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A Note on Quine's principles of quantification

Published online by Cambridge University Press:  12 March 2014

Hao Wang
Hao Wang*
Affiliation:
Harvard University
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Extract

In his Mathematical logic Quine characterizes the theorems of quantification theory by six principles:

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 12 , Issue 4 , December 1947 , pp. 130 - 132
Copyright
Copyright © Association for Symbolic Logic 1947

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References

1 New York, 1940; 2nd printing, Cambridge, Mass., 1947. In this note, references to metatheorems (*112, *159, etc.) and definitions (D4) are all to this book. Cf. especially pp. 88–95.

To Professor Quine I am indebted for criticisms of an early draft of this note.

2 this Journal, vol. 6 (1941), pp. 23–27.

3 It should be noted that Qpl is a special case of: Qpl′. If φ is tautologous, ├┌(α)φ┐.

Accordingly we may of course use Qpl′ in place of Qpl. Qpl′ is an immediate consequence of *100 plus *112.

4 In accordance with the convention of Mathematical logic (p. 92), the square brackets indicate use of *111 (i.e., Qp4).

5 Grundzüge der theoretischen Logik, 2nd edn., Berlin, 1938.