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Constructible falsity

  • David Nelson (a1)

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.

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Gödel, Kürt. [1] Zur intuitionistischen Arithmetik und Zahlentheorie, Ergebnisse eines mathematischen Kolloquiums, vol. 4 (for 19311932, published 1933), pp. 3438.
Gödel, Kürt. [2] On undecidable propositions of formal mathematical systems, mimeographed lecture notes, Institute for Advanced Study, 1934.
Heyting, Arend. [3] Die formalen Regeln der intuitionistischen Logik, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 1930, pp. 4256.
Kleene, S. C. [4] General recursive functions of natural numbers, Mathematische Annalen, vol 112 (1936), pp. 727742.
Kleene, S. C. [5] On notation for ordinal numbers, this Journal, vol. 3 (1938), pp. 150155.
Kleene, S. C. [6] Recursive predicates and quantifiers, Transactions of the American Mathematical Society, vol. 53 (1943), pp. 4173.
Kleene, S. C. [7] On the interpretation of intuitionistic number theory, this Journal, vol. 10 (1945), pp. 109124.
Nelson, David. [8] Recursive functions and intuitionistic number theory, Transactions of the American Mathematical Society, vol. 61 (1947), pp. 307368.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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