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When maer ceased to maer
The disappearance of the philosophical problem of maer from physics in the
late nineteenth century
Marij van Strien
Version: March 2024
Introducon
The idea that all physical phenomena should ulmately be reducible to maer and moon was
inuenal throughout the nineteenth century, although this ideal was never realized and never
without crics. But could the noon of maer itself be understood? A unied concepon of maer
was lacking in nineteenth century physics. Physicists used dierent concepons of maer, and
debated the queson of the true nature of maer on the basis of philosophical as well as empirical
arguments; it turned out to be very challenging to develop a concepon of maer that was
consistent with experimental ndings as well as philosophically sasfactory. Towards the end of the
nineteenth century, physicists increasingly rejected the queson of the true nature of maer,
arguing that this queson was irrelevant for physics or altogether meaningless. This was somemes
seen as an emancipaon of physics from philosophy, and somemes as a result of philosophical
reecon on physics.
Concepons of maer in the nineteenth century
In eighteenth century natural philosophy, maer was conceptualized in various ways: somemes
maer was taken to consist of atoms, and somemes it was taken to be connuously extended.
Atoms could be conceptualized as perfectly hard bodies, or they could be taken to be deformable, in
order to account for elasc collisions in which moon is preserved. Another popular and inuenal
concepon of atoms was that of point parcles: according to this concepon, developed around the
mid-eighteenth century by Boscovich, parcles are unextended, their mass being concentrated in a
point, and each parcle exerts a force on other parcles. These types of maer all have dierent
properes and are irreducible to each other. They are also subjected to dierent dynamics: point
parcles only interact through forces which act between pairs of parcles, depending on their
distance
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; rigid bodies can rotate and can collide with each other; and deformable connua can
addionally undergo internal stresses (Stan 2017).
Around the beginning of the nineteenth century, it seemed for a while that unity could be
achieved through the research program developed in France by Laplace and his collaborators.
Laplace aimed to account for all natural phenomena, including phenomena of heat, electricity,
magnesm and chemistry, in terms of elementary parcles which he termed ‘molecules’ and which
he treated as point parcles (Fox 1974). Within France this research program became extremely
inuenal, and some notable successes were achieved. However, there was no complete agreement
1
In Boscovich’s theory, point parcles exert a force on each other which becomes innitely repulsive at very
short distances, so that parcles never collide.
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on the properes of these molecules, which were oen seen as point parcles but somemes as
having a certain extension; and despite the fact that the explicit aim of this program was to reduce all
natural phenomena to the moon of molecules, in pracce even the Laplacians found it more
convenient to treat maer as connuous in some of their calculaons (Brading & Stan 2024).
2
Aer a
brief period of great success, Laplace’s program collapsed between 1815 and 1825, and most
physicists came to agree that its ontology of point parcles was too restricve to account for all
natural phenomena (Fox 1974).
From then on, all of the above concepons of maer were again in use. In pracce it was
somemes more convenient to model maer as connuously extended, while in other contexts it
was more convenient to work with an atomisc concepon of maer. Therefore, how a certain
physicist treated maer in his calculaons did not necessarily have to match his views on the
ulmate constuon of maer. For example, in the 1820s, Cauchy worked with a connuum
concepon of maer, despite his convicon that maer is actually molecularly constuted – his
ontological commitments did not seem to maer to his physics (Brading & Stan 2024).
Throughout the nineteenth century, physicists debated the nature of maer on the basis of
philosophical as well as empirical arguments (Harman 1982; Wilholt 2008). The queson of the
essence of maer was deeply connected with the quesons of the nature of force, energy, and the
ether. On the philosophical level, there was the idea that there should be fundamental elements of
maer through which all properes of macroscopic maer could be explained. However, several
conceptual dicules were raised again and again. If atoms are extended, it seems they should be
divisible and therefore they cannot be basic elements; but if they are point parcles without
extension it is dicult to see how they can constute extension and how there can be anything
besides empty space. Furthermore, if atoms are perfectly hard, it is dicult to explain how they can
collide elascally and how moon can be conserved in collisions, but if atoms are deformable then
this seems to imply that they have an inner structure, and therefore they cannot be basic elements in
terms of which all properes of maer can be explained. More generally, it seemed that any
property that was aributed to atoms could not be explained in terms of atoms and therefore had to
remain fundamentally unexplainable.
Besides these conceptual dicules, there were also empirical challenges to the concepon
of maer. In the early nineteenth century John Dalton showed that chemical substances react in
xed raos and argued that this demonstrated that chemical substances consist of small elements
which he termed atoms. Though many indeed saw Dalton’s work as evidence for the existence of
atoms, there were also crics of Dalton’s conclusions (Nye 1976). Furthermore, in Dalton’s theory,
there is a dierent atom for each chemical substance; it thus seemed that Dalton’s atoms did not
full the philosophical ideal of simple atoms, and therefore, not everyone accepted the idea that
Dalton’s chemical atoms were ulmate parcles.
Further research on the properes of chemical elements became possible through the work
of Gustav Kirchho and Robert Bunsen on spectroscopy. In the 1850s, Bunsen invented a gas burner
which has a hot ame with minimal luminosity. Kirchho and Bunsen discovered that if a chemical is
heated in this ame and you look at the light of the colored ame through a prism, you observe a
spectrum with a few bright lines, with a characterisc paern of lines for each chemical element;
each chemical element thus has a characterisc spectrum [g. 1]. With the assumpon that chemical
substances are constuted by atoms, this suggested that the atoms of a specic chemical element
2
Furthermore, Laplacian physics was never fully dominant even in France, as there was a rival, more abstract
approach to mechanics developed by Lagrange, which did not depend on a specic ontology of maer.
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can vibrate at specic frequencies, which causes an emission of light of these exact frequencies. This
in turn suggested that atoms have a complex inner structure which is dierent for each chemical
element, which further strengthened the idea that chemical atoms could not be atoms in the
philosophical sense of being basic elements.
Fig. 1. Source: Kirchho, G. and R. Bunsen (1860). Chemical Analysis by Observaon of
Spectra. Annalen der Physik und der Chemie, 110: 161-189. Courtesy of Linda Hall Library of
Science, Engineering & Technology.
Further complicaons arose from the kinec theory of gases. This theory, developed from the mid-
nineteenth century, explained the behavior of gases through the assumpon that gases consist of
small parcles, molecules or atoms, which move rapidly in all direcons. This theory was successful
and was seen as a conrmaon of atomism, but it also had problems. A main issue was what came to
be known as the specic heats problem: it turned out that measured values of the specic heats of
gases were hard to reconcile with the evidence from spectroscopy as well as with the assumpon
that atoms are rigid bodies or that they are point parcles. Take γ = Cp/Cv, with Cp and Cv the specic
heat of a gas at constant pressure and volume, respecvely. Within the kinec theory of gases it is
possible to derive a value for γ given the number of degrees of freedom of atoms. This derivaon is
based on the equiparon theorem, which says that in thermal equilibrium, the kinec energy of a
system is equally divided over all its degrees of freedom. If you take atoms to be point parcles, then
the only moon of atoms is translaonal and they thus have three degrees of freedom, which yields
γ=1.67 (this is the value which Rankine derived in 1853). If atoms are rigid, extended bodies, they can
undergo both translaonal and rotaonal moon, with which you arrive at γ=1.33 (as Maxwell
showed in 1860). However, if atoms can vibrate, as suggested by spectroscopy, this adds addional
degrees of freedom, which brings γ close to 1. None of these results agreed with the experimentally
determined value of ca. γ=1.4 (Nyhof 1988; De Regt 1996).
In this way, by 1860, the inner structure of atoms had become a scienc problem. Physicists
aempted to develop models of the atom which could account for the seemingly contradictory
ndings of spectroscopy and the kinec theory of gases. In 1867, William Thomson (the later Lord
Kelvin) argued that spectroscopy suggests that atoms are capable of vibraon; but to aribute
vibraon to an atom “is at once to give it that very exibility and elascity for the explanaon of
which, as exhibited in aggregate bodies, the atomic constuon was originally assumed” (Thomson
1867, 17). This statement was repeated almost word for word by James Clerk Maxwell some years
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later.
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Thomson notes that it is sll possible to argue that the parcles which are analyzed in
spectroscopy are not atoms in the philosophical sense, but molecules which are each composed of
many philosophical atoms. However, “Such a molecule could not be strong and durable, and thus it
loses the one recommendaon which has given it the degree of acceptance it has had among
philosophers” (Thomson 1867, 17). The scienc challenge which spectroscopy posed to the
understanding of maer was thus at the same me a challenge to philosophical concepons of
maer: spectroscopy showed that chemical atoms could not be the simple foundaonal elements
through which all properes of maer could be explained.
For Maxwell, spectroscopy not only posed a challenge to concepons of maer, but also
revealed something signicant about the ulmate nature of maer and even about divine creaon.
In an entry he wrote for the 1875 edion of the Encyclopedia Britannica tled ‘Atom’, Maxwell
pointed out that spectroscopy shows that all hydrogen ‘molecules’ have the exact same periods of
vibraon, no maer where they come from: spectral lines idencal to those of terrestrial hydrogen
have also been observed in the spectra of sunlight and the light from stars, which shows that
hydrogen molecules can also be found in stars, and that terrestrial and celesal hydrogen molecules
have the exact same periods of vibraon. According to Maxwell, this can only be explained through a
common origin. Maxwell compares the vibrang molecules to bells, which must all have been tolled
the exact same way; he also compares them to “manufactured arcles” (Maxwell 1890, 483). For
Maxwell, this was an argument for divine creaon.
In the second half of the nineteenth century, a new concepon of maer was developed by
Thomson and other Brish physicists, namely the vortex theory of maer (Kragh 2002). This theory
built on work in uid moon by Hermann von Helmholtz, who had shown that in an ideal uid there
could be stable vortex rings of xed volume. In Thomson’s view, this suggested that these rings were
“the only true atoms” (Thomson 1867, 15). According to the vortex theory of maer, atoms were
vorces in a hypothecal uid, which later came to be idened with the luminiferous ether.
Thomson argued that this theory could solve both conceptual and empirical issues with the noon of
maer. In 1867 he wrote that unl now, in order to account for the permanence of maer people
needed the “monstrous assumpon of innitely strong and innitely rigid pieces of maer”; but now,
with the vortex theory, this assumpon is not needed anymore, as it can be proven mathemacally
that vortex rings are stable (Thomson 1867, 15). This means that only God can create or destroy
vortex moon. Thomson argued furthermore that the vortex theory held the promise of explaining
properes of maer such as elascity. It was to some degree possible to study the properes of
vortex rings experimentally through experiments with smoke rings, which are vorces in the air, and
which could be shown to collide elascally:
A magnificent display of smoke-rings, which [the author] recently had the pleasure of witnessing in
Professor Tait's lecture-room, diminished by one the number of assumptions required to explain the
properties of matter on the hypothesis that all bodies are composed of vortex atoms in a perfect
homogeneous liquid. Two smoke-rings were frequently seen to bound obliquely from one another,
shaking violently from the effects of the shock. (Thomson 1867, 16) [Fig. 2]
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“We may indeed suppose the atom elasc, but this is to endow it with the very property for the explanaon
of which, as exhibited in aggregate bodies, the atomic constuon was originally assumed” (Maxwell 1890,
471; originally published in 1875).
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Fig. 2. Source: Tait, P. G. (1876), Lectures on Some Recent Advances in Physical Science (London:
Macmillan), p. 292.
Furthermore, because vortex rings can vibrate there was the promise that this theory would be able
to account for the results of spectroscopy. Vorces could be interlinked and knoed in complex
ways, creang a set of dierently formed vorces which might represent dierent chemical elements
(Kragh 2002).
Maxwell was very interested in vortex theory, although he considered it a promising research
program rather than a worked out theory. Maxwell argued that from a metaphysical point of view
the vortex theory had great advantages, mainly because it involved no arbitrary assumpons: “When
the vortex atom is once set in moon, all its properes are absolutely xed and determined by the
laws of moon of the primive uid, which are fully expressed in the fundamental equaons”
(Maxwell 1890, 471). He saw it as a return to a Cartesian concepon of maer, since according to
this theory maer consists of moon in a uid which completely lls up space. Maxwell did remark
that it would be very dicult to develop the theory of vortex atoms further. In this he turned out to
be right: the vortex theory was popular in Britain for a while, but eventually it lost momentum
because of the great mathemacal dicules involved in calculang dierent types of vortex moon
and a lack of concrete results (Kragh 2002).
In a 1873 lecture tled ‘Molecules’, Maxwell argued that the philosophical problem of the
essence of maer was as present in the science of his me as it had been in ancient mes:
The mind of man has perplexed itself with many hard questions. Is space infinite, and if so in what
sense? Is the material world infinite in extent, and are all places within that extent equally full of
matter? Do atoms exist, or is matter infinitely divisible?
The discussion of questions of this kind has been going on ever since men began to reason, and to
each of us, as soon as we obtain the use of our faculties, the same old questions arise as fresh as ever.
They form as essential a part of the science of the nineteenth century of our era, as of that of the fifth
century before it. (Maxwell 1890, 361)
…though many a speculator, as he has seen the vision recede before him into the innermost sanctuary
of the inconceivably little, has had to confess that the quest was not for him, and though philosophers
in every age have been exhorting each other to direct their minds to some more useful and attainable
aim, each generation, from the earliest dawn of science to the present time, has contributed a due
proportion of its ablest intellects to the quest of the ultimate atom. (ibid, 364)
Maxwell argued that we are not jused in aribung the properes of sensible maer, such as
extension, to atoms, and that also the idea that two atoms can never coincide is a prejudice which
derives from our experience with sensible maer (Maxwell 1890, 448).
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However, despite his acknowledgment of the philosophical problem of maer, Maxwell
argued that one can do physics without a commitment to a specic noon of maer. Maxwell argued
that in physics it is oen fruiul to work with clear and detailed mechanical models, but that it is
important not to be commied to their literal correspondence with nature; they should rather be
conceived as pictures or analogies that are useful as long as you don’t mistake them for reality. It can
be useful to model maer as a connuous substance, whether or not it actually is connuous; and
this it possible as long as the maer you are dealing with is homogeneous enough at the scale you’re
looking at:
…if a railway contractor has to make a tunnel through a hill of gravel, and if one cubic yard of the
gravel is so like another cubic yard that for the purposes of the contract they may be taken as
equivalent, then, in estimating the work required to remove the gravel from the tunnel, he may,
without fear of error, make his calculations as if the gravel were a continuous substance. But if a worm
has to make his way through the gravel, it makes the greatest possible difference to him whether he
tries to push right against a piece of gravel, or directs his course through one of the intervals between
the pieces; to him, therefore, the gravel is by no means a homogeneous and continuous substance.
(Maxwell 1890, 450).
We have seen that for Maxwell, a discussion of the nature of maer was part of his natural
philosophy and even natural theology. Nevertheless, he thought that within physics it is not
necessary to decide on a specic concepon of maer. This argument was increasingly made by
physicists in the late nineteenth and early tweneth century, and increasingly physicists argued that
the queson of the nature of maer should be le out of physics altogether.
The queson of the nature of maer gets dismissed
An inuenal discussion of the problem of the nature of maer can be found in Emil Du Bois-
Reymond’s famous 1872 lecture, “On the Limits of Our Knowledge of Nature” (in Du Bois-Reymond
1898). Here, Du Bois-Reymond argued that there are two quesons which are forever beyond the
reach of science, namely the queson of the nature of maer and that of consciousness. He argues
that whenever we ask about the nature of maer, we get into contradicons. The philosophical
concept of an atom is that of a fundamental element, which is passive and without properes: Du
Bois-Reymond characterizes the philosophical atom as “a presumably indivisible mass of inert and
eectless substratum from which forces emanate through empty space into the distance” (Du Bois-
Reymond 1898, 25). But he argues that this concepon of atoms is full of contradicons. In order for
an atom to actually exist, it has take up at least some space; however, if an atom is extended, it must
be divisible. Moreover, to be extended, atoms must be impenetrable, which requires a repulsive
force; but then the atom is not eectless (Wirkungslos) anymore. According to Du Bois-Reymond,
such contradicons are unavoidable: they arise when we try to explain the properes of maer in
terms of smaller bits of maer, which is in principle impossible (Du Bois-Reymond 1898, 27; Wilholt
2008). Therefore, we have to accept that no understanding of the nature of maer is possible. In Du
Bois-Reymond’s view, the queson of the nature of maer is thus unanswerable and should simply
be set aside. The success of science does not in any way depend on having a consistent fundamental
ontology; in fact, Du Bois-Reymond argues in this lecture that everything but the nature of maer
and the nature of consciousness can in principle be explained in terms of the moon of atoms. By
isolang the scienc enterprise from the problems of maer and consciousness, Du Bois-Reymond
makes science independent of philosophy.
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In 1884 Heinrich Hertz held a series of lectures at the university of Kiel, the manuscripts of
which were published in 1999. In these lectures, Hertz argues that it is possible to gain scienc
knowledge of maer: chemistry and the kinec theory of gases have given us evidence for the
existence of atoms, and it seems likely that spectroscopy will teach us a lot about their inner
structure. But this scienc knowledge of maer can never sasfy the philosopher. Philosophers will
always keep asking quesons, for example asking whether or not atoms are extended and what is the
dierence between empty and full space (Hertz 1999, 31; Wilholt 2008). He argues that the noon of
maer includes the properes of extension, moveability, impenetrability and indestrucbility, but if
we ask what exactly is meant by each of these concepts, it turns out that dierent and somemes
even contradictory meanings are aached to them and that it is not clear whether maer even
necessarily has these properes. We nd that these properes “are composed of the results of our
observaon and of the demands of our understanding; they therefore correspond only in part to the
properes of things, and in part rather to the properes of our mind” (Hertz 1999, 117).
Is it to be hoped that a satisfactory structure can be built on such an uncertain foundation? Can we
expect to unravel the complicated relationships of matter as long as its most elementary properties
are still unclear to us? The success of physics seems to give us certainty on this point. But can we also
understand how this is possible, how the study of matter can be useful to us, a thing whose simplest
properties we are unable to specify? Certainly we can understand this. (Hertz 1999, 17)
Hertz argues that in order to do physics, it is not actually needed to have a conceptually consistent
account of the nature of maer. He makes a comparison between maer and money: there are
contexts in which the material constuon of money maers, for example, money should be dicult
to forge. However, the essence of money does not lie in its physical properes, and e.g. for the eld
of economics the physical properes of money are completely irrelevant. Similarly, the queson of
the ulmate nature of maer is of philosophical interest but is largely irrelevant in physics. Physics
and philosophy can exist in parallel, and should each respect each other’s endeavors:
If the philosopher wanted to reject everything the physicist says about matter because of its uncertain
definition, he would be in the position of a man who does not want to accept payment because he
dislikes the way the coins are minted; on the other hand, the physicist who ridicules the philosopher's
endeavours concerning matter is in the position of someone who denies the usefulness of a well
minted coin. (Hertz 1999, 119)
Physicists and philosophers are simply interested in dierent aspects of maer. Hertz points out that
it is important not to confuse these aspects: otherwise, you may nd yourself trying to melt paper
money because you have heard that money can be cast into silver spoons, or you may try to
“construct the universe from the properes of extension, mobility, etc. that our minds have given to
the concept of maer. Not a few philosophers have been guilty of such a ridiculous blunder” (Hertz
1999, 119).
Hertz argues that in physics we can work with an image of maer: for example, it is ne to
picture atoms as ny billiard balls, as long as we keep in mind that this is only an image which does
not fully correspond to nature. He developed this noon of images further in his Principles of
Mechanics, rst published in 1894, in which he argued that “Various images of the same objects are
possible, and these images may dier in various respects” (Hertz 1899, 2). In this work, Hertz argued
that the noon of force was conceptually unclear, and in order to avoid dicules with the noon of
force he developed a formulaon of mechanics in which force did not enter as a primive noon, but
within which a claried noon of force could be derived. It seems that in Hertz’s view, the conceptual
unclaries in our noon of maer did not necessitate such a reformulaon of physics because they
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did not actually maer for physics, in contrast to the problems with the noon of force (on the laer,
see Eisenthal 2021). As Hertz argued in his 1884 lectures, the philosophical endeavor of developing a
conceptually consistent noon of maer was not altogether irrelevant, but physics was neatly
isolated from such concerns.
Also Henri Poincaré thought that in pracce, our concepon of maer did not actually maer
for physics. In Science and Hypothesis (rst published in 1902), he characterized atomism as an
“indierent hypothesis”: the existence of atoms can be neither proven nor disproven, and in
calculaons you can start from the assumpon that maer is connuous or that it is made out of
atoms – this will not make a dierence in the results of the calculaon, but only in the diculty with
which the results are obtained (Poincaré 2018, 109). Thus, like Du Bois-Reymond and Hertz, Poincaré
argues that we cannot know the nature of maer and that this does not maer for physics. We can
work with a noon of atoms or we can take maer to be connuous, whatever is most convenient
for our purposes.
Towards the end of the nineteenth century, there was increasing skepcism among physicists
about the existence of atoms and about the fruiulness of the atomisc hypothesis. Several
physicists, including Poincaré, argued that physical theories which were based on an atomic
concepon of maer, notably the kinec theory of gases, were speculave and not very fruiul.
Ludwig Boltzmann is known for his fervent defense of atomism against these cricisms. However,
this does not mean that he thought that all philosophical quesons about maer could be answered.
In fact, like Maxwell and Hertz, whom he cited as inuences, Boltzmann argued that in science we
work with images which do not correspond with nature in every way (de Regt 1999). He wrote in
1899 that if we realize that science can provide no more than pictures of nature, philosophical
quesons about the nature of maer dissolve:
Many questions that used to appear unfathomable thus fall away of themselves. How, it used to be
said, can a material point which is only a mental construct, emit a force, how can points come
together and furnish extension, and so on? Now we know that both material points and forces are
mere mental pictures. The former cannot be identical with something extended, but can approximate
as closely as we please to a picture of it. The question whether matter consists of atoms or is
continuous reduces to the much clearer one, whether [the idea of enormously many particulars or the
idea of] the continuum is able to furnish a better picture of phenomena. (Boltzmann 1974, 91).
4
In an address held in 1904, Boltzmann argues that in the past, sciensts le the queson of the
nature of maer to philosophers, but that this has not yielded very good results, as philosophers
mostly have pointed out contradicons in our concepon of maer. Referring to Kant’s second
annomy in the Crique of Pure Reason, Boltzmann writes that Kant had shown that “[i]t is strictly
provable that the divisibility of maer can have no limit and yet innite divisibility contradicts the
laws of logic”;
This is by no means the only occasion when philosophical thought becomes enmeshed in
contradictions, rather we meet it at every step. The most ordinary things are to philosophy a source of
insoluble puzzles (Boltzmann 1974, 164)
According to Boltzmann, philosophers tend to get into contradicons because they tend to have
“excessive condence in the so-called laws of thought” (Boltzmann 1974, 165). Boltzmann gave an
evoluonary account of the laws of thought: these are a priori principles which make experience
4
The part within the square brackets is taken from Wilholt (2008), who notes that these words appear in the
German original but are missing from the translaon.
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possible, and they are innate, having evolved in a biological process of evoluon. However, we
should not aribute absolute certainty and infallibility to these principles: they have evolved to get
us through daily life and not to deal with abstract philosophical problems. Therefore, the queson of
the nature of maer should not be approached through a priori reasoning, and rather than asking
what is the true nature of maer, we should ask what picture of maer gives the best account of the
phenomena. If we realize that both atoms and connuous maer are mental pictures we have
constructed, we can simply ask which of these pictures “can be developed more clearly and more
easily while most correctly and denitely reproducing the laws of phenomena” (Boltzmann 1974,
145). “Of course this does not answer the old philosophic queson, but we are cured of the urge to
want to decide it along a path that is devoid of sense and hope” (Boltzmann 1974, 169).
Thus, like Du Bois-Reymond and Hertz, Boltzmann argued that aempts to solve the
philosophical problem of the nature of maer only lead to contradicons. However, unlike them, he
did not think that physics should free itself from philosophy. Philosophers may have a tendency to
get stuck in contradicons, but physicists do need philosophical reecon on the concepts and
assumpons they use. Boltzmann argued that physicists and philosophers should work together: “the
me for a pact” between sciensts and philosophers had come (Boltzmann 1974, 172). According to
Boltzmann we can in fact use philosophical reecon to show where a priori reasoning goes wrong
and to unmask certain problems as pseudoproblems (Preston 2023).
In this way Boltzmann argued that the queson of the ulmate nature of maer could be
reduced to the more praccal queson of which picture of maer is most appropriate. And he did in
fact have an opinion on this: he argued that atomic theories had been highly fruiul and should be
pursued further. Boltzmann worked on developing an atomic model which was compable with the
ndings of the kinec theory of gases and spectroscopy. In the 1870s, he proposed a soluon to the
specic heats problem according to which molecules of a gas consist of two atoms which are rigidly
connected, similar to a dumbbell: such molecules have ve degrees of freedom (three degrees of
freedom of translaon, two of rotaon, and none of vibraon), with which the rao for the specic
heats comes out correctly. This model could not explain spectral lines, but Boltzmann argued that it
was possible to account for both the specic heats of gases and spectroscopy if molecules mostly
behave like rigid dumbbells, and if they vibrate only briey aer collisions, aer which these
vibraons are passed on to the surrounding ether (De Regt 1996).
Moreover, Boltzmann gave a peculiar argument for atomism based on his views on the
philosophy of mathemacs: he argued that any noon of the connuum has to start from discrete
elements, or atoms, and then one has to take the limit in which these elements become innitely
small. However, in Boltzmann’s view, one cannot assume actual innity in nature, and therefore this
limit cannot be taken to be actual. According to Boltzmann it is therefore more clear and economical,
and goes less beyond the facts, to sck with the discrete elements (Wilholt 2002; Van Strien 2015). It
is not so easy to see how this mathemacal argument for atomism diers from the type of
philosophical reasoning about the ulmate nature of maer which he claimed to reject.
Philosophy and physics are deeply connected in the work of Ernst Mach, who argued not only
that we cannot know the true nature of maer, but also that the noon of a material body is
generally misleading. All we have are sensaons, and our noon of body is an abstracon which we
use to refer to relavely stable complexes of sensaons. It is wrong and naïve to think that there
must be some “dark lump” (dunklen Klumpen) of maer behind the sensaons, or that bodies are
absolutely unchangeable (Mach 1882, 17). It is true that mass is conserved, but this is merely an
abstract equaon and does not indicate something real behind our sensaons. Mach argues that the
concept of atom is even more problemac than that of bodies in general:
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Modern atomistics is an attempt to turn the concept of substance in its most naïve and crudest form,
as it is held by those who consider bodies to be absolutely stable, into the basic concept of physics.
(Mach 1896, 428)
Mach points out that “atoms are somemes ascribed properes that contradict all previously
observed properes” (Mach 1883, 463). Moreover, he argues that we are not jused in conceiving
of atoms as enes in three-dimensional space. Three-dimensional spaality is a feature of our
percepons; however, we cannot perceive atoms, and therefore we should not conceive of them as
spaal. In a footnote in one of his later works, Mach menons that it was his own research on
spectroscopy which led him to the idea that we need not think of atoms as three-dimensional
enes:
Still caught up in the atomistic theory, I tried to explain the line spectra of gases by the vibrations of
the atomic constituents of a gas molecule relative to each other. In 1863, the difficulties I encountered
in this endeavour led me to the idea that non-sensory things need not necessarily be represented in
our sensory space of three dimensions. (Mach 1906, 418)
Mach argues that atoms should be regarded as “provisional aids” (provisorische Hülfsmiel) and that
they are mental enes (Gedankendinge), comparable to mathemacal enes, which funcon in
our theories but do not actually exist (Mach 1883, 463). Mach thus used a posivist and empiricist
philosophy to dispel the problem of maer altogether. He expressed the hope that as natural science
becomes more sophiscated, it will abandon its “mosaic game with lile stones”, and will recognize
that its aim should be merely to nd the most economical descripon of the phenomena (Mach
1882, 21).
Conclusions
There are signicant dierences between the authors discussed: Boltzmann, Du Bois-Reymond and
Hertz took maer to consist of atoms while Mach and Poincaré were skepcal or downright crical
of atomism, Hertz argued that although the philosophical queson of the nature of maer is largely
irrelevant to physics it is sll a legimate queson, while Mach and to a degree also Boltzmann
dismissed it altogether as a pseudoproblem, and Hertz and Du Bois-Reymond thought that natural
science should become independent of philosophy while Mach and Boltzmann thought that
(anmetaphysical) philosophical reasoning was needed to dissolve the (metaphysical) problem of the
nature of maer. But despite these dierences, they all agreed that physicists need not engage with
the philosophical queson of the true nature of maer.
We have seen that this was movated in part by the dicules in developing a model of the
atom that could account for the ndings of spectroscopy and the specic heats of gases, and in part
by the fact that any such model of the atom would go against the philosophical idea of atoms as
basic elements through which all properes of maer could be explained, and by the seemingly
widespread idea that all philosophical aempts to develop a consistent concepon of maer had led
to contradicons.
Despite the desire of Du Bois-Reymond and Hertz to separate physics from philosophy,
philosophical and physical aspects of the problem of maer were thus closely intertwined. De Regt
(1996) has argued that in the debate about the scienc heats problem “there was a close mutual
interacon between science and philosophy”, arguing in parcular that the philosophical views of
Maxwell and Boltzmann inuenced their scienc results regarding the specic heats problem.
11
The fact that towards the end of the nineteenth century many physicists dismissed the
queson of the true nature of maer falls under what John Heilbron has called ‘descriponism’
(Heilbron 1982). Heilbron has pointed out that in the late nineteenth century there was a widely
shared view among physicists that we can never know the true nature of things and that the aim of
science should merely be to describe the phenomena. It is true that also during other historical
periods one can nd sciensts expressing a similar view, but it seems to have been parcularly
widespread in the late nineteenth century. This view was shared among physicists in dierent
countries, and among physicists who otherwise had highly divergent views on the philosophy of
science, including physicists who came to be known as ‘realist’, such as Boltzmann, as well as
‘anrealists’ such as Mach. Heilbron argued that there was lile internal movaon in physics for
such a modest view of the aims of physics, and that descriponism was mainly rhetorical and mostly
found in public lectures: his claim is that in a me in which natural science was oen seen as
materialisc and arrogant, sciensts took care to present their endeavors in a modest way, arguing
that they were merely describing the phenomena.
5
It has been argued that this is not enrely correct
and that descriponism did in fact maer for the pracce of physics (Porter 1994; Staley 2008). My
account of the discussions on the nature of maer in this period supports the view that there were
internal causes for descriponism: the widespread rejecon of the queson of the nature of maer
was movated by conceptual puzzles as well as scienc problems.
In 1908, the existence of atoms was conrmed by Jean Perrin’s work on Brownian moon
and atomism became almost universally accepted among physicists. But this does not necessarily
imply that the nature of maer could be known aer all. In 1912, Poincaré admied that there was
now experimental proof for the existence of atoms; however, he maintained that these were not
atoms in the philosophical sense:
The atom of the chemist is now a reality; but this does not mean that we are about to arrive at the
ultimate elements of matter. When Democritus invented the atoms, he considered them as absolutely
indivisible elements beyond which there is nothing to seek. That is what that means in Greek; and it is
for this reason, after all, that he had invented them. Behind the atom, he wanted no more mystery.
The atom of the chemist would therefore not have given him any satisfaction; for this atom is by no
means indivisible; it is not truly an element; it is not free of mystery; this atom is a world. (Poincaré
1963, 91; and see Ivanova 2013)
In Niels Bohr’s atomic model of 1913, electrons orbit the nucleus of an atom, which led to
comparisons between the atom and the solar system: in this sense the atom indeed became a world.
Although the above quote from Poincaré dates from before Bohr’s atomic model, the idea of orbing
electrons was already around. (Another analogy: the ancient Greek work ‘hule’ (ὕλη) can mean
maer, wood, or forest. Upon entering the forest, you may nd that you cannot see the forest for
the trees anymore).
By the early tweneth century, studies on radioacvity had shown that maer can decay; it
turned out that the atoms of physics are not immutable and that they are in fact divisible into smaller
parcles. Moreover, these smaller parcles were electrically charged, and it seemed that no
understanding of maer would be possible without taking into account its electrodynamic
properes. The philosophical ideal of primive, essenally property-less bits of maer was now fully
abandoned.
5
Heilbron’s claim is modeled on the more famous ‘Forman thesis’ in the history of quantum mechanics.
12
References
Boltzmann, L. (1974). Theorecal Physics and Philosophical Problems, ed. B. McGuinness. Dordrecht:
D. Reidel.
Brading, K. and M. Stan (2024). Philosophical Mechanics in the Age of Reason. Oxford University
Press.
De Regt, H. (1996). Philosophy and the Kinec Theory of Gases. Brish Journal for the Philosophy of
Science, 47: 31–62.
De Regt, H. (1999). Ludwig Boltzmann’s Bildtheorie and Scienc Understanding. Synthese 119: 113–
34.
Du Bois-Reymond, E. (1898). Über die Grenzen des Naturerkennens. In E. Du Bois-Reymond, Über die
Grenzen des Naturerkennens - Die sieben Welträthsel, Zwei Vorträge von Emil Du Bois-
Reymond, 15-66. Verlag Von Veit & Comp., Leipzig.
Eisenthal, J. (2021). Hertz's Mechanics and a Unitary Noon of Force. Studies in History and
Philosophy of Science Part A, 90, 226-234.
Fox, R. (1974). The Rise and Fall of Laplacian Physics. Historical Studies in the Physical Sciences 4: 89–
136.
Harman, P. M. (1982). Energy, Force and Maer: The Conceptual Development of Nineteenth-Century
Physics. Cambridge University Press.
Heilbron, J. L. (1982). Fin-de-Siècle Physics. In Science, Technology & Society in the Time of Alfred
Nobel, ed. C. Bernhard, E. Crawford and P. Sörbom, 51–73.
Hertz, H. (1899). The Principles of Mechanics Presented in a New Form. Macmillan and Co.
Hertz, H. (1999). Die Constuon der Materie, Eine Vorlesung über die Grundlagen der Physik
aus dem Jahre 1884, ed. A. Fölsing. Berlin: Springer.
Ivanova, M. (2013). Did Perrin’s Experiments Convert Poincaré to Scienc Realism? HOPOS: The
Journal of the Internaonal Society for the History of Philosophy of Science, 3(1), 1-19.
Kragh, H. (2002). The Vortex Atom: A Victorian Theory of Everything. Centaurus 44: 32–114.
Mach, E. (1882). Die ökonomische Natur der physikalischen Forschung. Wien: KK Hof-und
Staatsdruckerei.
Mach, E. (1883). Die Mechanik in ihrer Entwickelung, historisch-krisch dargestellt. Leipzig: F. A.
Brockhaus.
Mach, E. (1896). Die Principien der Wärmelehre, historisch-krisch entwickelt. Leipzig: Verlag von
Johann Ambrosius Barth.
Mach, E. (1906). Erkenntnis und Irrtum: Skizzen zur Psychologie der Forschung. (2nd ed.). Leipzig:
Verlag von Johann Ambrosius Barth.
Maxwell, J. C. (1890). The Scienc Papers of James Clerk Maxwell, Vol. 2, ed. W. D. Niven.
Cambridge University Press.
Nye, M. J. (1976). The Nineteenth-Century Atomic Debates and the Dilemma of an ‘Indierent
Hypothesis’. Studies in History and Philosophy of Science 7(3): 245-268.
Nyhof, J. (1988). Philosophical Objecons to the Kinec Theory. Brish Journal for the Philosophy of
Science 39, 81–109.
Poincaré, H. (2018). Science and Hypothesis (M. Frappier, A. Smith and D. J. Stump, transl.).
Bloomsbury.
Poincaré, H. (1963). Mathemacs and Science: Last Essays (J. W. Bolduc, transl.). New York: Dover
Publicaons.
13
Porter, T.M. (1994). The Death of the Object: Fin de Siècle Philosophy of Physics. In Modernist
Impulses in the Human Sciences, 1870–1930, ed. D. Ross, 128–151. Balmore: Johns Hopkins
University Press.
Preston, J. (2023). The Idea of a Pseudo-Problem in Mach, Hertz, and Boltzmann. Journal for General
Philosophy of Science, 54(1), 55-77.
Staley, R. (2008). The Fin-de-Siècle Thesis. Berichte zur Wissenschasgeschichte 31: 311–330.
Stan, M. (2017). Euler, Newton, and Foundaons for Mechanics. In The Oxford Handbook of Newton,
ed. C. Smeenk and E. Schliesser, 1-22. Oxford University Press.
Thomson, W. (1867). On Vortex Atoms. Philosophical Magazine 34, 15–24.
Van Strien, M. (2015). Connuity in Nature and in Mathemacs: Boltzmann and Poincaré. Synthese
192 (10): 3275–3295.
Wilholt, T. (2002). Ludwig Boltzmann’s Mathemacal Argument for Atomism. In M. Heidelberger & F.
Stadtler (Eds.), History of Philosophy and Science: New Trends and Perspecves, 199–211.
Kluwer academic publishers.
Wilholt, T. (2008). When Realism Made a Dierence: The Constuon of Maer and its Conceptual
Enigmas in Late 19th Century Physics. Studies in History and Philosophy of Modern Physics 39,
1–16.
