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Modality and description

Published online by Cambridge University Press:  12 March 2014

Arthur Francis Smullyan
Arthur Francis Smullyan*
Affiliation:
University of Washington
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Extract

There are logicians who maintain that modal logic violates Leibniz's principle that if x and y are identical, then y has every property of x. The alleged difficulty is illustrated in the following example due to Quine.1

A. It is logically necessary that 9 is less than 10.

B. 9 = the number of the planets.

C. Therefore, it is logically necessary that the number of the planets is less than 10.

Type
Articles
Information
The Journal of Symbolic Logic , Volume 13 , Issue 1 , March 1948 , pp. 31 - 37
Copyright
Copyright © Association for Symbolic Logic 1948

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References

1 Quine, W. V., Notes on existence and necessity, The journal of philosophy, vol. 40 (1943), pp. 113–127.CrossRefGoogle Scholar

We assume, at this stage of the discussion, that ‘9’ and ‘10’, as they occur in the illustration, are names of familiar logical properties. This is in order to simplify the introductory discussion. In due course we shall consider the problem in a more general way.

2 Alonzo Church, this Journal, vol 7 (1942), p. 100.

3 See Carnap, R., Meaning and necessity (1946), pp. 147–150Google Scholar, where certain inelegancias of the Principia approach to class theory are indicated.

4 Quine, W. V., New foundations for mathematical logic, The American mathematical monthly, vol. 44 (1937). pp. 70–80.CrossRefGoogle Scholar