual perception, our notions are almost in one-to-one
correspondence with some conspicuous elements of perception.
In our theories we construct higher levels of language. The concepts
of the higher levels do not replace those of the lower levels, as
they should if the elements of the language reflected things "as
they really are", but constitute a new linguistic reality, a
superstructure over the lower levels.
Predictions produced by the higher levels are formulated in terms
of the lower levels. It is a hierarchical system, where the top
cannot exist without the bottom.
We loosely call the lower-level concepts of the linguistic
pyramid concrete, and the higher-level abstract. This is a very
imprecise terminology because abstraction alone is not sufficient
to create high level concepts. Pure abstraction from specific
qualities and properties of things leads ultimately to the lost
of contents, to such concepts as `something'. Abstractness of a
concept in the language is actually its `constructness', the
height of its position in the hierarchy, the degree to which it
needs intermediate linguistic objects to have meaning and be
used. Thus in algebra, when we say that x is a variable, we
abstract ourselves from its value, but the possible values
themselves are numbers, which are not `physical' objects
but linguistic objects formed by abstraction present
in the process of counting. This intermediate linguistic level of
numbers must become reality before we use abstraction on the next
level. Without it, i.e. by a direct abstraction from countable
things, the concept of a variable could not come into being.
In the next metasystem transition we deal with abstract algebras,
like group theory, where abstraction is done over various operations.
As before, it could not appear without the preceding
metasystem level, which is now the school algebra.
There is another parameter to describe concepts of a language.
This is the degree to which the language embedding the concept or
concepts is formalized. A language is formal, or formalized, if
the rules of manipulation of linguistic objects depend only on
the `form' of the objects, and not on their `human meanings'. The
`form' here is simply the material carrier of the concept, i.e. a
liguistic object. The `human meaning' is the sum of associations it
evokes in the human brain. While `forms' are all open for
examination and manipulation, i.e. are objective,
`human meanings'are subjective, and are communicated indirectly.
Operations in formal languages can be delegated to mechanical devices,
machines. A machine of that kind becomes an objective model of reality,
independent from the human brain which created it. This makes it
possible to construct hierarchies of formal languages, in
which each level deals with a well-defined, objective reality of
the previous levels. Exact sciences operate using such hierarchies,
and mathematics makes them its object of study.
Classification of languages by these two parameters leads
to the following four types of language-related activities :
|Concrete language||Abstract language|
| Unformalized language||Art||Philosophy|
| Formalized language||Descriptive sciences||Theoretical sciences, mathematics|
Art is characterized by unformalized and concrete language.
Words and language elements of other types are important only as
symbols which evoke definite complexes of mental images and
emotions. Philosophy is characterized by abstract informal thinking.
The combination of high-level abstract constructs used in
philosophy with a low degree of formalization requires great
effort by the intuition and makes philosophical language the most
difficult type of the four. Philosophy borders with art when it
uses artistic images to stimulate the intuition. It borders with
theoretical science when it develops conceptual frameworks to be
used in construction of formal scientific theories. The language
of descriptive science must be concrete and precise;
formalization of syntax by itself does not play a large part, but rather
acts as a criterion of the precision of semantics.