Logic Realism Theory (LRT) proposes that the Three Fundamental Laws of Logic (3FLL)—Identity, Non-Contradiction, and Excluded Middle—are not merely rules of reasoning but ontological constraints constitutive of physical distinguishability. The core evidence is an asymmetry: we can conceive of 3FLL violations, yet physical reality never produces them. This asymmetry indicates that 3FLL constrain reality, not merely cognition. This paper develops the philosophical foundations of this claim. We argue that: (1) 3FLL have a dual character, functioning both epistemically and ontologically; (2) quantum mechanics emerges as the unique "interface" structure mediating between non-Boolean possibility and Boolean actuality; (3) this framework resolves longstanding interpretive puzzles while maintaining scientific realism. The result is a form of structural realism grounded in logical necessity rather than contingent physical law.
Logic Realism Theory (LRT) proposes that the Three Fundamental Laws of Logic (3FLL)—Identity, Non-Contradiction, and Excluded Middle—are not merely rules of reasoning but ontological constraints constitutive of physical distinguishability. The core evidence is an asymmetry: we can conceive of 3FLL violations, yet physical reality never produces them. This asymmetry indicates that 3FLL constrain reality, not merely cognition. This paper develops the philosophical foundations of this claim. We argue that: (1) 3FLL have a dual character, functioning both epistemically and ontologically; (2) quantum mechanics emerges as the unique "interface" structure mediating between non-Boolean possibility and Boolean actuality; (3) this framework resolves longstanding interpretive puzzles while maintaining scientific realism. The result is a form of structural realism grounded in logical necessity rather than contingent physical law.
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.
Logic Realism Theory (LRT) derives non-relativistic quantum mechanics from the claim that the Three Fundamental Laws of Logic are ontological constraints constitutive of physical distinguishability. This paper extends LRT to quantum field theory through a tiered derivation structure with explicit physical inputs at each level. We establish three principal results: (1) Fock space structure is derived from LRT axioms plus Lorentz invariance and locality; (2) the spin-statistics connection follows from Lorentz invariance and microcausality via the standard Pauli argument; (3) the uniqueness of complex QFT is established. The paper distinguishes derivations from interpretations. Cluster decomposition, vacuum uniqueness, and the spectral gap are physical inputs (Tier 4), not consequences of logical constraints. Renormalization is interpreted as 3FLL-restoration at UV scales, but this does not derive renormalization group equations. Four predictions and six strong falsifiers are identified.
This working paper derives quantum non-decomposability, Bell's theorem, and Kochen-Specker contextuality from Logic Realism Theory's single foundational equation A_Ω = L₃(I∞), where I∞ is the Infinite Information Space, L₃ is the Three Fundamental Laws of Logic acting as a selection functional, and A_Ω is the actualized domain. The paper establishes that LRT is a one-equation theory: all results are downstream of the core equation with no independent primitives introduced. Key results: (1) the Unique Necessary Successor (UNS) constraint is derived as a theorem of L₃ via Identity and Excluded Middle, tightened by Leibniz Identity of Indiscernibles; (2) quantum probability is reinterpreted as epistemic underdetermination of state description, with the Born rule as the unique consistent measure over incomplete descriptions via Gleason; (3) the Joint Resolution Condition (JRC) is proved equivalent to Schmidt rank > 1, establishing that entangled states are logically forced by tensor product structure; (4) the Non-Decomposability Theorem shows that decomposing a JRC-satisfying configuration into local sub-descriptions necessarily violates Excluded Middle; (5) Bell's theorem and Kochen-Specker contextuality follow as downstream consequences. LRT is distinguished from hidden variable programs (Bohm, 't Hooft) by its grounding direction: from logic to physics, not from physics to supplemented physics. Three open formalizations for Lean 4 are identified.
This companion paper provides the rigorous mathematical constructions underlying Logic Realism Theory. We prove three key results: (1) the Hardy kernel construction derives inner product structure directly from the distinguishability metric D without presupposing Hilbert space or the Born rule; (2) LRT axioms imply all five Masanes-Müller axioms, including MM5 (entanglement connectivity) via the Lee-Selby theorem applied to CBP-enforced purification uniqueness; (3) complex quantum mechanics is the unique theory satisfying LRT axioms. The derivation chain from logical constraints (3FLL) to quantum mechanics is complete—no conditional hedges or irreducible gaps remain.
Contemporary foundations of physics divides into two programs that address different questions and leave a third unanswered. Reconstruction programs derive quantum structure from operational axioms but do not explain why those axioms hold. Interpretational programs address what the quantum formalism describes but presuppose its mathematical structure. Neither program asks what the necessary conditions for any physically admissible theory are. This paper addresses that third question by proposing the Triadic Reality Model (TRM): the claim that any framework capable of coherently grounding physics must instantiate three irreducible co-primitives: L3 (the classical laws of logic as an ontological constraint on actualized states), I-infinity (an infinite configurability space of L3-respecting informational structures), and A (a primitive actualization principle prior to and generative of temporal structure). The three are defended individually and shown to be irreducible. The TRM is not a rival dynamical theory but an ecumenical meta-framework specifying necessary conditions that any admissible physical theory must satisfy. Classical mechanics and quantum mechanics are analyzed as triadic models. Falsifiability is addressed. The bridge equation is decomposed into three explicitly distinguished claims: grounding, characterization, and plenitude identity.Keywords: foundations of physics, logical realism, actualization, quantum reconstruction, philosophy of physics, triadic ontology, transcendental necessity, information
Logic Field Theory: A Foundational Program In this position paper, J. D. Longmire introduces Logic Field Theory (LFT), an ontological reconstruction of quantum mechanics rooted in the three classical laws of logic. By defining the physical state space as Ω = L(S) ,\Omega \;=\; L(S)\,, where SS is the Boolean algebra of all information configurations and LL enforces identity, non-contradiction, and excluded-middle, LFT demonstrates how orthomodular lattice structure, Hilbert-space representations, and unitary dynamics emerge naturally. Three central conjectures—(1) uniqueness of the complex Hilbert representation, (2) strong-continuity of the automorphism group yielding Schrödinger evolution, and (3) a pilot-wave ontology from logical non-distributivity—are verified in a finite C4\mathbb{C}^4 lattice model. A uniform counting measure over microstates reproduces the Born rule, and a perturbative “logic-scale” bound γ<4×10−17\gamma<4\times10^{-17} m from hydrogen spectroscopy (with a proposed muonic-hydrogen test to γ>10−20\gamma>10^{-20} m) offers a clear path to experimental falsification. LFT thus reframes quantum foundations as constraint-satisfaction in an information field, uniting measurement, non-locality, and the “unreasonable effectiveness” of mathematics under logical necessity.