From Boolean Contexts to Ontological Actualization The COAF Framework in the BBMT Model

This article develops a contextual Boolean formalization of the Bell-Bohm-Modal-Thomistic (BBMT) model under the provisional name Contextual Ontological Actualization Framework (COAF). Its central thesis is deliberately limited: Boolean algebra does not prove the Aristotelian-Thomistic metaphysics of potency and actuality, but it can represent, within compatible quantum contexts, a disciplined sequence of determination, modality, actualization, and renewed determination. That is, it aims to show a path to accessing analogical ontology from BBMT. In this case, the idea is to maximize the algebraic route and postpone conceptual interpretation until the last moment. As I will show in subsequent articles, other options exist, but for now we will follow this path. Under this proposal, the global network of quantum propositions is distinguished from Boolean subalgebras associated with compatible observables, while a privileged beable algebra linked to position is examined as the domain in which a defined valuation can be assigned without postulating a prohibited global valuation1. On the other hand, the transition from physical-mathematical structure to ontology is governed neither by univocal identity nor by equivocal separation, but by a composite analogy. At this point, it is necessary to keep in mind two elements of the realist ontological framework that inspire BBMT-COAF: 1) Reality is divided into actual and potential; that is, potency is part of reality, because otherwise it would be impossible for a being to become actual. 2) The entity, as a transcendental concept, is analogous, and this analogy is twofold: it possesses a horizontal dimension expressed in proportionality and a vertical dimension expressed in its attributive predicability. This last element is the position subscribed to by the author in the discussion of specialists, which should be taken beforehand as a hermeneutical prejudice. Horizontally, a proper proportionality analogy compares the relation between physical possibility and physical actuality with that between potentiality and act. Vertically, an analogy of intrinsic attribution orders physical actuality and potentiality to their ontological analogs. Building on Ángel González Álvarez's synthesis of the Thomistic analogy and Santiago Ramírez's proposed correction to the Cayetano-Suárez opposition, this work also clarifies the conception of being that should govern the interpretation: a being is not an abstract logical unity, but rather the inseparable unity of essence and existence, intrinsically realized in diverse ways. Consequently, COAF is presented as a research program and a formal correspondence, not as a deduction of ontology from quantum mechanics. Furthermore, we must not forget that we are attempting to demonstrate that the analogical realist interpretation is not contradictory; that is, we begin with analogy and then demonstrate that this interpretive option of scientific realism does not lead to contradiction. This technique does not imply circularity and is used in various sciences when direct demonstration, whether experimental or deductive, is not possible. It thus proves that a proposition considered true will maintain this condition as long as no derived contradiction is found. Moreover, we must also remember that the BBMT model and its COAF form part of a hermeneutic and, consequently, interpretive thesis.