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Two cybernetic systems are involved in human language and thought.
The first system is the human brain. It creates models of reality whose material body is the nerve nets, and which we therefore call
neuronal models. Neuronal models use neuronal, or intuitive,
concepts (functional elements).
The second system is language. Its functioning is linguistic activity
in society. Linguistic activity creates models of reality whose material
body consists of linguistic objects. The functional elements of this
system are logical (linguistic concepts.
The two systems are tightly interrelated. Language is an offspring,
and, in a certain sense, a continuation of the brain: using language
we create new modesl of reality, which were not imbedded in our brain
by nature. Some substructures in our brain are representations of the
states of the world. Some of the linguistic objects are representations
of those representations: we refer to them as most concrete, or low-level,
concepts. Such words as "cat", "apple", "to run" , and the concepts
they fixate, are of that kind.
But human language (like human brain) is a multilevel hierarchical system.
We create theories, where we use abstractions of higher levels,
logical concepts the machinery of which (do not forget that concepts
are functional units) requires something in addition to the brain:
some material linguistic objects. Thus while we can regard small
numbers, like two or three, as neuronal concepts because we immediately
recognize them, bigger numbers, like 137, can function only using
some external to the brain representations.
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. We cannot throw away the
concepts of the lower levels even if we wished to, because then
we would have no means to link theories to observable facts.
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 correct as long as one keeps in mind that abstraction
is not always abstraction in scope from things observable, but also,
and most importantly,
an abstractions from abstractions of the lower levels of the same
linguistic system. Pure abstraction from specific
qualities and properties of things leads ultimately, as its scope
increases, to the loss of contents, to such concepts as some
and something. Abstractness of a
concept 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 from its value, but the possible values
themselves are numbers, i.e. linguistic objects formed by abstraction
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.