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On relations as coextensive with classes

Published online by Cambridge University Press:  12 March 2014

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

In a previous note I showed a new way to define the ordered pair. I made use of the notations ‘Nn’ (for class of natural numbers) and ‘Sv’ (for successor of v), remarking that they are readily defined without appeal to ordered pairs or relations. Adopting the auxiliary abbreviation:

I defined the ordered pair thus:

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 11 , Issue 3 , September 1946 , pp. 71 - 72
Copyright
Copyright © Association for Symbolic Logic 1946

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References

1 On ordered pairs, this Journal, vol. 10 (1945), pp. 95-96.

2 I.e., the class of all ordered pairs belonging to x. It is expressed in Mathematical logic by applying a dot.