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In cybernetics we say that a purposive cybernetic system `S` has some
*knowledge* if the system `S` has a *model* of some part
of reality as it is perceived by the system. Informally, a model of
some process occurring in a system is a another system which somehow
mimicks, or simulates, that process;
thus by using the model it becomes possible to know
something about the modelled process without actually running it,
or predict developments before they actually happen.

The definition of the modeling scheme includes
an important assumption of *non-interference*:
that the procedure `R` (which is a sequence of actions), when it acts
on a state `w` of the world, *does not change* that state.
But we know from quantum mechanics that this assumption, strictly
speaking, never holds. When we deal with macroscopic phenomena we can,
nevertheless, use the non-interference assumpiton, because the impact of the instruments we use in `R`
on the state `w` can always be made insignificant.
But on the atomic and subatomic levels, we cannot abstract from the
action of the means we use to get information about the objects
studied.

There is one more non-interference assumption: the modeling procedure `M_a`
imitating the action `a` does not alter in any way the course of the action,
including the final result `w_2`.
Usually, this assumption is easily true; the most
salient case is that of an astronomer. His computations, certainly,
do not change the motion of celestial bodies. But when we try to apply
the modelling scheme to self-description, we may have problems.

So, a generalization of the modelling scheme is necessary, which would be
applicable even though the assumption of non-interference may not be true. Consider these two two-staged processes which we see in the
modeling scheme, and let them run in parallel
so that the mutual influence is not excluded:

The first process:

1. `R(w_1)` results in `r_1`;
2. `M_a(r_1)` results in `r_2`.

The second process:

1. `a` results in `w_2`;
2. `R(w_2)` results in `r_2'`.

The prediction produced by the model is that `r_2 = r_2'`.
We can go further, however, in the formalization of the concept
of prediction and making it more universal.
Wait for the time when both processes end and start the third
process `C` which compares `r_2` and `r_2'`.
All three processes together constitute one
complex process, which is nothing else but the process of
testing the model. If our model is correct, then the process `C`,
and with it the whole complex process that tests the model, will
succeed, that is `r_2` and `r_2'` will be found identical.
The model *predicts* that its test will succeed.
Therefore we introduce the formal concept of a *prediction*

However, even the definition of knowledge as a generator of predictions
is not general enough
to cover the whole concept. Pieces of our knowledge
(statements, or propositions) may not
necessarily produce verifiable predictions, but only some objects
that will be used to produce prediction. Moreover, they may produce objects
which produce objects which produce predictions, and so forth to any depth
of the hierarchy of knowledge objectifications.

A simple example from mathematics:
the equation `x + y = y + x` is not immediately verifiable, but it produces
-- this is a shortcut for 'we know how to use it to produce' -
such equations as `7 + 4 = 4 + 7`. This object, in its turn, is still too
abstract for a direct verification. We can, however, verify the prediction
that four apples and seven apples can be added in either order with the
same result: eleven apples.

We come, therefore, to the following definition: a piece of knowledge is
an object which we can use to produce (generate) predictions or other
pieces of knowledge. This definition is *recursive*; it allows
a piece of knowledge which is not an immediate prediction,
or prediction generator, to produce other similar pieces (including itself)
any number of times, before some of its products
will produce predictions. The possibility is not excluded that
an object legitimately regarded as a piece of knowledge will
infinitely produce other pieces
without ever producing a single prediction: call this piece empty.
This is because with our very general definition of recursive production
(which we want to keep) we cannot always say in advance if a given
piece will ever produce predictions. So we formally allow the existence
of an empty piece of knowledge. Of course, if we can prove that a given
object is an empty piece of knowledge we need not to regard it as
knowledge at all.

A cybernetic system makes predictions in order to achieve certain goal,
ultimately -- survival and proliferation.

True knowledge is an instrument of survival. Knowledge is
power. There is no criterion of truth other than the prediction power it
gives. Since powers, like multidimensional vectors, are hard to
compare, there is no universal and absolute criterion of truth.
Proclamation of any truth as absolute because of being given
through a "revelation" is sheer self-deception.

Copyright© 1991 Principia Cybernetica -
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