Christina Lafont has argued that the early Heidegger's reflections on truth and understanding are incompatible with ‘the supposition of a single objective world’. This paper presents her argument, reviews some responses that the existing Heidegger literature suggests, and offers what I argue is a superior response. Building on a deeper exploration of just what the above ‘supposition’ demands, I argue that a crucial assumption that Lafont and Haugeland both accept must be rejected, namely, that different ‘understandings of Being’ can be (...) viewed as offering ‘rival perspectives’ on a common subject-matter. I develop this case by drawing on an alternative account of what a Heideggerian ‘understanding of Being’ might be like. (shrink)