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Progressive formalization

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.

Copyright© 1997 Principia Cybernetica - Referencing this page

V. Turchin,

Oct 6, 1997 (modified)
Aug 1993 (created)


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