People of my side ≈ people of the other side socionumerical systems in central brazil [Leute meiner Seite ≈ Leute der anderen Seite. Sozionumerische Systeme in Zentralbrasilien]

In this philosophical inquiry into the foundations of Xavante mathematical thought, numbers emerge as categories structured by social praxis in central Brazil. Clans, moieties, age-sets, and specific kin relations can be viewed as conventional symbols, or numerals, representing essential constituencies of the Xavante socionumerical system. As in other Gê-speaking societies of the Brazilian Amazon, Xavante numbers catalyze a set of presuppositions about dialectical mathematical systems whose rationality is informed by the pervasive dualism that governs social interaction for an estimated 8,000 Xavante today. The binary nature of this numerical system is a product of an omnipresent dialectical view of the world, always oscillating between an "us" and a "them" - or people of my side ≈ people of the other side. Accordingly, a unit is defined as the union of 2 fundamental parts, and numerical place value assumes the significance of reciprocal social relationships. The dialectical association of beings, human or not, material or symbolic, within the dynamism of Xavante dualism synthesizes these and other key ideas about the philosophy of Gê mathematical thought.