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The Modal Framework of Physical Reality: Structured Contingency and the Quantum Foundations of Modality

James Anthony Ducey

Published Sep 10, 2026• 0 citations
Publisher

Abstract

Abstract: The classical architecture of physical science and analytic metaphysics has often been associated with deterministic necessitarianism, according to which a complete specification of antecedent conditions and governing laws uniquely determines subsequent physical states. The advent of quantum mechanics challenges this picture without thereby implying unconstrained modal chaos. This paper develops a tripartite modal framework comprising Strong PSR ($S$), Unconstrained Contingency ($U$), and Structured Contingency ($W$). Let $\mathcal{P}$ denote the broad domain of logically and mathematically formulable physical configurations, and $\mathcal{A}$ the subset physically realizable under the relevant nomological framework. Structured Contingency is defined as $W \iff (|\mathcal{A}|>1)\land(\mathcal{A}\subsetneq\mathcal{P})$. Using a dual-front methodology, the paper first draws deductive consequences from two empirically grounded premises: quantum openness ($E_1$), represented by $|\mathcal{A}|>1$, and structural constraint ($E_2$), represented by $\mathcal{A}\subsetneq\mathcal{P}$. Together these yield the formal synthesis $E_1\land E_2\vdash W$, while $E_1$ independently excludes Strong PSR under the framework's specified modal interpretation. The paper then conducts a comparative abductive evaluation of $W$ against Unconstrained Contingency, arguing that $W$ provides superior descriptive adequacy and explanatory parsimony because it accommodates genuine physical plurality while preserving the objective structural regularities exhibited by quantum theory. The resulting Lemma of Structured Contingency is offered not as a new mathematical theorem, but as a formal synthesis of modal plurality and nomological constraint. The framework thus provides an analytically austere account of physical modality as simultaneously open and structurally bounded.

DOI
10.5281/zenodo.22711036

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Abstract: The classical architecture of physical science and analytic metaphysics has often been associated with deterministic necessitarianism, according to which a complete specification of antecedent conditions and governing laws uniquely determines subsequent physical states. The advent of quantum mechanics challenges this picture without thereby implying unconstrained modal chaos. This paper develops a tripartite modal framework comprising Strong PSR (SSS), Unconstrained Contingency (UUU), and Structured Contingency (WWW). Let P\mathcal{P}P denote the broad domain of logically and mathematically formulable physical configurations, and A\mathcal{A}A the subset physically realizable under the relevant nomological framework. Structured Contingency is defined as W  ⟺  (∣A∣>1)∧(A⊊P)W \iff (|\mathcal{A}|>1)\land(\mathcal{A}\subsetneq\mathcal{P})W⟺(∣A∣>1)∧(A⊊P). Using a dual-front methodology, the paper first draws deductive consequences from two empirically grounded premises: quantum openness (E1E_1E1​), represented by ∣A∣>1|\mathcal{A}|>1∣A∣>1, and structural constraint (E2E_2E2​), represented by A⊊P\mathcal{A}\subsetneq\mathcal{P}A⊊P. Together these yield the formal synthesis E1∧E2⊢WE_1\land E_2\vdash WE1​∧E2​⊢W, while E1E_1E1​ independently excludes Strong PSR under the framework's specified modal interpretation. The paper then conducts a comparative abductive evaluation of WWW against Unconstrained Contingency, arguing that WWW provides superior descriptive adequacy and explanatory parsimony because it accommodates genuine physical plurality while preserving the objective structural regularities exhibited by quantum theory. The resulting Lemma of Structured Contingency is offered not as a new mathematical theorem, but as a formal synthesis of modal plurality and nomological constraint. The framework thus provides an analytically austere account of physical modality as simultaneously open and structurally bounded.
Abstract Contingency is everywhere, but what is it? This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and on cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, actuality, chance, counterfactuals, and a host of related modal notions. The framework is a modal realist one, in the tradition of David Lewis: all genuine possibilities are on a par, and the actual world is simply the one that we ourselves inhabit. It departs from Lewisian modal realism in that quantum possible worlds are not philosophical posits but scientific discoveries. Contingency and other modal notions have often been seen as beyond the limits of science. Rationalist metaphysicians argue that the metaphysics of modality is strictly prior to any scientific investigation: metaphysics establishes which worlds are possible, and physics merely checks which of these worlds is actual. Naturalistic metaphysicians respond that science may discover new possibilities and new impossibilities. This book’s quantum theory of contingency takes naturalistic metaphysics one step further, allowing that science may discover what it is to be possible. As electromagnetism revealed the nature of light, as acoustics revealed the nature of sound, as statistical mechanics revealed the nature of heat, so quantum physics reveals the nature of contingency.
Contingency is everywhere, but what is it? This book defends a radical new theory of contingency as a physical phenomenon. Drawing on the many-worlds approach to quantum theory and on cutting-edge metaphysics and philosophy of science, it argues that quantum theories are best understood as telling us about the space of genuine possibilities rather than as telling us solely about actuality. When quantum physics is taken seriously in the way first proposed by Hugh Everett III, it provides the resources for a new systematic metaphysical framework encompassing possibility, necessity, actuality, chance, counterfactuals and a host of related modal notions. The framework is a modal realist one, in the tradition of David Lewis: all genuine possibilities are on a par, and the actual world is simply the one that we ourselves inhabit. It departs from Lewisian modal realism in that quantum possible worlds are not philosophical posits but scientific discoveries. Contingency and other modal notions have often been seen as beyond the limits of science. Rationalist metaphysicians argue that the metaphysics of modality is strictly prior to any scientific investigation: metaphysics establishes which worlds are possible, and physics merely checks which of these worlds is actual. Naturalistic metaphysicians respond that science may discover new possibilities and new impossibilities. This book’s quantum theory of contingency takes naturalistic metaphysics one step further, allowing that science may discover what it is to be possible. As electromagnetism revealed the nature of light, as acoustics revealed the nature of sound, as statistical mechanics revealed the nature of heat, so quantum physics reveals the nature of contingency.
The interpretation of quantum mechanics due to Everett (1957) postulates the existence of many worlds. The analysis of modality due to Lewis (1986) is supported by the postulation of the existence of many worlds. Accordingly, if we take the modally relevant plurality of worlds (or multiverse) to be the one that this bit of physics gives us, we might obtain a unified and comprehensive naturalistic cosmology: a theory which accounts for all modal truth in terms of being, and which carries the epistemological authority of natural science. Thus the quantum modal realism (QMR) of Alastair Wilson in The Nature of Contingency. This is a thoroughly stimulating and clearly written work that argues for a genuinely big idea. Taking on both the philosophy of physics...
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.
Every physical measurement ever conducted has yielded exactly one outcome: self-identical, non-contradictory, determinate. This paper argues that the Three Fundamental Laws of Logic (Identity, Non-Contradiction, and Excluded Middle) are not cognitive conventions but ontological constraints constitutive of physical distinguishability. From this thesis, quantum mechanics emerges as the unique stable structure at the interface between non-Boolean possibility and Boolean actuality. The framework derives rather than postulates: complex Hilbert space structure follows from interface constraints combined with the physical requirement of compositional consistency (local tomography); the Born rule follows from Gleason's theorem; unitary dynamics follows from information preservation requirements. One structural prediction, that quantum mechanics requires complex amplitudes, has been experimentally confirmed (Renou et al., 2021). The framework specifies twelve explicit conditions that would falsify it. Logic Realism Theory provides unified explanation for seventeen quantum phenomena that other interpretations treat as independent postulates, while maintaining realism, locality, and parsimony.
Classical and quantum physics are standardly contrasted through continuity versus discreteness, determinism versus probability, and definite properties versus measurement-dependent outcomes. This paper argues that beneath these real differences lies a deeper philosophical convergence: both theories rely on mathematical spaces of possibility that must not be confused with reality itself. Classical mechanics describes continuous ranges of possible trajectories, yet actualizes only one constrained path under given causes and conditions. Quantum mechanics describes structured possibilities through states, operators, eigenstates, and eigenvalues, yet these are not realities existing in advance but formal expressions of what may become definite under a physical context of measurement. The paper makes three contributions. First, it develops the concept of constrained actualization as a single modal grammar spanning both theories: reality is neither the free unfolding of all possibilities nor the mere execution of mathematics, but the actualization of what constraints permit. Second, it constructs an eigenvalue bridge from macroscopic to quantum systems: strings, membranes, and engineered structures exhibit constrained eigenmodes, and the decisive difference is that classical eigenmodes reveal the constrained forms of motion, while quantum eigenstates reveal the constrained forms of definite physical answer. Third, it situates the model against Heisenbergian potentia realism, propensity interpretations, dispositionalist metaphysics, and structural realism, showing it to be ontologically more minimal, relational rather than property-based, situational rather than essentialist, and event-preserving, while its compatibility with decoherence and its support from the Kochen–Specker theorem are made explicit. Quantum mechanics, on this account, radicalizes an insight classical mechanics conceals: constraint operates within the very structure of possible outcomes.