Ontological Leakage and the Failure of Translation Across Multi-Topos Systems A Structural Account of Non-Compositionality in Descriptive Frameworks

Abstract This paper develops a structural account of ontological leakage as a limitation on translation between heterogeneous descriptive systems. Departing from strong commensurability assumptions in philosophy of science, it is argued that certain translation failures arise from incompatibilities in inferential structure, temporal organization, and conditions of compositionality across systems. Building on work on incommensurability (Kuhn, 1962; Quine, 1960) and localized coordination (Galison, 1997), a three-level framework—structural, material, and network—is introduced. These levels are interpreted as interacting regimes of representation rather than ontologically distinct domains. Ontological leakage is defined as the failure of structure-preserving mappings across such regimes. A case study in distributed computational systems is used to illustrate the model. The paper concludes with a minimal subject-theoretic interpretation in which subjectivity is understood as a stable pattern emerging from persistent non-equivalence between descriptive domains. Keywords: incommensurability, philosophy of science, translation, category theory, systems theory, subjectivity