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A System of Mutually Contradictory n Abstractions Whose Proper Sub-Systems Are all Mutually Consistent

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono  and
Minolu Ohta
Katuzi Ono
Affiliation:
Mathematical Institute, Nagoya University
Minolu Ohta
Affiliation:
Mathematical Institute, Nagoya University
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It has been pointed out by K. ONO that there is a pair of mutually contradictory abstractions, each of which is self-consistent. Afterwards, Y. INOUE pointed out that there is a vast class of such pairs which is as vast as the class of all the Russell-type paradoxes. It must be a natural course of matter to ask the following question: For every number n, is there a system of mutually contradictory abstractions whose proper subsystems are all mutually consistent?

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 395 - 397
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Inoue, Yoshinobu: On systems of self-consistent abstractions, Nagoya Math. J., 28 (1966), 179–185.Google Scholar
[2] Ono, Katuzi: Mutual contradiction of two self-consistent abstractions, Nagoya Math. J., 28 (1966), 59–61.Google Scholar
[3] Quine, Willard Van Orman: Set theory and its logic. Cambridge, Mass., xv+359.Google Scholar
[4] Quine, Willard Van Orman: New foundation for mathematical logic, Amer. Math. Monthly, 44 (1937), 70–80.Google Scholar