Determiner phrases (DPs) under intensional operators give rise to multiple interpretations, known as the de re/de dicto ambiguity. Formal theoretical approaches to modeling this ambiguity must rely on nuanced semantic judgments, but inconsistent judgments in the literature suggest that informal judgment collection may be insufficient. In addition, little is known about how these ambiguities are resolved in context and how preferences between these readings vary by context and across individuals, etc. We reported three controlled experiments to systemize the truth-value judgment collection of de re/de dicto readings. While the de dicto readings were robustly accepted by nearly all English speakers, de re readings exhibited strongly bimodal judgments, suggesting an inherent disagreement among speakers. In addition, the acceptability of de re judgments was affected by the DP's internal structure as well as idiosyncratic scenarios. More broadly, our experimental results lend support to the practice of including quantitative data collection within semantics.