---
title: Closure Challenge in Consciousness Science
url: https://www.emergentmind.com/topics/closure-challenge
type: topic
---

# Closure Challenge in Consciousness Science

The **Closure Challenge** is the claim that, once the closure of the physical is formulated with sufficient precision about physical events and measurement records, any two theories of consciousness that satisfy that closure become empirically indistinguishable in every experiment. In Kleiner and Hartmann’s analysis, this result creates a direct conflict with scientific practice, because experimental outcomes must be stored or transmitted by physical devices and thus remain fixed whenever the underlying physical-event descriptions remain unchanged. The challenge is therefore directed at research programmes that seek to ground a physical functionalist or identity-based understanding of consciousness on empirical observations while leaving the ontology and laws of the physical untouched [2110.03518].

## 1. Formal statement of the closure of the physical

Kleiner and Hartmann formulate the closure of the physical relative to a theory of consciousness \(T\). They distinguish between \(P_T\), the set of physical-event descriptions to which \(T\) is committed, and \(P_p\), the set of physical-event descriptions that natural science explains, predicts, or otherwise determines. A theory \(T\) obeys the closure of the physical iff it does not add to or alter the physical-event descriptions that natural science already has. Formally, this is expressed by the existence of an injective map
\[
i : P_T \longrightarrow P_p
\]
such that for each event-description \(E_{\mathrm{phys}} \in P_T\), the corresponding description \(i(E_{\mathrm{phys}}) \in P_p\) has exactly the same content. On this formulation, nothing in \(T\) changes the ontology or laws of the physical as given by \(P_p\) [2110.03518].

This definition is not a merely verbal restatement of “physical closure.” It is the structural assumption that drives the subsequent argument. The relevant point is not only that consciousness theories may be “physicalist” in some broad sense, but that closure prevents them from introducing any new physically efficacious differences into the domain that scientific measurement can access. The challenge arises precisely because experimental science operates through such physically encoded differences.

## 2. Measurement, records, and physical event determination

For any experiment \(M\), a theory \(T\) that makes contact with \(M\) must specify which data-sets \(O_T \subseteq O_M\) can occur when \(M\) is run under \(T\), where \(O_M\) is the class of all logically possible data-sets for \(M\). Kleiner and Hartmann then impose a requirement that is ordinary scientific practice rather than a special assumption: any measurement result in \(M\) must be stored or transmitted by some physical device \(D\), with \(O_D\) the class of all records that \(D\) can instantiate.

Let \(P\) denote the full set of physical events. The records on \(D\) are determined by the physical events that occur. This is formalized by a function
\[
d_D : \mathcal P(P) \longrightarrow \mathcal P(O_D),
\]
mapping each set of physical events to those records on \(D\) that must result. The paper states in particular that if \(P_2 \supseteq P_1\), then
\[
d_D(P_2)=d_D(P_1),
\]
and that replacing \(P_1\) by its image under the embedding \(i\) does not change the data:
\[
d_D(i(P_1))=d_D(P_1).
\]

Restricting attention to the part of the data on \(D\) that represents the measurement result of \(M\) yields a map
\[
d_M : \mathcal P(P) \longrightarrow \mathcal P(O_M).
\]
If a theory \(T\) commits to a subset \(P_T \subseteq P\) as the physical events that actually occur, then the only possible \(M\)-outcomes are
\[
d_M(P_T) \coloneqq O_T.
\]
The central methodological point is that reports, button-presses, EEG traces, files on a hard drive, marks on paper, and spoken reports are all physical encodings. Once measurement is represented in this way, the empirical content of a theory is mediated entirely by its implications for physical records [2110.03518].

## 3. Why closure yields empirical indistinguishability

The decisive step is to compare two theories \(T_1\) and \(T_2\) that both satisfy closure. Since both admit injective embeddings into the same \(P_p\), and since the physical records instantiated by the measuring device are fixed by the relevant physical events, Kleiner and Hartmann derive
\[
d_M(P_{T_1}) = d_M(P_{T_2}),
\]
and therefore
\[
O_{T_1}=O_{T_2}
\]
for every experiment \(M\). The paper’s informal lemma is that if an assumption forces every pair of theories satisfying it to be empirically indistinguishable, then that assumption is incompatible with empirical science. From this, Theorem 1 is stated succinctly: **the closure of the physical is unscientific** [2110.03518].

The force of the result lies in its generality. It is not restricted to one experimental paradigm, one kind of neural measure, or one family of behavioral reports. The claim is that *all* closure-adhering theories become empirically indistinguishable in *any* experiment once the role of physical record formation is made explicit. This suggests that the issue is not a local defect in a particular methodology, but a structural incompatibility between closure and empirical discrimination among consciousness theories.

## 4. Conflict with standard scientific practice

Standard experiments in neuroscience and psychology typically assume that verbal reports, button-presses, EEG signals, and related readouts can distinguish rival theories of consciousness. Kleiner and Hartmann argue that this assumption is incompatible with closure. If all such physical readouts supervene exactly on the same bare physical events, as closure requires, then no experiment can discriminate between theories that differ only in how they interpret consciousness while leaving the physical unchanged.

The paper identifies the resulting flaw in the standard paradigm directly: experimental paradigms presuppose a causal link from “consciousness-differences” to “recorded-data-differences,” yet the closure principle forbids any such link in the physical realm. The challenge is therefore not that present experiments are insufficiently precise, insufficiently multimodal, or insufficiently theory-driven. Rather, the claim is that the very idea of using purely physical measurements to adjudicate among closure-adhering theories is internally unstable [2110.03518].

A common misunderstanding, on the paper’s terms, is to suppose that a theory may differ in its account of consciousness while still yielding discriminable empirical predictions through ordinary measurement practice, provided the theory remains neutral about physical laws. The argument denies precisely this. Under closure, no \(T\)-specific variation remains in \(O_T\).

## 5. Scope of the challenge for theories of consciousness

The challenge is not restricted to one doctrinal family. Kleiner and Hartmann state that all functionalist, identity, epiphenomenalist, illusionist, or weak-emergentist accounts that do not posit changes in physical laws or events fall prey to the Closure Challenge. The threat is thus framed at the level of any research programme that aims to ground a physical functionalist or identity-based understanding of consciousness on empirical observations while retaining closure [2110.03518].

This scope matters because much of contemporary consciousness science proceeds by comparing candidate mappings between conscious states and neural, cognitive, or functional organization while taking the physically described experimental world as fixed. On the present argument, such programmes inherit a methodological limitation from their background assumption. If closure is maintained, the goal of comparing and falsifying theories of conscious experience by means of physically recorded outcomes is undercut.

The paper’s appeal to Einstein’s remark—“It is the theory which decides what we can observe”—sharpens this point. Here the remark is used to emphasize that a theory of consciousness must specify how observable differences could arise. If the theory disallows any differences in the physical channel through which observations are registered, it deprives itself of empirical traction.

## 6. Proposed routes forward

Kleiner and Hartmann identify two routes forward. The first is to **abandon closure in theory**. On this route, theories must explicitly state how consciousness, or a “non-physical” variable, enters the causal-physical stream to produce different records. In the paper’s terms, one must introduce new physical events or laws, that is, violate closure.

The second is to **reconstrue measurement**. This would require measurements of consciousness to exploit wholly new physics—examples given in the reconstruction include quantum collapse and novel electromagnetic couplings—so that different conscious states imply different physical trajectories in \(P_p\). The paper does not present these as established solutions; they are possible remedies to the impasse created by closure [2110.03518].

The concluding consequence is stated in stark form: to be empirical, consciousness theories must either abandon closure by postulating novel causal powers or modifications of the physical, or admit that they have no empirically testable consequences. A plausible implication is that the Closure Challenge is less a dispute about one metaphysical slogan than a demand for a revised account of how consciousness theories connect to measurement, data, and experiment.

Source: https://www.emergentmind.com/topics/closure-challenge