Two methods to find truth-value gaps and their application to the projection problem of homogeneity

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 truth-value 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 truth-value 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 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 two, to some extent (i.e., 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.

Choice and prohibition in non-monotonic contexts

“…We then turn to a third solution, based on a homogeneity account of free choice (Goldstein 2018). This solution can account for our results, given certain assumptions about the projection of homogeneity in complex sentences (Križ 2015;Križ and Chemla 2015;among others), though it too leaves a variety of issues open with related cases.…”

“…To see how this account extends to our non-monotonic cases, we have to ask how homogeneity effects work in complex sentences that involve non-monotonic phrases-in other words, how homogeneity projects in sentences like (9a) and (10a). What projection behavior we predict for homogeneity triggers will depend on what account of homogeneity we endorse (see Križ and Chemla 2015 for discussion and experimental data on homogeneity projection with plural definites). Here we remain neutral as to what particular account of homogeneity one should adopt.…”

Homogeneity effects in natural language semantics

“…Overall, Križ and Chemla, found the following truth and falsity conditions for (34), which are captured by the principle just discussed. Every boy found his presents. true if every boy found all of his presents false if at least one boy found none of his presents undef.…”

“…This is correct for the affirmative (10a) but not for its negation (10b). (10b) is true as soon as one of John's children read none of the books and does not carry an additional entailment that none of the children read only some of the books (see Križ and Chemla, for experimental data confirming this).…”

“…Negated sentences did not feature in the experiment. Križ and Chemla () presented both affirmative and negated sentences with the three answer options completely true , completely false , and neither . For undefined sentences, answers were predominantly split between completely false and neither , with only a small proportion of completely true responses, whereas sentences that were either true or false received very consistent responses.…”