Weakening the trivalent semantics of quantifiers: Evidence from Mandarin Chinese
Yaxuan Wang, Brian Buccola
August 2023 

A vexing question in current presupposition theory is what a sentence with a presupposition trigger presupposes when it is in the scope of different quantifiers. Four dominant theories in the area, namely, Universal Theories, Existential Theories, Similarity Theory, and Trivalent Logic Theory, make different predictions about presuppositions of sentences like Each/Some/None of the boys knows he is lucky. The current paper argues that previous experimental studies are not sufficient to adjudicate among the four theories, and this work is designed to investigate this issue. Native Mandarin Chinese speakers were recruited to evaluate the naturalness of different quantified sentences with presupposition triggers under different contexts. The results are generally consistent with previous studies, with new findings that (i) a trigger type effect is attested once individual variation is taken into consideration; (ii) existential presuppositions are highly available from none sentences (pace Chemla 2009); (iii) no participant showed a pattern in which universal presuppositions projected from all types of quantifiers (pace Sudo et al. 2012). None of the current theories is sufficient to account for such results. We propose to modify the Trivalent Logic Theory (Fox 2013) by weakening the assumed universal statement in the truth conditions of quantified sentences to an existential one. We extend the triggering source of the repair mechanism (A-operator) and eliminate the redundant Pragmatic Strengthening strategy. This study mainly lends support to the trivalent logic approach and the assumption that presuppositions can be collapsed with truth conditions. It also suggests that the lexical meaning of quantifiers at the presupposition level should be existential rather than universal, independent of quantifier type.

Format:	[ pdf ]
Reference:	lingbuzz/007483 (please use that when you cite this article)
Published in:	WCCFL 41
keywords:	presupposition projection, trivalent logic, experimental semantics, mandarin chinese, semantics
previous versions:	v2 [August 2023] v1 [August 2023]
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