This chapter critiques the dualist methodological assumptions underpinning conventional approaches to meaning and translation in IR, which treat texts and traditions as bounded entities whose meanings can be fixed, compared, and transferred across geocultural contexts. It shows that both orthodox and reflexive approaches to comparison—discursive, contrapuntal, and vernacular—remain structured by implicit binary distinctions that reproduce epistemic separations between traditions. In response, the chapter develops Archimedean Meeting, drawing on Raimon Panikkar’s imparative philosophy, as a nondualist methodological framework that reorients cross-cultural enquiry beyond comparison. Central to this framework is the practice of crisscross reading, through which meaning emerges across multiple, intersecting interpretive movements rather than from a single epistemic standpoint. This approach is operationalised through the mutual encounter procedure (MEP), which reconfigures how researchers engage with diverse textual traditions by foregrounding relational movement, reflexivity, and openness to transformation. Applied to contexts of ethno-religious conflict, the chapter demonstrates how Archimedean Meeting enables the reinterpretation of competing truth claims without reinforcing binary oppositions, thereby offering a post-binary methodological pathway for engaging with global political life.