Perspectivist Account of Truth-Theoretic Semantics in Quantum Mechanics

Abstract: According to various no-go results in the foundations of quantum mechanics, for any system associated to a Hilbert space of dimension higher than two, it is not possible to assign definite truth values to all propositions pertaining to the system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton uniqueness theorem is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. On this basis, a perspectivist/contextual account of truth valuation in the quantum domain is produced that satisfies Tarski's criterion of material adequacy for a theory of truth. In light of the latter, perspectivist truth conforms to perspective or context-bound correspondence of a de re nature, designating locally an objectively existing state of affairs. Such an account derives by virtue of the microphysical nature of physical reality in displaying a context-dependence of facts; thus, it essentially opposes a non-perspectival, metaphysically fixed point of reference, or a panoptical standpoint from which to state all facts of nature.

• The paper introduces a formal account of truth in quantum mechanics that is fundamentally context-dependent and hinges on perspectivist principles.
• It employs results like the Kochen-Specker and Bub-Clifton theorems to restrict truth assignments to specific Boolean sublattices of quantum propositions.
• The framework challenges classical, non-contextual views and informs practical applications in quantum computation and semantic theory.

Perspectivist Account of Truth-Theoretic Semantics in Quantum Mechanics

Introduction

The paper "Perspectivist Account of Truth-Theoretic Semantics in Quantum Mechanics" (2604.11823) develops a rigorous philosophical and formalist account of truth in quantum mechanics, grounded in the theory of perspectivism and contextuality. The author leverages foundational results, notably the Kochen-Specker theorem and the Bub-Clifton uniqueness theorem, to argue against classical, non-contextual conceptions of truth and semantics in quantum theory. Instead, the paper delivers a perspectivist/contextual account, linking the attribution of truth values to quantum propositions with particular measurement contexts, and aligns this approach with Tarski's material adequacy condition for theories of truth.

Theoretical Foundations: Scientific Perspectivism and Quantum Contextuality

Contemporary scientific perspectivism challenges the duality between metaphysical realism (context-independent universal truth) and epistemic constructivism (radical relativism). Within this framework, all knowledge claims are irreducibly context-bound—no claim or observation in science is independent of the historically and conceptually situated perspective from which it is made. The author extends this notion, characterizing perspectives as formal, endo-theoretical constructs defined by sets of descriptive variables relevant to the targeted system. In quantum physics, this translates concretely to the selection of subsets of observables or, equivalently, to maximal Boolean subalgebras of the non-Boolean lattice of quantum event structures.

Quantum mechanics is shown to encode perspectival reasoning at its core by virtue of contextuality: the impossibility of noncontextual global truth value assignments to all projection operators on Hilbert spaces of dimension greater than two (as established by the Kochen-Specker theorem). Quantum propositions, expressed as projection operators in a Hilbert space, do not admit simultaneous, global, two-valued truth assignments—if such were attempted, a contradiction necessarily arises.

The paper stresses that empirical knowledge acquisition in quantum theory is thus necessarily mediated by context-bound perspectives, each instantiated by a set of mutually compatible observables (Boolean subalgebra). These provide the only admissible frames for ‘probing’ quantum systems and for making sense of measurement outcomes.

The Bub-Clifton Uniqueness Theorem and Maximal Determinate Sublattices

Building on the problem that the full lattice of quantum propositions does not allow for noncontextual bivalent truth assignments, the author invokes the Bub-Clifton uniqueness theorem. This theorem identifies, for a given quantum system in state $D$ and a choice of preferred observable $A$, a unique maximal sublattice of the full projection lattice, denoted ${\mathcal L}_{\mathcal H}(\{D_{A_i}\})$, within which propositions can be consistently assigned determinate truth values. Any such sublattice is a Boolean algebra, generated by the non-zero projections of $D$ onto the eigenspaces of $A$ (the $D_{A_i}$). There exist exactly $k$ two-valued homomorphisms on this sublattice, corresponding to the $k$ possible measurement outcomes for $A$.

Attempts to extend the truth assignment to all propositions (i.e., to enlarge the sublattice) result in reintroducing the Kochen-Specker contradiction; thus, the context (identified by chosen $A$ and state $A$0) sharply circumscribes the domain of definiteness for quantum truth. The maximal information encodable about a quantum system at time $A$1 aligns with the Boolean algebra defined by the state preparation and measured observable, yielding empirical access via a particular perspectival frame.

Perspectivist/Contextual Semantics and Tarski-style Material Adequacy

The author formulates an explicit alethic scheme denoted as Perspectivist/Contextual Correspondence (PCC):

The proposition $A$2-in-$A$3 is true if and only if there is a state of affairs $A$4 such that (1) $A$5 expresses $A$6 in $A$7, and (2) $A$8 obtains.

Here, the context $A$9 is formally identified as the physical specification of state ${\mathcal L}_{\mathcal H}(\{D_{A_i}\})$0 and measured observable ${\mathcal L}_{\mathcal H}(\{D_{A_i}\})$1, i.e., the experimental context. This framework yields an account of correspondence truth that is context-dependent in a deep structural sense, not merely as a pragmatic or epistemic addendum. In particular, this account satisfies Tarski’s condition of material adequacy:

${\mathcal L}_{\mathcal H}(\{D_{A_i}\})$2

Critically, truth-makers for quantum propositions are not global, monolithic facts, but context-dependent states of affairs revealed under specific measurement arrangements. The logic of quantum theory thereby forces a rejection of classical metaphysical fixed points of reference (the “God’s eye view”), replacing them with a plurality of empirical standpoints, each grounded in an operationally specified Boolean frame.

Theoretical and Practical Implications

The analysis reframes the notion of truth in quantum mechanics: quantum mechanical propositions are not true or false simpliciter, but only relative to experimentally specified local contexts. The PCC scheme is not an expression of alethic relativism but a formal recognition that the physical world, at the microlevel, is not amenable to context-independent elaboration. This perspective has decisive implications for the semantics of quantum theory, the study of quantum measurement, the architecture of quantum information protocols, and the ongoing debate about the interpretation of quantum mechanics.

Practically, this perspectivist semantics highlights that all information extracted from a quantum system is fundamentally context-dependent, bounding the ambitions of objectivist or realist interpretations that postulate pre-existing, measurement-independent realities. The framework may inform new approaches in quantum computation and communication, where quantum contextuality is recognized as a computational resource, and provides a principled basis for resisting naive classical analogues in modeling quantum truth assignment.

Conclusion

The paper establishes, with technical and philosophical precision, that quantum mechanics necessitates a perspectivist and contextual account of truth-theoretic semantics. The inability to globally assign bivalent truth values (Kochen-Specker) and the existence of uniquely maximal definite sublattices (Bub-Clifton theorem) collectively enforce a rejection of non-perspectival, metaphysically fixed conceptions of truth. The resultant PCC framework aligns with both formal semantic desiderata (Tarski) and physical practice, offering a robust basis for further investigation into the semantic and ontological architecture of quantum theory. The approach has continuing relevance for interpretational debates and suggests fruitful directions for theoretical development in the foundations of quantum mechanics and the philosophy of science.