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A Note on Quine's principles of quantification
Published online by Cambridge University Press: 12 March 2014
Extract
In his Mathematical logic Quine characterizes the theorems of quantification theory by six principles:
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- Copyright © Association for Symbolic Logic 1947
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.