Manuel Križ and Emmanuel Chemla (2014). “Two methods to find truth value gaps and their application to the projection problem of homogeneity”. Manuscript, University of Vienna and LSCP.

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Abstract: Presupposition, vagueness, oddness can lead some sentences to fail to have a truth value. Homogeneity of definite descriptions may also create truth value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them is, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying two methods of general interest to identify truth value gaps. Method A consists in collecting both truth value judgments (completely true vs not completely true) and, independently, false value judgments (completely false vs not completely false). Method B is based on one shot 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 non-monotonic quantifiers such as exactly 3, to some extent. We assess our results in light of different approaches of homogeneity, whether these approaches are based on presuppositions, scalar implicatures or supervaluations. We identify free parameters in these theories and assess various variants thereof based on our results. We identify critical situations to further distinguish between these approaches (and their variants). In the future, the methods may also be applied to study other phenomena that cause some sort of failure of a sentence to have a truth-value.