Are There Alternative Logics?

  • F. Waismann


I. preliminary remarks.The writers of text-books of logic commonly take it for granted that there is a single theory, a set of rules embodying what are called the ‘laws of thought’; and that these laws are universally the same. This conception seems scarcely to accord with the present level of knowledge. For we do already possess distinct logics — if this term is used to denote precisely elaborated formalized systems: e.g., logics including or excluding a Theory of Types, systems admitting or barring the law of excluded middle, etc. Perhaps one might add that the rise of a conventionalistic mode of thinking — emanating from mathematics — today favours attempts to construct novel logics. Here two ways present themselves.


Free Variable Propositional Calculus Partial Negation Double Negation Strong Negation 
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  1. 1.
    For a symbolic system with a simple hierarchy of types see: F. P. Ramsey, ‘The Foundations of Mathematics’, Proc. Lond.Math. Soc., vol. 25, 1945.Google Scholar
  2. For a symbolic system without a hierarchy of types see: A. Church, ‘A Set of Postulates for the Foundation of Logic’, Annals of Math., 33, 1932.Google Scholar
  3. His system has been proved inconsistent by S. C. Koeene and J. B. Rosser, Annals of Math., 36, 1935.Google Scholar
  4. The impossibility of a system along such lines has not been proved either. Cf. K. Gödel, ‘Russell’s Mathematical Logic’, in The Philosophy of Bertrand Russell, Evanston, 1944, p. 150.Google Scholar
  5. 2.
    L. E. J. Brouwer, ‘Über die Bedeutung des Satzes von ausgeschlossenen Dritten …’, J. Math., 154, 1925.Google Scholar
  6. A. Heyting, ‘Die formalen Regeln der intuitionistischen Logik’, Ber. Akad Berlin, 1930. See Intuitionism, Amsterdam, 1956.Google Scholar
  7. 1.
    G. Birkhoff and J. V. Neumann, ‘The Logic of Quantum Mechanics’, Ann. of Math., 37, 1936.Google Scholar
  8. M. Strauss, ‘Zur Begrndung der statistischen “Transformationstheorie” der Quantenphysik’, Ber. Akad., Berlin, 1936.Google Scholar

Copyright information

© The Literary Executors of F. Waismann, and R. Harré 1968

Authors and Affiliations

  • F. Waismann
    • 1
  1. 1.University of OxfordUK

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