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On ω-inconsistency and a so-called axiom of infinity

Published online by Cambridge University Press:  12 March 2014

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

The purpose of the present paper is to dispel such mystery as may be traceable to use of the ill-chosen term ‘ω-inconsistency’ and to a certain application of the term ‘axiom of infinity’. The application of ‘axiom of infinity’ which I have in mind is made by Rosser in his penetrating studies of the system of my New foundations. Let me begin with a synopsis of that system, which I shall call NF.

NF assumes as primitive just the membership connective ‘ϵ’, the truth functions, and quantification over a single style of variables ‘x’, ‘y’, etc. without type distinctions. The axioms, superimposed on standard quantification theory, comprise the axiom of extensionality ‘(x)(x ϵ y · = · x ϵ z) · y ϵ w · ⊃· z ϵ w’ and the axioms of abstraction, these latter being all sentences of the form ‘(∃y)(x)(x ϵ y · = Fx)’ in which the sentence supplanting ‘Fx’ is stratified (i.e., adaptable to type theory by some assignment of types to variables).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 18 , Issue 2 , June 1953 , pp. 119 - 124
Copyright
Copyright © Association for Symbolic Logic 1953

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References

BIBLIOGRAPHY

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