Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-09T13:13:26.493Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Quine's principles of quantification

Published online by Cambridge University Press:  12 March 2014

Hao Wang
Hao Wang*
Affiliation:
Harvard University
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.