The method in which we propose to develop philosophy is that of
progressive formalization
(see V.Turchin, 
On Cybernetic Epistemology)
This is the method universally used in science. We first rely on an
intuitive understanding of simple concepts, then on the basis
of this understanding we convey the meaning of more formal and exact,
but also more complex, concepts and ideas.
This statement itself is an illustration of our method. We used in it
the words 'understanding', 'meaning', 'formal'. In due course,
these notions should be analyzed and 'more formal and exact' meanings
should be given to them, in their turn. These new meanings, however, will
not come to replace the original meanings, but to make an
addition to them.
Compare this with the situation in physics.
We start this branch of science speaking about bodies and their masses,
measuring distances in space by applying rulers, etc.
Later, when we study the structure of matter, we find that
those bodies and rulers, are nothing else but certain structures consisting
of huge numbers of atoms. This concept of a ruler is, however, a new
concept, even though it refers to the same thing. To come to the
concept of a ruler as an atomic structure, we must pass a long path,
at the beginning of which a ruler is a simple thing the usage of which
is easy to explain.
In the Principia Cybernetica Project, we approach philosophy
with the standards and methods of science.
We try to define and explain such basic things as `meaning',
`understanding', `knowledge', `truth', `object', `process' etc.
But to explain, e.g., understanding,
we must rely on understanding in its usual
intuitive sense, because otherwise we will not know if
we ourselves understand what we are saying; so, there will be little
chance for our words to be meaningful.
Or take the concept of an object. We have a conceptual node devoted to it.
But we cannot do without speaking about objects long before we come
to that node -- in a close analogy with the two concepts of a ruler
in physics.
Relations between things in this world are very often circular,
so we are often at a loss when trying to start and finish definitions.
Using various levels of formalization allows us to avoid
vicious circles in definitions.
Suppose we use informally some concept A to define a concept B.
Let us represent the fact that A conceptually precedes B,
or B relies on A as A < B.
Then we want to make A more exact: A'.
We define it, and discover that it now depends on
the already defined B. Hence if we were to require that
in a formal definition of a concept all the concepts
on which it relies are formally defined,
we would either have to limit ourselves to a strictly hierarchical
subset of concepts (which will be far from universal),
or never finish the job, moving in a vicious circle.
Instead, we recognize that there are various levels of
formalization of concepts which refer to the same parts of the world,
concept, and we allow these concepts to coexist.
Thus after defining B with the use of A, we define A'
using the informal concept B; since B relies on A, the
old, informal version of A is not discarded, but stays in the system
of concepts. Now we could make the definition of B more formal, basing it
on A' instead of A; on the next turn of this spiral, we may wish
to define even more formal concept A'', etc.:
A < B < A' < B' < A'' < B'' ... etc.
Whenever we want to understand a definition, we start unwinding the chain
of dependent definitions from right to left, until we come to basic intuitive
notions about which there should be no disagreements.
