Empirical Structure Physicalism

• Empirical structure physicalism is a framework that redefines physicalism by mapping empirical distinctions of special sciences onto physics via theory supervenience.
• It establishes a reduction approach that emphasizes history-descriptions and empirical structures over traditional ontological entities.
• Debates challenge whether structural analyses alone can account for observer phenomena and consciousness in both physics and mind.

Searching arXiv for papers on empirical structure physicalism and related structural realism/observer papers. arXiv search: "empirical structure physicalism" Empirical structure physicalism is a form of physicalism that reconstructs reduction and dependence in terms of the empirical structures of theories rather than in terms of ontology, reference, or entity identity. In its canonical formulation, the thesis is that the current special sciences supervene both on current physics and on future physics, where supervenience means that physics refines the empirical distinctions the special sciences can make (Gyenis, 26 Jul 2025). In adjacent debates, however, the expression is also used polemically for a stronger structure-only view according to which observers, observables, and consciousness are exhausted by relational or formal structure alone; several papers argue that this stronger thesis fails because structure does not by itself fix the physical meaning of observables or secure any reliable correspondence between memory and world (Stoica, 2023).

1. Definition, empirical structure, and theory supervenience

In the formulation introduced in "Empirical structure physicalism and realism, Hempel's dilemma, and an optimistic meta-induction" (Gyenis, 26 Jul 2025), the basic unit is not an entity or a property but a theory-relative history-description $h$ of a region $R$. A history-description is empirically adequate to a space-time region $R$ according to a theory $T$ if the idealization used by $h$ is admissible by $T$, $h$ can be taken to represent happenings throughout and restricted to $R$, and what $h$ says about observable quantities approximately matches the reports of observables in $R$, within the approximation allowed by $R$0.

The paper then defines the empirical content of a region $R$1 according to $R$2 as

$R$3

where $R$4 is the set of history-descriptions of $R$5, and $R$6 is the empirical adequacy relation. The empirical structure of $R$7 is the partition of all space-time regions according to sameness of empirical content:

$R$8

Two regions are therefore placed in the same cell exactly when the theory treats them as empirically indistinguishable.

On this basis, the paper introduces theory supervenience as a relation between empirical structures. Three equivalent formulations are given. The empirical-content formulation is

$R$9

The no-collapse formulation is

$R$0

The partition-refinement formulation is

$R$1

The notation

$R$2

means that $R$3 supervenes on $R$4, or equivalently that $R$5 refines the empirical structure of $R$6. If both directions hold, $R$7, the theories have the same empirical structure. If only $R$8 but not conversely, then $R$9 strongly supervenes on $T$0, and $T$1 renders $T$2 empirically dispensable and non-fundamental (Gyenis, 26 Jul 2025).

This framework yields a reductive relation without requiring identity of vocabularies, ontologies, or history-descriptions. What matters is whether a physical theory can preserve and sharpen the empirical discriminations already made by another theory.

2. Canonical doctrine and the response to Hempel’s dilemma

The core doctrine is explicitly divided into three theses (Gyenis, 26 Jul 2025):

Thesis	Formula	Content
Currentist empirical structure physicalism	$T$3	Current special sciences are currently empirically dispensable
Futurist empirical structure physicalism	$T$4	Current special sciences are empirically dispensable in the future
Full empirical structure physicalism	$T$5	The conjunction of $T$6 and $T$7

The formal statements are:

$T$8

$T$9

$h$0

This reconstruction is proposed as a solution to a generalized Hempel’s dilemma. The dilemma, as reconstructed in the paper, turns on four claims: metaphysical physicalism; the need to fix “physical” by a theory or theories of physics; the likely incompleteness of current physics; and the current unknowability of future physics. If physicalism is tied to current physics, it risks falsity because current physics is incomplete. If it is tied to future physics, it risks present indeterminacy. If it is tied to an ideal theory, it risks triviality.

Empirical structure physicalism changes the target relation. Instead of asking whether special-science truths are made true by the ontology of physics, it asks whether physics can distinguish the same empirical differences that the special sciences distinguish. On this reconstruction, the incompleteness of current physics is not automatically fatal to $h$1, because the thesis does not require shared ontology or shared descriptive resources. It requires only that whenever the special sciences distinguish two regions empirically, current physics also distinguishes them empirically (Gyenis, 26 Jul 2025).

The future-directed horn is addressed by combining $h$2 with future empirical structure realism $h$3. The paper defines $h$4 as past empirical structure realism, $h$5 as future empirical structure realism, and $h$6 as the general claim that later physics refines the empirical structure of earlier physics. The transition from present to future is then secured by transitivity of supervenience: if current special sciences supervene on current physics and current physics supervenes on future physics, current special sciences supervene on future physics. The paper presents this as a deductive consequence rather than an ad hoc appeal to an unknown future theory (Gyenis, 26 Jul 2025).

This same architecture is used to argue that mental theories remain empirically dispensable in the future. The conclusion is explicitly not eliminativist about vocabulary: just as “pressure” and “temperature” may remain in physics while being empirically dispensable relative to deeper theory, mental vocabulary might remain in future physics while still being non-fundamental (Gyenis, 26 Jul 2025).

3. Observers, observables, and the anti-structural critique

A distinct cluster of papers argues that empirical structure physicalism fails when it is interpreted as the thesis that observers are nothing over and above structure. In "Are observers reducible to structures?" (Stoica, 2023), a physical system is represented by a state vector $h$7 in a Hilbert space $h$8, and physical properties are represented by Hermitian operators $h$9, with definiteness condition

$T$0

A preferred basis $T$1 defines the wavefunction

$T$2

The paper treats a system’s structure as the pattern encoded in this wavefunction—factorization, entanglement, correlations, and related features—and defines an observer-like structure as a structure isomorphic to the structure of an observer.

The central argument is symmetry-based. In quantum theory, unitary transformations and, in classical theory, canonical transformations preserve the form of the laws. For a unitary $T$3,

$T$4

and specifically

$T$5

The transformed parameter space is denoted $T$6, and the transformed wavefunction is

$T$7

The paper’s claim is not merely that different parametrizations underdetermine interpretation, but that if every isomorphic observer-like structure counted as a genuine observer, then the memory of the external world would be no better than random guess. The probability of accurate memory is written as

$T$8

Given a uniform measure over symmetry-related possibilities, the paper argues that favorable cases in which memory matches the environment are no more privileged than unfavorable cases. The result is that memory would correlate with the world no better than chance (Stoica, 2023).

The paper formulates the symmetry principle as Meta-Relativity: observer-like structures on any two parameter spaces $T$9 and $h$0 agree upon the laws of physics iff $h$1 and $h$2 are isonomic, but in general disagree about the physical properties associated with observables and about physical space. Proposition 1 states that observer-like structures from different parameter spaces identify different physical spaces, and Corollary 2 states that the parameter space supporting observers is unique up to spacetime and gauge symmetries (Stoica, 2023).

A parallel argument appears in "Sentient observers and the ontology of spacetime" (Stoica, 2024). There the claim is that there is no unique, structure-only way to identify the observables that represent space or spacetime. If $h$3 is any unitary transformation, then

$h$4

stand in the same formal relations as the original observables, and nothing in the abstract Hilbert-space structure uniquely selects the original $h$5 as “the” positions and momenta. Definition 1 introduces an observer-like structure by the condition

$h$6

Theorem 1 then states: If observers were reducible to structures, any property of the external world would be unknown to them. Theorem 2 adds that the parameter space determined by the existence of the observers is unique up to spacetime and local gauge symmetries (Stoica, 2024).

The same line is developed in "What makes you an observer?" (Stoica, 17 Mar 2025). That paper characterizes empirical structure physicalism as the view that all physical reality is exhausted by relational or structural facts, then argues that a state vector plus Hamiltonian do not uniquely determine physical meaning. For any $h$7 commuting with $h$8, transformed observables $h$9 and $R$0 preserve the Hamiltonian’s form. The paper identifies two puzzles: first, that structure is insufficient to recover physical reality from operators; second, that observations do not resolve the ambiguity and instead imply that observers know nothing about the external world. Its positive conclusion is that there must be an intrinsic essence of the “stuff in relation” that grounds observerhood and the mapping from operators to physical properties (Stoica, 17 Mar 2025).

Taken together, these papers do not reject all uses of “empirical structure.” They reject the stronger claim that structure alone suffices to constitute observers, consciousness, or the physical meaning of observables. They also explicitly maintain that the result is independent of the measurement problem and applies in both quantum and classical physics (Stoica, 2023).

4. Relation to structural realism, principle theories, and reduction

Empirical structure physicalism sits within a broader dispute about structural realism and reduction. "Einstein Was Not a Flat Physicalist: Principle Theories, Constructive Theories, and the Direction of Constraint" (Weinstein, 15 Dec 2025) argues that Einstein’s distinction between principle theories and constructive theories is methodological rather than metaphysical. On this reconstruction, principle theories articulate empirically distilled constraints—impossibilities, invariances, and restrictions—that delimit the space of admissible constructive theories. Thermodynamics and relativity are the paradigm cases: they do not give micro-ontologies, but specify what any acceptable microscopic account must respect.

The paper’s compact summary is:

$R$1

$R$2

It argues that Hemmo and Shenker’s Flat Physicalism reverses this direction of constraint by treating principle theories as high-level summaries to be explained away by microphysical constructive theory. Against that inversion, the paper proposes a structurally richer physicalism, explicitly suggesting a structural physicalism or Empirical Structure Physicalism-type view in which principle-level invariances, impossibilities, and robust macro-regularities have explanatory and ontological weight (Weinstein, 15 Dec 2025).

This emphasis on structural content rather than primitive microontology is developed differently in metaphysical proposals built around relational physics. "A Proposal for a Metaphysics of Self-Subsisting Structures. I. Classical Physics" (Vassallo et al., 2022) advances a framework of self-subsisting structures, defined as configurations whose individuation and behavior are described in purely relational terms and without any need for a background spacetime. The technical implementation is Pure Shape Dynamics (PSD), where for an $R$3-body system the shape space is the quotient

$R$4

PSD replaces parametrized dynamics with an unparametrized curve $R$5 in shape space, with evolution determined by intrinsic geometric properties $R$6. The view is presented as ontologically parsimonious, empirically adequate, and stable through theory change because it preserves structural features that remain empirically efficacious (Vassallo et al., 2022).

A more mathematically austere structuralist case is causal set theory. In "The structure of causal sets" (Wuthrich, 2012), structure is defined in a set-theoretic and relational sense as $R$7, or more generally $R$8, with the discussion restricted to relational structures. A causal set is

$R$9

where $h$0 is reflexive, antisymmetric, transitive, and locally finite. The paper argues that causal set theory is naturally structural because the fundamental content is a discrete causal order, but it also insists that structural interpretation still involves relata rather than “relations all the way down.” It further distinguishes between the mathematical structure of a model and the physically significant structure represented by the model, a distinction that is central to any physicalist appeal to empirical structure (Wuthrich, 2012).

These lines of work indicate that empirical structure physicalism is not simply equivalent to a generalized “relations only” ontology. In some versions it is a theory-reduction thesis; in others it is a broader structural metaphysics; and in still others it is precisely the target of criticism for failing to accommodate observerhood or consciousness.

5. Consciousness, substrate, and the mind–matter extension

Debates over empirical structure physicalism extend directly into the philosophy of mind. One extension retains physicalism but revises the locus of structure. "Consciousness, natural and artificial: an evolutionary advantage for reasoning on reactive substrates" (Sritriratanarak et al., 17 Oct 2025) argues for a computational model in which consciousness is physical, computational, and not independent of its substrate. A reasoning entity is written as

$h$1

with substrate

$h$2

and reasoning process

$h$3

The paper models consciousness as a boolean control switch $h$4 that distinguishes real, present perception from hypothetical simulation, thereby preventing imagined scenarios from triggering autonomous substrate responses. It claims that this provides a computational model that “confirms the physicalism hypothesis,” while also implying that arbitrarily intelligent AI need not be conscious if implemented on non-reactive substrates (Sritriratanarak et al., 17 Oct 2025).

A different response appears in "Simultaneity of consciousness with physical reality: the key that unlocks the mind-matter problem" (Sanfey, 2023). That paper advances what it calls Abstract Realism, described as a structurally physicalist but anti-identity view. It rejects psycho-physical identity as fundamental and argues instead that any difference from nothing, whether subjectively experienced or objectively described, contains an observer function. Consciousness is said to have causal consequences not by violating physical law, but by virtue of simultaneity and the observer-observed relation, which create additional degrees of causal freedom unavailable to temporally sequential observation. The proposed bridge is therefore structural, but it is not an identity between consciousness and a physical structure of the IIT type (Sanfey, 2023).

By contrast, the anti-structural-reduction papers contend that consciousness cannot be recovered even from complete structure and dynamics. "What makes you an observer?" (Stoica, 17 Mar 2025) argues that pure structuralism, computationalism, and strong functionalism cannot explain why some observer-like systems have reliable world-directed memory while symmetry-related isomorphic systems do not. "Are observers reducible to structures?" (Stoica, 2023) similarly concludes that observers are not reducible to structure alone and that the unique correspondence between observables and physical properties becomes manifest through observers rather than being derivable from abstract state-space structure.

The literature therefore contains at least three incompatible mind-oriented developments: a substrate-dependent computational physicalism; a structurally physicalist but anti-identity observer-function account; and a critique claiming that no structure-only account can explain consciousness or objective knowledge. All three preserve the centrality of structure, but they disagree sharply about whether structure is sufficient.

6. Major controversies and current fault lines

Several recurrent controversies organize the current discussion.

First is the dispute over what the doctrine is fundamentally about. In (Gyenis, 26 Jul 2025), empirical structure physicalism is a claim about theory supervenience, empirical dispensability, and refinement of empirical distinctions. It is explicitly compatible with multiple realization, the pessimistic meta-induction about entities and reference, and continued use of special-science vocabulary. In (Stoica, 17 Mar 2025) and (Stoica, 2023), by contrast, empirical structure physicalism functions as a label for the thesis that reality is exhausted by relational structure and that observers are reducible to observer-like structure; that thesis is then rejected.

Second is the dispute over whether structure fixes meaning. The pro-supervenience view requires only that physics preserve empirical differentiations. The anti-structural-observer view argues that preservation of formal or empirical pattern does not yet determine which operators represent which physical properties, which basis represents position, or why a memory state corresponds to one worldly fact rather than another (Stoica, 2023).

Third is the dispute over the status of higher-level laws and regularities. The critique of Flat Physicalism argues that thermodynamics, relativity, and similar principle theories are not merely phenomenological surfaces to be reduced away, but restrictive principles that constrain admissible microphysical models. This suggests a physicalism that is fully naturalistic yet not flattening, and in which principle-level invariances and robust macrostates possess explanatory and ontological significance (Weinstein, 15 Dec 2025).

Fourth is the dispute over realism. Some neighboring work supports a robust structural ontology, as in causal set theory and self-subsisting structures (Wuthrich, 2012); other work argues that structural realism is incomplete or false precisely where observerhood, sentience, or the physical meaning of observables are at issue (Stoica, 2024).

A plausible implication is that “empirical structure physicalism” now names not one settled doctrine but a live research site at the intersection of philosophy of physics, philosophy of mind, and scientific realism. In its strongest theory-relative form, it proposes a nontrivial and scientifically responsive version of physicalism grounded in refinement of empirical structure (Gyenis, 26 Jul 2025). In its strongest object-level form, it becomes the thesis that structure alone exhausts reality, observerhood, and meaning—a thesis that recent observer-centered arguments regard as untenable (Stoica, 17 Mar 2025). The contemporary literature is therefore defined less by consensus than by a precise question: whether empirical and structural resources are sufficient for physicalism, or whether observers, sentience, intrinsic nature, or principle-level constraints must also be treated as physically indispensable.