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Quantifiers Are Logical Constants, but Only Ambiguously

  • Sun-Joo ShinEmail author
Part of the Synthese Library book series (SYLI, volume 373)

Abstract

Why is it crucial to categorize quantifiers as logical constants? After clarifying the importance of the issue in a larger context of logical theories, the paper investigates the following question: Why do we encounter a more contentious debate on the logical constancy of quantifiers than in the case of sentential connectives? Starting from the intuitive and naive rationale and moving to more complicated arguments for the well-accepted view that quantifiers are logical constants, I identify two tiers of the meanings assigned to quantifiers: At the first-level the interpretation is changing, and at the meta-level a constant meaning is assigned. I claim the tension arises from this ambiguous nature of the quantifier-semantics and illustrate the effects of the tension both in relevant literature and in a non-classical logic where the interpretation of the universal quantifier includes the empty domain. The double features of the universal quantifier – varying at one level and constant at another level – could raise skepticism toward the debate on logical constants itself, and in turn, toward the Tarskian analysis of logical consequence whose success heavily relies on the clear-cut status of logical constants.

Keywords

Logical Consequence Inference Rule Universal Quantifier Logical Truth Semantic Function 
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.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of PhilosophyYale UniversityNew HavenUSA

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