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Constructible falsity

Published online by Cambridge University Press:  12 March 2014

David Nelson
David Nelson*
Affiliation:
The George Washington University, Washington, D. C.
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Extract

The present note introduces a constructible interpretation for the logical connectives of number theory which is divergent from that of the intuitionists. Under the intuitionistic interpretation, the principle of excluded middle and certain other classically acceptable principles of logic must be rejected. Under the present interpretation, while some classical principles may be reinstated, other principles, acceptable both classically and intuitionistically, may be shown to be invalid. Among these is the principle of contradiction.

Type
Articles
Information
The Journal of Symbolic Logic , Volume 14 , Issue 1 , 16 May 1949 , pp. 16 - 26
Copyright
Copyright © Association for Symbolic Logic 1949

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References

Gödel, Kürt. [1] Zur intuitionistischen Arithmetik und Zahlentheorie, Ergebnisse eines mathematischen Kolloquiums, vol. 4 (for 1931–1932, published 1933), pp. 34–38.Google Scholar
Gödel, Kürt. [2] On undecidable propositions of formal mathematical systems, mimeographed lecture notes, Institute for Advanced Study, 1934.Google Scholar
Heyting, Arend. [3] Die formalen Regeln der intuitionistischen Logik, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 1930, pp. 42–56.Google Scholar
Kleene, S. C. [4] General recursive functions of natural numbers, Mathematische Annalen, vol 112 (1936), pp. 727–742.CrossRefGoogle Scholar
Kleene, S. C. [5] On notation for ordinal numbers, this Journal, vol. 3 (1938), pp. 150–155.Google Scholar
Kleene, S. C. [6] Recursive predicates and quantifiers, Transactions of the American Mathematical Society, vol. 53 (1943), pp. 41–73.CrossRefGoogle Scholar
Kleene, S. C. [7] On the interpretation of intuitionistic number theory, this Journal, vol. 10 (1945), pp. 109–124.Google Scholar
Nelson, David. [8] Recursive functions and intuitionistic number theory, Transactions of the American Mathematical Society, vol. 61 (1947), pp. 307–368.CrossRefGoogle Scholar