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A new symbolism for the propositional calculus

Published online by Cambridge University Press:  12 March 2014

William Tuthill Parry*
Affiliation:
The University of Buffalo

Extract

This paper reviews various symbolisms for the two-valued propositional calculus, and introduces a new set of signs which embodies the principles of Leśniewski's symbolism, yet resembles better known signs. This type of symbolism, serving as a diagram, may be used either in place of or as auxiliary to the usual symbolisms.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1954

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References

BIBLIOGRAPHY

Black, M., Critical thinking, New York, 1946.Google Scholar
Boll, M. and Reinhart, J., Les étapes de la logique, Paris, 1946.Google Scholar
Church, A., Introduction to mathematical logic, Part I, Princeton, 1944.Google Scholar
Curry, H. B., A theory of formal deducibility, Notre Dame, 1950.Google Scholar
Gottschalk, W. H., The theory of quaternality, this Journal, vol. 18 (1953), pp. 193 ff.Google Scholar
Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, Berlin, 1928.Google Scholar
Leśniewski, S., Grundzüge eines neuen Systems der Grundlagen der Mathematik, Fundamenta mathematicae, vol. 14 (1929), pp. 1 ff.CrossRefGoogle Scholar
Łukasiewicz, J., Elementy logiki matematycznej, Warsaw, 1929.Google Scholar
Łukasiewicz, J., Aristotle's syllogistic, Oxford, 1951.Google Scholar
Peirce, C. S., The simplest mathematics (1902), Collected papers, vol. 4, pp. 189 ff., Cambridge, Mass., 1933.Google Scholar
Quine, W. V., Mathematical logic, New York, 1940.Google Scholar
Quine, W. V., Methods of logic, New York, 1950.Google Scholar
Quine, W. V., The problem of simplifying truth functions, American mathematical monthly, vol. 59 (1952), pp. 522 ff.CrossRefGoogle Scholar
Reichenbach, H., Elements of symbolic logic, New York, 1948.Google Scholar
Sheffer, H. M., A set of five independent postulates for Boolean algebras, Transactions of the American mathematical society, vol. 14 (1913), pp. 481 ff.CrossRefGoogle Scholar
Sobociński, B., An investigation of protothetic, Brussels 1949.Google Scholar
Standley, G. B., Ideographic computation in the propositional calculus, this Journal, vol. 19 (1954), pp. 169171.Google Scholar
Tarski, A., Introduction to logic, New York, 1941.Google Scholar
Whitehead, A. N. and Russell, B., Principia mathematica, vol. 1. Cambridge, England, 1910.Google Scholar
Wittgenstein, L., Tractatus logico-philosophicus, New York and London, 1922.Google Scholar
Woodger, J. H., The axiomatic method in biology, Cambridge, England, 1937.Google Scholar