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Logical truth and logical implication

Published online by Cambridge University Press:  12 March 2014

William S. Hatcher
William S. Hatcher*
Affiliation:
The University of Toledo
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Extract

In [1], page 85, Quine states: “… ponentials of logically true statements are logically true.” It is perhaps of some interest that this assertion is not completely precise as can be seen from counterexamples. One simple example is the following:

Let L be some language in which ‘c’ and ‘b’ are atomic sentential constants. Let ‘c’ be false and ‘b’ true. Suppose that L includes parentheses and the material conditional ‘⊃’ as logical notation, but that ‘b’, at least, counts as extra-logical.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 4 , December 1966 , pp. 561
Copyright
Copyright © Association for Symbolic Logic 1997

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References

[1]Quine, W. V., Mathematical Logic, Rev. Ed., Harvard University Press, Cambridge, Mass., 1961.Google Scholar