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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:
- Valentin F. Turchin, The Cybernetic Foundation of Mathematics,
Technical report (170 pages) of the City College, City University
of New York, 1983.
-
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:
Copyright© 2008 Principia Cybernetica -
Referencing this page
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Author
Turchin,
Date
Apr 9, 2008 (modified)
Jun 24, 1997 (created)
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