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Element and number

Published online by Cambridge University Press:  22 April 2025

W.V. Quine*
Affiliation:
New York University

Extract

Rosser pointed out recently that the system of my Mathematical logic, when curtailed by leaving out the elementhood principle *200, would hold true even of a universe wherein the only entity is the null class. In other words, all theorems of the curtailed system remain true when all atomic formulae ⌜α∊β⌝ are construed as false for all values of their variables. This observation constitutes a consistency proof of that curtailed system, in an extraordinarily strict sense; for it shows that every theorem of that curtailed system is of a very special kind such that if all its quantifiers be simply rubbed out and all its atomic formulae be marked ‘F’ then the whole will receive a “T” under the ordinary truth-table computation.

Information

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1941

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