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Knowledge is both objective and subjective because it
results from the interaction of the subject (the cybernetic system)
and the object (its environment). Knowledge about an object is
always relative: it exists only as a part of a certain subject.
We can study the relation between knowledge and reality (is the
knowledge true or false, first of all) if the subject of
knowledge, a cybernetic system S , can become part of a metasystem S'
in whose terms the knowledge about S and its relation to reality
can be expressed.
The metasystem transition from S to S' generates
a new type of knowledge. It is of the same nature as the
metasystem transition from using a tool to making a new kind of
tool, "metatools" , which serve to produce and improve tools. A
We can study the relation between knowledge and reality: first of all,
whether a piece of knowledge is true or false. For that purpose
the subject of knowledge, a cybernetic system S, must become part
of a metasystem S' in whose terms the knowledge of S and its relation
to reality can be expressed. But this only makes the knowledge relative to
the system S'. This kind of metasystem transition may be repeated
many times, resulting, possibly, in
ever deepening knowledge, but at any time the knowledge will be
still relative to a definite cybernetic system, for
which it is a model used for obtaining predictions: nothing more,
nothing less. The cybernetic concept of knowledge features
an organic unity of the object and the subject of knowledge.
Some philosophers of the 19th century started reasoning with
the distinction between "I" and "not-I"as the most primordial
and self-evident fact of being. This sounded metaphysical
and unnecessary to contemporary scientists, because they
thought about the world as existing independently of my "I",
and about their descriptions of the world's phenomena as completely
objective. My "I" was simply part of the world, as well as your "I"
and his "I".
The development of physics, however, demanded a careful attention
to the process of obtaining our knowledge. The "I" crept into science
as the observer of Einstein's relativity and the experimenter of quantum
mechanics. We often speak of a reference system instead of the observer,
and a measuring device instead of the experimenter, but this is a futile
attempt to ban "I". A reference system and a measuring device are only
ways to describe the activity of "I".
With the cybernetic notion of knowledge and meaning, "I" is firmly
built into knowledge.
The following metaphor may help understand it. Knowledge is a tool.
Each tool has a handle which you grasp when you use it. Different
people (or even creatures from other planets) may use the same tool,
but whenever it is used, somebody grasps the handle, and this is the "I"
of knowledge, meaning and truth.
In the cybernetic foundation of mathematics [...] we show that if
we start with the
principle that a meaningful mathematical proposition is a generator
of predictions, we come to the necessity of introducing the user of
the mathematical tools into the formalism. The tools of mathematics
do not work autonomously, like Turing machines, but rather in an interactive
mode. The user of such machines is, like Einstein's observer, a form
Semantic analysis discovers "I" in some of our most important
notions. Take causality. What do we mean by saying that A causes B?
We cannot observe this relation between phenomena. We can observe only
a time sequence "B after A", but this may be two consequences of a
common cause, or just a coincidence. The real meaning of the statement of
causality includes my freedom to allow or not to allow A happen,
to choose between A and not-A.
Then the meaning of "A causes B" is: if I allow A happen, B will
take place too, but if I do not allow A, B will not take place.
This is a meaningful proposition, a model of reality; but this model
inextricably includes "I". To test causality, there must
be a freedom to allow or not to allow A. "I" is the only source
of this freedom. (See Causality for more detailed treatment.
The theory of probability relies heavily on "I". Recall the old paradox:
we believe that events with probability zero (or vanishingly small)
cannot happen. Meanwhile, every event that happens has the probability
zero. The error here is thinking in terms of "objective reality".
Probability is not an objective attribute of events. It is an instrument
of decision taking, thus it becomes completely meaningless if there is
nobody there to take decisions. Probability describes a relation between
the subject of knowledge, "I", who now appears as a decision maker,
and various events. Before an event we can speak of its probability,
and it may be very small. After it took place, we cannot speak of its
probability, because in decision taking we consider future, not past,