Is the basic mechanism behind presupposition projection fundamentally asymmetricor symmetric? This is a basic question for the theory of presupposition, and alsobears on broader issues concerning the source of asymmetries observed in naturallanguage: are these simply rooted in superficial asymmetries of language use—language use unfolds in time, which we experience as fundamentally asymmetric—or can they be, at least in part, directly referenced in linguistic knowledge andrepresentations? In this paper we aim to make progress on these questions byexploring presupposition projection across conjunction, which has typically beentaken as a central piece of evidence that presupposition projection is asymmetric.As a number of authors have recently pointed out, however, whether or not thisconclusion is warranted is not clear once we take into account independent issues ofredundancy. Building on previous work by Chemla & Schlenker (2012) and Schwarz(2015), we approach this question experimentally by using an inference task whichcontrols for redundancy and presupposition suspension. We find strong evidence forleft-to-right filtering across conjunctions, but no evidence for right-to-left filtering,suggesting that, at least as a default, presupposition projection across conjunction isindeed asymmetric.