Many metaethicists agree that as ordinary people experience morality as a realm of objective truths, we have a prima facie reason to believe that it actually is such a realm. Recently, worries have been raised about the validity of the extant psychological research on this argument’s empirical hypothesis. Our aim is to advance this research, taking these worries into account. First, we propose a new experimental design for measuring folk intuitions about moral objectivity that may serve as an inspiration for future studies. Then we report and discuss the results of a survey that was based on this design. In our study, most of our participants denied the existence of objective truths about most or all moral issues. In particular, many of them had the intuition that whether moral sentences are true depends both on their own moral beliefs and on the dominant moral beliefs within their culture. This finding suggests that the realist presumptive argument may have to be rejected and that instead anti-realism may have a presumption in its favor.