Virtual reconstruction should go beyond merely presenting images and 3D models by docu-menting the scientific context and reasoning underlying the reconstruction process, rather thanjust showcasing the final product. For instance, the collapsed transverse arch in the nave ofNotre-Dame de Paris serves as a case study to demonstrate an interdisciplinary reconstructionworkflow. By letting the voussoirs speak, we mean that the materiality of the voussoirs andimmateriality of digital surrogates are the support to make explicit the argumentation of thereconstruction. The 3D visualization moves away from a static and finalized illustrative outputof the reconstruction study and toward an open and dynamic visualization of reconstructiondata. The data explicitly records both factual information on the physical and digital objects,as well as the counterfactual propositions of the reasoning of reconstruction hypotheses. Theproposed experiment is twofold: (1) setting up of the 3D dataset of the arch reconstructionwith archaeological argumentation where the hypotheses are modeled as versions, and (2)evaluation of the scientific narrative of reconstruction argumentation through both a custom3D visualization and competency questions on the enriched 3D data combining hypothesesand arguments. The humanistic question of reconstruction is the starting point for a nonlinearscientific narrative composed of hypotheses and argument loops. We consider the conflictinginterpretations of the voussoirs and the knowledge encapsulated in relation to the spatialconfiguration of the arch. The results of the queries and 3D visualization are interdependent:they demonstrate that hypothetical reasoning facets of the arch reconstruction are embeddedin the spacetime volumes of the voussoirs.