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ON THE GENERAL INTERPRETATION OF FIRST-ORDER QUANTIFIERS

Published online by Cambridge University Press:  25 October 2013

G.ALDO ANTONELLI
G.ALDO ANTONELLI*
Affiliation:
University of California, Davis
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CALIFORNIA, DAVIS DAVIS, CA 95616 (USA) E-mail: [email protected]
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Abstract

While second-order quantifiers have long been known to admit nonstandard, or“general” interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretation’s first-order domain. This paper explores some of the consequences of such “general” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 4 , December 2013 , pp. 637 - 658
Copyright
Copyright © Association for Symbolic Logic 2013 

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