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Modifications of Quine's ML and inclusive quantification systems1

Published online by Cambridge University Press:  12 March 2014

George Goe
George Goe*
Affiliation:
Rensselaer Polytechnic Institute
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Extract

In a paper that was written some time ago but appeared only recently [1], I indicated that Quine's system of quantification in [2], as well as his inclusive system of [3] can be modified so as to make it possible to prove *119 of [2] by another method than the one discovered by Berry. The reason originally given in [1, p. 136] for preferring the modified systems was wrong. (See [1, p. 158] for correction of previous remark.) But, at the cost of a slight complication of one of the axiom schemata, a considerable simplification of the proof of *119 is achieved in the modified systems, by dispensing with the use of *115 and *117 as intermediaries.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 39 - 42
Copyright
Copyright © Association for Symbolic Logic 1968

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Footnotes

1

Work for the completion of this paper was supported by the National Science Foundation, Grant GS-1425.

References

[1]Goe, George, A reconstruction of formal logic, Notre Dame journal of formal logic, vol. 7 (1966), pp. 129–157, and Corrections to my paper “A reconstruction of formal logic”, ibid. p. 158.CrossRefGoogle Scholar
[2]Quine, W. V., Mathematical logic, revised edition, Harvard University Press, Cambridge, Mass., 1951.CrossRefGoogle Scholar
[3]Quine, W. V., Quantification and the empty domain, this Journal, vol. 19 (1954), pp. 177–179.Google Scholar