# Toward a Reassessment of Entropy in the Philosophy of Science

Quentin Petit

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Quentin Petit. Toward a Reassessment of Entropy in the Philosophy of Science. Possibility and Necessity in Philosophy of Science, Prof. Alexandre Guay, UCLouvain, May 2025, Louvain la-Neuve, Belgium. hal-05108005

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Submitted on 11 Jun 2025

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# Toward a Reassessment of Entropy in the Philosophy of Science<fnref n="1" />

## Introduction

In his powerful and thought-provoking 2017 article<fnref n="2" />, Tim Maudlin defends the view that the hypothetical evaporation of a black hole—via its radiation at the event horizon—does not in fact entail a loss of information. This paradox, originally formulated by Stephen Hawking in 1975, continues to divide the scientific community. If information falls into a black hole and is encoded on its boundary, what becomes of this information when the boundary radiates and the volume of gravitational mass progressively diminishes?

This paradox serves as a pretext for a deeper epistemological reflection. Faced with a theoretical system's apparent contradiction, three possible responses emerge: (1) We may lack intellectual rigor and need to make better use of existing mathematical tools; (2) We may require entirely new theoretical instruments—a new physics yet to be discovered; or (3) The answer may lie entirely beyond our grasp, suggesting that the universe might be trying to communicate something different from what we expect. This tripartite structure implicitly underpins the argument of this paper.

Throughout the article, Maudlin's various arguments aimed at denying the paradox point toward the first option—namely, an insufficient mastery of our mathematical and physical tools. This includes, for example, a flawed geometrical representation and/or interpretation of Cauchy surfaces, and the influence of conceptual biases—such as the assumption of a temporally progressive sequence of observations, as if the process of evaporation could be apprehended from an overarching, external vantage point.

<footnote n="1">¹ This work is the only fruit of my personal reading, research and thinking; I however did use IA for help with the English formulation of my original ideas.</footnote>

<footnote n="2">² MAUDLIN Tim, “(Information) Paradox Lost”, Department of Philosophy New York University, New York 2017</footnote>
In the context of black hole evaporation, the core issue remains the first law of thermodynamics. Does the paradox genuinely contradict this principle? More fundamentally, are quantum assumptions adequately reflected within General Relativity? We aim to offer some answers to these questions by giving voice to entropy itself, and by arguing that a deeper philosophical appreciation of its implications would enrich the philosophy of science—particularly in relation to theoretical physics. This would open the door to a broader reflection on our epistemological stance toward what we call ‘nature’ or the ‘world’ and the modes of communication in relation to our rational expectations.

## 1. *Arguments contra/ pro the information paradox*

In his article, Tim Maudlin presents coherence scenarios in which the transition formulas governing information remain consistent with our current physical framework. He notably draws on the concept of foliation, which enables a precise equivalence between the dynamics of the phenomenon and its two-dimensional representability, without any loss of information. At a deeper level, is the supposed information loss due to black hole radiation not, in fact, our own information loss—stemming from a lack of theoretical rigor when adapting metric or geometrical figuration using an existing body of formulas and theorems whose full potential has yet to be adequately explored? This is precisely the criticism Maudlin levels at those who sustain the idea of a paradox, thereby generating a pseudo-problem.

Maudlin makes technical use of several geometrical tools for modeling phenomena, notably the integrability of Cauchy surfaces, to which he attributes a richer interpretive capacity than they are traditionally granted within the context of a Penrose diagram. He argues that the formal representation of information transfer—both in and out of the black hole—can be achieved by defining a Cauchy surface whose critical form ($\Sigma_{crit}$) would encompass the entirety of that information. This constitutes both a mathematically and geometrically sound method, and a sufficient explanation for the transition toward the bi-dimensionality of a (hyper)surface, dynamically considered in relation to the center of the black hole.

As a reminder, Cauchy surfaces function both as a mathematical tool and a physical concept. Within the framework of General Relativity (GR), a hypersurface qualifies as a Cauchy surface if every causal curve—whether representing a particle, wave, energy, or information—intersects it exactly once. Cauchy surfaces thus provide the complete initial conditions for a system and for the full range of phenomena that may emerge within it. In lay
terms, this means that nothing escapes or enters from outside the system, thereby affirming
both coherence and conservation of actual and possible phenomena<fnref n="3" />.

In their 2018 article<fnref n="4" />, responding to Maudlin, Manchak and Weatherall raise several
formal objections to the first author’s demonstrations. One of their strongest arguments is that
Maudlin appears to assign a disproportionately demonstrative weight to the theoretical force of
Cauchy surfaces. Far from resolving the paradox, these surfaces—if interpreted in the full
scope of their operative extension—may in fact reintroduce the problem even more acutely.

Indeed, Maudlin’s modeling through the theoretical apparatus of Cauchy surfaces, in
the case of a black hole, seems to provoke a clash among three propositions whose joint
assumption necessarily requires the exclusion of one to avoid logical contradiction. Maudlin
principally advocates the compatibility of two major positions, each with philosophical
implications: the first, labeled (CCH), asserts that spacetime is reasonably and globally
hyperbolic; the second, labeled (BHE), maintains that evaporation in spacetime is physically
reasonable. According to a standard interpretation within GR, however, one cannot coherently
maintain both (CCH) and (BHE), since a system cannot simultaneously preserve both curvature
and non-completion. From Manchak and Weatherall’s perspective, Maudlin’s interpretation of
Cauchy surfaces significantly departs from their classical representational scope and stretches
the formal use of the tool beyond what has traditionally been justified. For both authors, this
usage appears forced and insufficiently grounded.

Maudlin, nevertheless, chooses to uphold both premises—(CCH) and (BHE)—and
rejects the third, (RST), which posits that it is physically reasonable for a region of spacetime
to be sufficiently curved to contain a trapped surface—i.e., to sustain a singularity—thus
implying the inevitability of geodesic incompleteness. This move aligns with Maudlin’s
consistent refusal to concede the existence of an information paradox. Manchak and
Weatherall’s reply not only challenges the exclusion of (RST), but also offers insight into a
potential compatibility between (CCH) and (BHE)—an avenue not pursued by Maudlin, but
one that will prove useful for our subsequent analysis:

<footnote n="3">³ For the purposes of this paragraph, and to enhance general comprehension, I have drawn upon and been inspired by Gregory GALLOWAY’s 1985 article, “Some Results on Cauchy Surface Criteria in Lorentzian Geometry,” published in the Illinois Journal of Mathematics (full citation provided in the bibliography). In just a few paragraphs, the paper succinctly outlines the formal connections between Cauchy surfaces and other key mathematical and conceptual elements.</footnote>

<footnote n="4">⁴ MANCHAK J.B. - WEATHERALL J.O., “(Information) Paradox Regained? A brief comment on Maudlin on Black Hole Information Loss”, Springer Nature, 48: 611-627, Berlin 2018</footnote>
We do not deny that there may be good reasons to reject (RST). After all, the arguments in favor of (BHE) rely on a semi-classical analysis according to which **spacetime is treated classically and the radiation is treated quantum field theoretically**. One might well expect that a full understanding of Hawking radiation will wait on a theory of quantum gravity – and on several approaches to quantum gravity, the description of space and time as a smooth manifold breaks down, because space and time turn out to be fundamentally discrete. (Maudlin himself does not offer an argument along these lines.) But whatever else is the case, observing that (RST) may be rejected does not simply dissolve the paradox [...]. Indeed, there are good reasons to think that Maudlin's rejection of (RST) yields at best a pyrrhic victory. (pp. 618-619)

If Maudlin's position is accepted, then the singularity of a black hole does not constitute a rupture in the strong sense of a breakdown of the laws of physics. If a rupture exists, it would pertain only to isolated theoretical frameworks. Physics itself already contains formal tools capable of modeling the behavior of black holes without requiring the inference of an information paradox. Conversely, if we follow Manchak and Weatherall, Maudlin's explanation comes at a cost—namely, the admission that projecting the phenomenon into an extended formalism of Cauchy surfaces is no longer sufficient to account for the very possibility of a singularity. In doing so, it forfeits a certain metaphysical necessity: confronting paradoxes in order to reach for something beyond, rather than defending a theoretical system at all costs—especially when that system appears to generate more paradoxes than it resolves.

## 2. *Transcending the question*

What interests us in this clash of arguments—beyond the highly specialized and technical nature of the debate—is the absence of the underlying subject: why does physics, almost as a reflex or defense mechanism, assume such a strong allegiance to the principle of information conservation? This question leads us directly to the heart of entropy and the derivative laws of thermodynamics. What we seek to propose in this paper is a philosophical revaluation of those laws, with the aim of refining our epistemological posture in the face of certain phenomena—phenomena we tend to label as paradoxical, whether in General Relativity or Quantum Mechanics.

The exchange between Maudlin and his colleagues from the University of California brings into focus the third path of our epistemological trilemma: the possibility that the universe might be trying to tell us something else. If the issue is indeed about information sharing and encoding—about how these processes give rise to supposed paradoxes or demand that we
relinquish certain conceptual biases—then perhaps we ought to begin by challenging the initial premise. Is the universe itself as invested as we are in maintaining the conservation of its information as a supreme principle?

If the answer is yes, then Maudlin's path remains coherent. But if the answer is not necessarily, we are led to a different hypothesis: that our very concept of the world may refer instead to a complex substratum, whose dynamics are best captured by the principle of indeterminacy—precisely because it does not impose rigid boundaries. In this view, the universe would still be a communicator of information, yet would operate more like a sequencer of its own energy. Sometimes, its sequencing might follow parameters we already believe ourselves to understand; at other times, it might involve a leap that eludes all forms of representation and cannot be detected by any a priori theoretical tool.

We would then call paradox our inability to apprehend the phenomenon. However, according to a consequence of thermodynamic laws—which we will explore in a following section—the impossibility of observing a phenomenon does not imply its non-existence. There is even a rational possibility that some phenomena may be knowable only philosophically—that is, without ever being encountered empirically.

### 3. A turn through *Quantum Mechanics and the holographic proposal*

This is precisely what comes into play in quantum mechanics, where various hypotheses, in one way or another, advocate for an understanding of matter as being primarily expressive of its own information. How so? Several proposals—each with as many benefits as limitations—suggest the possibility of an alternative physics, one that might better align with the trajectory of current theories, which, despite their initial successes, are increasingly failing to accommodate emerging observations.

String theory, for instance, now inspires more skepticism than support among physicists. Yet the proposal remains compelling: what model could better account for the dual wave–particle behavior than one which posits an entity whose vibrational modes can generate different particles at will? The central issue with string theory lies in its heavy reliance on mathematically complex formulations and its dependence on a high number of dimensions, which collectively result in what some scientists have described as a lack of physicality—that is, a theory that proves exceedingly difficult, if not impossible, to test or falsify. It thus struggles
to establish itself within the domain of demonstrable physics, where experimental verification
can no longer keep pace. Actually, on a more general perspective, it is precisely this lack of
physicality that need to be better explored and could receive a higher sense when considering
entropy and as we will shortly discuss in the following lines of this paper.

Getting back to fundamental physics, the hypothesis that currently seems to us the most
promising in integrating the probabilistic dimension of information is the holographic model.
This model draws on the AdS/CFT correspondence, a theoretical framework capable of
describing how information emitted by matter is encoded on a gravitational boundary—that is,
within a spacetime field. Whether one accepts it or not, this mode of sequencing entails a
probabilistic definition of particle behavior, while also incorporating the intuition underlying
string theory. More importantly, it infers the possibility of transmitting information across
different metric systems, corresponding to any observational framework, at any level of
resolution.

This brings us back to Maudlin, who likewise defends the notion of an encoding-based
transfer between volume and surface, without any loss of information.

When we follow this line of intuition to its end, what is at stake in these physical
theorizations is not so much a direct understanding of the phenomena themselves—black holes
for Hawking, Maudlin, Manchak & Weatherall; quantum mechanics for others—but rather the
preservation of the four laws of thermodynamics as a broader framework. Our proposition,
therefore, is not to promote a form of unifying physics—we still do not know whether the
universe requires unification, even if such a prospect would be convenient for us—but rather
to return to the question of what entropy is capable of revealing across both scenarios, at the
outer limits of our theoretical assumptions in physics.

4. *Why would we need to pay attention to a reassessment of entropy in the Philosophy of Science?<fnref n="5" />*

We will now move further into the implications of entropy, especially when
reinterpreted through a philosophical lens. While the four laws of thermodynamics are well

<footnote n="5">⁵ For this section and the ones that follow, I drew inspiration from and interpreted in my own way the views of astrophysicist, scientist, and popular science communicator *David Elbaz* — primarily his lecture available as a podcast on Spotify, “L’univers a-t-il un sens” (see bibliography for the link).</footnote>
known, we often forget that they follow a precise sequence—and that this sequence carries its
own epistemic significance. In other words, one should never adopt any single law in isolation.
They must always be considered in the order of their appearance, particularly when entropy is
being applied to an observed phenomenon.

The zeroth law states that if two systems are each in thermal equilibrium with a third,
then they are also in equilibrium with one another. In its most direct reading, this law asserts
the principle of thermal balance. On a deeper reading, it implies that no phenomenon can be
properly analyzed unless it is already embedded within the defined parameters of a system
(bearing in mind, for instance, the formal aim of Cauchy surfaces in physics).

The first law expresses the conservation of energy within a system, regardless of the
transformations that energy undergoes. It is a dynamic law that implies a movement toward
stability—an implication that only makes sense if the zeroth law has already been accepted,
that is, if the system has been appropriately delimited beforehand.

The second law asserts that the entropy of an isolated system can only increase (or
remain constant); in other words, energy transfers are irreversible and tend toward ever-greater
dispersion. This law potentially applies even to the universe itself, insofar as any theoretical
engagement with it presupposes treating it as if it were a closed system. In contrast to the
stabilizing dynamic of the first law, the second law suggests a movement of dissipation—a
trend that we have simplistically interpreted as a kind of chaos. In fact, what it indicates is that
energy (and information) transfers tend toward increasing complexity—both from a physical
and from an epistemological standpoint.

The third law, like the zeroth, is a limit-law: it states that the phenomenal properties of
a system's elements cease to manifest once the system reaches absolute zero. This law appears
to contradict the first law, insofar as energy conservation is no longer observable when the
system reaches its limiting point. Nevertheless, in physics, a quantity may remain conserved
even when it is no longer observable. In epistemology, however, one might say that what can
no longer be observed no longer retains empirical meaning—and thus, that we must be cautious
when making absolute claims. It is likely at this boundary that what we perceive as paradox
emerges.

We must now apply the laws of thermodynamics to the specific case of black holes. It
becomes immediately evident that our physical experience of observing black holes—and all
the related models of their informational behavior—converges on the domain of entropy as
framed by the first and second laws. It is in the interplay of these two premises that the so-
called paradox arises: how can the conservation of energy be maintained for matter falling into
a black hole, when the system undergoes a transition from volume to surface and ultimately to
radiation, culminating in the slow evaporation of mass? The paradox rephrases the question of
whether gravity can be resolved into informational encoding—a question that necessarily
invokes quantum mechanical laws.

5. *Epistemological asymmetry?*

At the level of our understanding, we are dealing with a logic of
observation/phenomenon correspondence that tends toward decoherence—not in the sense of
unintelligibility, but rather in the sense of a disjunction between the representability of some
supposed ontological reality (as mediated through information transfer—be it across the event
horizon or within the various field interpretations offered by holographic quantum gravity) and
what we refer to as physical behavior as such.

Since this is the central hypothesis of our work, we can simplify its interpretation by
stating that, as we strive to construct scientific discourse, we tend to agglomerate and
 synthesize in ways that seem to us the most rational. The system's closure thus occurs, entirely,
within our epistemic need to predefine its limits before we begin organizing and articulating
the elements that appear within it. The outcome of this operation is what we call 'science' and
we naively believe that it reflects what is actually occurring in the universe. But the universe
for us—is it really the universe in itself? Nothing authorizes such an abductive leap, not even
the objectivist ambitions of a rigidified analytic philosophy that still believes itself to be the
privileged mode of access to facts and to their literal expression.

Have we actually discovered anything new? Not at all, and Maudlin was right to assert
that there is no need for a new physics. A more sustained attention to entropic dynamics is
sufficient—and, in fact, already available. The combination of the first and second laws of
thermodynamics already contains, in latent form, the conceptual framework suggesting that the
preservation of information does not inherently contradict the irreversibility of its sequencing.
Put more philosophically, our interpretation of what the universe is willing to reveal leads us
toward an understanding of its representability, and this in turn opens onto an ever-widening
horizon of latent, future phenomena.
In Maudlin’s case, there is no necessity to take a position for or against a paradox—
only to recognize that the information encoded on the event horizon represents less a loss for
physics than a loss for us, owing to the increasing inaccessibility of that information. Viewed
positively, perhaps this time from the vantage point of quantum mechanics, the universe and
matter are indeed capable of communicating through various forms of information sequencing,
without requiring any global-scale homogeneity. To claim that all information can ultimately
reach us would require us to shift the physical question of entropy toward a philosophical one—
one that exposes our own rational limitations within a universe for which we can never define,
a priori, the strict parameters of an isolated system, an ideal system that exists only in
mathematics. We are, therefore, irreversibly condemned to elusiveness. And yet this is not a
tragedy, for it does not prevent us from truly encountering it nonetheless.

In this spirit, I endorse the view presented by Alexandre Guay in his 2020 article<sup>6</sup>,
which I have freely adapted and appropriated here. Guay challenges the idea of science—either
in a strong or weak sense—as holding epistemic authority sufficient to directly uncover the
identities of natural entities.

From our ‘entropic’ perspective, the issue becomes moot: science need not aspire to
read anything other than the information sequence that matter discloses when it encodes—on
whatever boundary that may be. As for going beyond that boundary, that remains the domain
of philosophy.

Guay wisely proposes a distinction between the “manifest image” and the “scientific
image” of the world, suggesting a feedback loop between the two, an interface governed by the
very rhythm of the epistemological process itself—adapting theoretical models in light of the
integration of new information. This approach is both unifying and intellectually serene<sup>7</sup>.

When it comes to our conceptual biases, even if science has progressed and we along
with it, we still tend to approach what we call the real, nature, or matter through a strongly
Newtonian and Kantian lens—as though reality were a vast container filled with discrete
elements that we are tasked with organizing, so that meaning can emerge and laws be derived,
leading to explanations or even, in the best of cases, predictions. It is difficult to let go of this
comforting need for a more or less deterministic perspective on phenomena. We may no longer

<footnote n="6">⁶ GUAY Alexandre, « La métaphysique de la nature comme une boucle de rétroaction », in Künstler, Raphaël (éd.), Métaphysique et Sciences, Nouveaux problèmes, Paris : Hermann, 2022, p. 183-197</footnote>

<footnote n="7">⁷ cf. *op cit*, pp. 192-197</footnote>
believe in God or a Great Watchmaker, yet we still—scientists foremost among us—believe in
a certain intelligibility of the world.

One possible reading of entropy would invite us to relinquish this bias and consider
ourselves merely observers of the increasing complexity of energy and information sequencing
in the universe. We may certainly create relative systems by choosing to parameterize certain
elements over others, but in absolute terms, we are increasingly distanced from any claim to
unification—because the universe encodes in the opposite direction. In short, our capacity to
render phenomena intelligible does not entitle us to claim that the world is, in itself, intelligible.
The universe has no need of our thirst for intelligibility in order to be what it is.

This conclusion brings us to highlight an agnostic claim in front of both physics and
the universe, as our even more sincere confrontation reading the information encoded - top our
bottom - by the universe is inversely proportional to the increasing volume (and surface!) of
the entire information a priori considered as part of any hypothetical and easy to use closed
system.

5. *Conclusive metaphor*

At the close of this work, I propose an epistemological-methodological archetype in
alignment with the philosophical revaluation advanced throughout this paper. This archetype
takes the figurative and metaphorical form of a caterpillar. The idea suggested by this image is
to render and preserve the undulating motion that enables the transmission of *momentum* across
the whole, wherein secondary movements are carried forward—though the two terminal points
of the motion follow opposing dynamics: the first serves to crystallize figurability, to provide
a point of anchorage (truth grasping); the second, conversely, releases that fixity, propelling
the wave into a new possible (where modality is only considered from its realistic frame). In
its entropic suggestion, the rigidity x of a given structure is always dequantified by the dispersal
y of another.

In more vulgarized word, and because when someone is driven by literal-only
disposition to get the meaning, he might not be available for willingly traveling with us -
answering that the proposition is too vague and metaphorical - the asymmetry we have
discussed above provokes the dispersion of information and the dispersion of any possible full
comprehension simultaneously. Applied epistemologically, this corresponds to the theorization
of any system via a representational unity—one that is perpetually reshaped by the ever-
expanding more, which remains as yet unknown.

Keeping in mind the image of this archetype, we may indeed be moving toward a
greater understanding of physical law, but the world itself moves faster in the sequencing of its
information. We are not equipped to match its pace. No one is. We would be gods. We would
have the overlooking position of an external vantage point<fnref n="8" />. Hence, when we say that entropy
is, above all, a philosophical question, it is because it touches us at our core. We are immersed
in the same system we are considering. The acceleration of the universe's informational
expansion—regardless of the perspective from which we choose to observe it—does not
indicate a loss of information, but rather, in some sense, a loss for us. When we configure a
system, we are also bounding our limits to travel across and beyond.

This does not imply that we are progressing toward an increasingly mistaken
understanding of the universe, but rather that, as our conceptual grasp of natural phenomena
deepens, the phenomena themselves reveal an ever-growing multiplicity—one that defies
unification. The only stance left to us may be that of a humble reader, attending to the phases
and rhythms of information-sequencing that the deep and complex background of the universe
allows us, at times, to glimpse. We are then meant — and probably happily — to miss the
unification of whatever.

<footnote n="8">⁸ I recommend to realize a meditative reflection on Willard Van Orman QUINE's quote in *Ontological Relativity and Other Essays*. Columbia University Press, 1969: "I see philosophy and science as in the same boat — a boat which, to revert to Neurath's figure as I so often do, we can rebuild only at sea while staying afloat in it. There is no external vantage point, no first philosophy." (pp. 126-127)</footnote>
REFERENCES :

ELBAZ David, « L’Univers a-t-il un sens », interview réalisé par la chaîne de podcasts Sismique, n°96, septembre 2022

https://open.spotify.com/episode/5XzMSrnwl1kKgkeebGU5xE?si=3a4f9518eb794211

GALLOWAY Gregory, "Some Results on Cauchy Surface Criteria in Lorentzian Geometry", Illinois Journal of Mathematics, Volume 29, Number 1, Spring 1985

https://projecteuclid.org/journalArticle/Download?urlId=10.1215%2Fijm%2F1256045837

GUAY Alexandre, « La métaphysique de la nature comme une boucle de rétroaction », in Künstler, Raphaël (éd.), Métaphysique et Sciences, Nouveaux problèmes, Paris : Hermann, 2022, p. 183-197

https://dial.uclouvain.be/pr/boreal/object/boreal%3A259948/datastream/PDF_01/view

HAWKING Stephen, "Breakdown of Predictability in Gravitational Collapse", Phys. Rev. D 14, 2460, Berlin 1978

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.14.2460

MANCHAK J.B. - WEATHERALL J.O., “(Information) Paradox Regained? A brief comment on Maudlin on Black Hole Information Loss”, Springer Nature, 48: 611-627, Berlin 2018

https://link.springer.com/article/10.1007/s10701-018-0170-3?fromPaywallRec=false

MAUDLIN Tim, “(Information) Paradox Lost”, Department of Philosophy New York University, New York 2017

https://arxiv.org/abs/1705.03541

QUINE Willard Van Orman, *Ontological Relativity and Other Essays*. Columbia University Press, 1969