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Foundation of Mathematics

The philosophy developed in MST theory leads to a certain view on the nature and workings of mathematics and gives certain answers to the long-standing questions about the foundations of mathematics.

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 of "I".

At present we have two documents on the foundation of logic and mathematics in the light of our epistemology and ontology:

  1. Valentin F. Turchin, The Cybernetic Foundation of Mathematics, Technical report (170 pages) of the City College, City University of New York, 1983.
  2. Valentin F. Turchin, A constructive interpretation of the full set theory. The Journal of Symbolic Logic, 52, pp. 172-201, 1987.
We plan to represent the contents of these documents in the format of Principia Cybernetica. We hope that the work along these lines will be discussed and continued.

The concept of the metasystem transition in formal systems is applied in a research program on computer program optimization through partial and lazy evaluation methods, culminating in a Supercompiler. For more information, see the following review paper:

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Apr 9, 2008 (modified)
Jun 24, 1997 (created)


Metasystem Transition Theory

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