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A proof procedure for quantification theory

Published online by Cambridge University Press:  12 March 2014

W. V. Quine
W. V. Quine*
Affiliation:
Harvard University
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Extract

The purpose of this paper is to present and justify a simple proof procedure for quantification theory. The procedure will take the form of a method for proving a quantificational schema to be inconsistent, i.e., satisfiable in no non-empty universe. But it serves equally for proving validity, since we can show a schema valid by showing its negation inconsistent.

Method A, as I shall call it, will appear first, followed by a more practical adaptation which I shall call B. The soundness and completeness of A will be established, and the equivalence of A and B. Method A, as will appear, is not new.

The reader need be conversant with little more than the fairly conventional use (as in [8]) of such terms as ‘quantificational schema’, ‘interpretation’, ‘valid’, ‘consistent’, ‘prenex’, and my notation (as in [7]) of quasi-quotation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 20 , Issue 2 , June 1955 , pp. 141 - 149
Copyright
Copyright © Association for Symbolic Logic 1955

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References

REFERENCES

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