This paper argues that probabilistic structure should not be treated as ontologically primitive. Instead, probability is defined relative to conditions of recordability: it organizes spaces of possible records rather than properties of events as such. The analysis distinguishes between events, records, and probabilistic structures, and shows that probability acquires meaning only when stable, distinguishable, and reproducible records are available. In this view, Kolmogorovian probability theory provides a formally consistent framework, but does not specify how probabilistic domains arise from empirical observation. As a result, probabilistic formalism underdetermines ontology. Different ontological models can generate identical probabilistic structures, which implies that probability cannot serve as a direct guide to the nature of reality. The paper critically examines Ontic Structural Realism (OSR), arguing that it risks conflating representational structure with ontological structure. It concludes that any ontological interpretation of probabilistic or correlational structures requires independent justification beyond formalism.
This paper argues that probabilistic structure should not be treated as ontologically primitive. Instead, probability is defined relative to conditions of recordability: it organizes spaces of possible records rather than properties of events as such. The analysis distinguishes between events, records, and probabilistic structures, and shows that probability acquires meaning only when stable, distinguishable, and reproducible records are available. In this view, Kolmogorovian probability theory provides a formally consistent framework, but does not specify how probabilistic domains arise from empirical observation. As a result, probabilistic formalism underdetermines ontology. Different ontological models can generate identical probabilistic structures, which implies that probability cannot serve as a direct guide to the nature of reality. The paper critically examines Ontic Structural Realism (OSR), arguing that it risks conflating representational structure with ontological structure. It concludes that any ontological interpretation of probabilistic or correlational structures requires independent justification beyond formalism.
This essay proposes fundamental ontological clarification within contemporary debates on quantum physics: the rigorous distinction between probability as a regime of prediction and the real as material dynamics. Against the widespread view according to which quantum indeterminacy would imply a vague, unstable, or “merely statistical” reality, the text argues that probability belongs to the epistemic plane of knowledge and anticipation, not to the ontological plane of what exists. Quantum physics does not describe an ontologically fluctuating world, but a world whose symbolic access is structurally limited. On this basis, the essay examines the role of Born’s statistical interpretation, decoherence theory, Bell’s theorems, and the Pusey–Barrett–Rudolph result, showing how these impose formal costs on any ontology that conflates formalism and reality. In critical dialogue with QBist, relational, and agential-realist approaches, the text develops a conception of concretion grounded in the notion of mark: the concrete emerges when a material interaction is irreversibly inscribed in a physical support. Stability, far from meaning fixity, is understood as emergent robustness—movement in regime—sufficient to sustain practices, techniques, and historical continuity. The essay concludes by arguing that quantum physics, rather than dissolving the real, demands a more exacting ontology capable of distinguishing precisely between the real, the concrete, and theory.
Ontological models are attempts to quantitatively describe the results of a probabilistic theory, such as Quantum Mechanics, in a framework exhibiting an explicit realism-based underpinning. Unlike either the well known quasi-probability representations, or the "r-p" vector formalism, these models are contextual and by definition only involve positive probability distributions (and indicator functions). In this article we study how the ontological model formalism can be used to describe arbitrary statistics of a system subjected to a finite set of preparations and measurements. We present three models which can describe any such empirical data and then discuss how to turn an indeterministic model into a deterministic one. This raises the issue of how such models manifest contextuality, and we provide an explicit example to demonstrate this. In the second half of the paper we consider the issue of finding ontological models with as few ontic states as possible.
This preprint develops a discrete, ray‑based constructive ontology for closed physical systems in which stable local records, finite‑speed causal propagation, and dynamically defined subsystem boundaries are treated as primitive structural features. The framework distinguishes realized events (actuality) from constrained sets of admissible futures (possibility), with dynamics governed by local actualization and entanglement‑limited pruning of ray bundles. Within this setting, the work establishes a statistical no‑go theorem: realist ontologies that combine locally triggered updates with unbounded, single‑step global actualization generically render stable interference statistically atypical. This yields a structural constraint on admissible ontological models for closed systems supporting definite records and repeated interference phenomena. To demonstrate that the constrained space is nonempty, the paper introduces the possibility/actuality (P/A) ontology as a concrete constructive witness. The P/A ontology satisfies the stated axioms while maintaining bounded update domains through event‑defined entanglement structure and constrained pruning dynamics. Numerical simulations show that this ray‑based model reproduces qualitative signatures of interference and Tsirelson‑bounded correlations using only finite combinatorial resources and local rules. The analysis provides a structural classification of admissible realist ontologies under minimal assumptions and presents an algorithmic realization in which constraint propagation across shared event histories governs probability, correlation, and emergent phenomenology. All simulation code used to generate the numerical results is available in the associated public GitHub repository.
The article discusses approaches to understanding the nature of probability in mathematics and physics with the consequences of these approaches, as well as the difficulties that arise. The ontological status of probability is discussed. It is shown that probability theory, contrary to R. Mises, should be classified as a mathematical science, using the definition formulated by A.N. Kolmogorov. The application of this definition in practice is provided within the framework of the classical approach, provided that the connection with physical reality is defined through the concept of equal opportunity. To do this, the concepts of simple and complex events are introduced, and the method of decomposing complex events into simple ones is explained. The point of view is substantiated, according to which a mathematical probability determined and related to physical reality in this way can be considered an objective probability, that is, existing independently of any tests. Various interpretations of quantum mechanics and approaches to understanding probability are also revealed. It is shown that in physics today the existing approaches to understanding the nature of probability contradict each other. In the Bohm interpretation, probability is an analogue of the classical approach – statistical objective probability, which has a mathematical formalization, and in quantum Bayesianism, probability quantifies the degree of reliability and depends on the subject conducting the experiment. The Copenhagen interpretation of quantum mechanics tries to eliminate the difficulties associated with combining the wave and corpuscular properties of light and electron beams into a single picture by giving the ontological status of probability, which leads to the problem of understanding physical reality. The article argues for the need for a new connection between the mathematical description of probability and physical reality. The empirical (frequency) approach of R. Mises is analyzed, which causes a lot of criticism, as it does not have a clear consistent formalization. The article argues that this approach is inconsistent with quantum mechanics. The probability given by M. Born in the Copenhagen interpretation of quantum mechanics is also considered, which formulates a new definition of probability, which does not exclude the difficulties associated with the physical interpretation of probability. Born’s approach is based on the classical approach and is reduced to a formal axiomatic definition, which assumes the interpretation of probability as a mathematical construct. The connection of probability with physical reality and the consistency of the statistical method of finding probability values remain unresolved problems, which creates a dualism of understanding probability: in mathematics – one thing, in physics – another. If in the mathematical approach, the solution of these problems is carried out through the connection of probability with physical properties, then in quantum mechanics, in the Copenhagen interpretation, problems persist, which is caused by giving the wave function an ontological status.
Contemporary discussions of probability and observation remain divided between deterministic, random, and epistemic interpretations, none of which fully account for the structured relationship between awareness, indeterminacy, and experienced outcomes. In both physics and philosophy of science, probability is typically treated either as a mathematical abstraction or as a feature of physical systems, while the role of awareness is addressed operationally rather than ontologically.This paper proposes a structural reinterpretation of probability within the Three-Circle Ontology, a meta-ontological framework that distinguishes between foundational reality (Circle 1), structured possibility (Circle 2), and rendered experience (Circle 3). Within this framework, probability is modeled not as randomness or determinism, but as a selection constraint operating within a pre-existing field of structured possibilities. Awareness is proposed to function as an interface condition that mediates which possibilities transition into experiential frames, without exercising outcome control or violating physical causality.Rather than advancing an empirical or predictive theory, the paper offers a conceptual formalization of probability and observation that clarifies their ontological placement. The scope of the proposal is explicitly limited to structural interpretation and does not seek to replace existing physical or neuroscientific models.The contribution of this work lies in providing a coherent meta-ontological account of probability and awareness that addresses long-standing conceptual ambiguities and opens avenues for interdisciplinary critique and further formal development.
This paper argues that, where deterministic and indeterministic formulations agree on empirically corroborated structure while differing in their completion of structure that remains empirically underdetermined, features invariant across these formulations warrant ontological commitment, whereas any warrant attaching to features that vary across them is categorically more provisional. Because deterministic and indeterministic completions are always formally available, while additional grounds for preferring particular completions are contingent and defeasible, empirically corroborated structure alone cannot determine whether reality is fundamentally deterministic or indeterministic, or whether that very distinction belongs only to specific representations of it.
On this basis, I advance a model-invariance criterion according to which structural features are candidates for realist commitment insofar as they are empirically corroborated within a regime and preserved across the admissible formulations of that structure. I show how such invariant content can be characterised in mathematically intelligible ways, yielding a fallibilist form of structural realism grounded in model-invariance rather than in the specific form of any given mathematical representation. Features such as conservation relations, invariant measures, symmetries, and probability or correlation structures over observable histories may satisfy this criterion. By contrast, the localisation of modal selection---whether in fine-grained initial conditions, stochastic outcomes, or state-update and collapse mechanisms---may vary across empirically admissible formulations and therefore constitute a gauge-like representational freedom.
This framework offers a realist ontology for modern physics that combines empirical openness with resistance to metaphysical overreach.