Two methods to find truthvalue gaps and their app

Authors: Manuel Križ Emmanuel Chemla

Publish Date: 2015/05/12

Volume: 23, Issue: 3, Pages: 205-248

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Abstract

Presupposition vagueness and oddness can lead to some sentences failing to have a clear truth value The homogeneity property of plural predication with definite descriptions may also create truthvalue gaps The books are written in Dutch is true if all relevant books are in Dutch false if none of them are and neither true nor false if say half of the books are written in Dutch We study the projection property of homogeneity by deploying methods of general interest to identify truthvalue gaps Method A consists in collecting both truth judgments completely true vs not completely true and independently falsity judgments completely false vs not completely false The second method employed in experiment series B and C is based on oneshot ternary judgments completely true vs completely false vs neither After a calibration of these methods we use them to demonstrate that homogeneity projects out of negation the scope of universal sentences and the scope of nonmonotonic quantifiers such as exactly two to some extent ie in two out of three conceivable kinds of gap situations We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions scalar implicatures and something like supervaluations respectively We identify free parameters in these theories and assess various variants of them based on our results Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value

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