Which Quantifiers Are Logical? A Combined Semantical and Inferential Criterion

  • Solomon FefermanEmail author
Part of the Synthese Library book series (SYLI, volume 373)


The aim of logic is to characterize the forms of reasoning that lead invariably from true sentences to true sentences, independently of the subject matter; thus its concerns combine semantical and inferential notions in an essential way. Up to now most proposed characterizations of logicality of sentence generating operations have been given either in semantical or inferential terms. This paper offers a combined semantical and inferential criterion for logicality (improving one originally proposed by Jeffery Zucker) and shows that any quantifier that is to be counted as logical according to that criterion is definable in first order logic.


Atomic Formula First Order Logic Propositional Variable Natural Deduction Logical Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I would like to thank Jeremy Avigad, Denis Bonnay, Fredrik Engström, Lauri Hella, Michael Rathjen, Dag Westerståhl and Jeffery Zucker for their useful comments on a draft of this article.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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