[1]Principia Cybernetica Web

                               Foundation of Mathematics

   The philosophy developed in [2]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 [3]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 [4]epistemology and ontology:
    1. Valentin F. [5]Turchin, The Cybernetic Foundation of Mathematics, Technical
       report (170 pages) of the City College, City University of New York, 1983.
    2. Valentin F. [6]Turchin, [externallink.GIF] [7]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 [externallink.GIF] [8]Supercompiler. For
   more information, see the following review paper:
     * [externallink.GIF] [9]R. Glueck & A. Klimov (1995): [externallink.GIF]
       [10]Metasystem Transitions in Computer Science and Mathematics (rtf format),"
       [externallink.GIF] [11]World Futures: the journal of general evolution 45, p.
       213.
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   [12]Copyright© 2008 Principia Cybernetica - [13]Referencing this page

   Author
   [14]Turchin,

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

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References

   1. LYNXIMGMAP:http://pespmc1.vub.ac.be/FOUNDMAT.html#PCP-header
   2. http://pespmc1.vub.ac.be/MSTT.html
   3. http://pespmc1.vub.ac.be/PREDICT.html
   4. http://pespmc1.vub.ac.be/EPISTEM.html
   5. http://pespmc1.vub.ac.be/TURCHIN.html
   6. http://pespmc1.vub.ac.be/TURCHIN.html
   7. http://ecco.vub.ac.be/~clement/temp/turchin-constructive-set-theory.pdf
   8. http://www.supercompilers.com/new_design/html/supercompilation.html
   9. http://www.diku.dk/~glueck/
  10. ftp://ftp.vub.ac.be/pub/projects/Principia_Cybernetica/WF-issue/Glueck&Klimov.rtf
  11. http://www.gbhap-us.com/journals/153/153-top.htm
  12. http://pespmc1.vub.ac.be/COPYR.html
  13. http://pespmc1.vub.ac.be/REFERPCP.html
  14. http://pespmc1.vub.ac.be/TURCHIN.html
  15. http://pespmc1.vub.ac.be/DEFAULT.html
  16. http://pespmc1.vub.ac.be/MSTT.html
  17. http://pespmc1.vub.ac.be/INTFREE.html
  18. http://pespmc1.vub.ac.be/POSBOOK.html
  19. http://pespmc1.vub.ac.be/MAKANNOT.html
  20. http://pespmc1.vub.ac.be/hypercard.acgi$annotform?

[USEMAP]
http://pespmc1.vub.ac.be/FOUNDMAT.html#PCP-header
   1. http://pespmc1.vub.ac.be/DEFAULT.html
   2. http://pespmc1.vub.ac.be/HOWWEB.html
   3. http://pcp.lanl.gov/FOUNDMAT.html
   4. http://pespmc1.vub.ac.be/FOUNDMAT.html
   5. http://pespmc1.vub.ac.be/SERVER.html
   6. http://pespmc1.vub.ac.be/hypercard.acgi$randomlink?searchstring=.html
   7. http://pespmc1.vub.ac.be/RECENT.html
   8. http://pespmc1.vub.ac.be/TOC.html#FOUNDMAT
   9. http://pespmc1.vub.ac.be/SEARCH.html