Brit. 7. Phil. Sci. 36
(I985),
299-329
Printed in Great Britain
299
Discussions
AN HISTORICAL NOTE ON ERNST MACH
A number of philosophersincluding Peter Clark ([I976] & [I982]) and
PaulFeyerabend[I980] in thisjournalandLarryLaudan[I976] andMichael
Gardner[I979] elsewherehave tried to suggest that perhapsErnstMach's
oppositionto atoms and Ludwig Boltzmann'skinetic theory of gases was
scientificand justified. Much as I respect Mach's independentjudgment
and expeciallyhis warningsaboutexcessiveidealisationin physics I cannot
agree.
As an historianof science, authorof a biographyof Mach [I972], and as
co-editor of forthcomingvolumes on the correspondencerespectivelyof
Mach and his principalmethodologicalcritic Ludwig BoltzmannI do not
believethatthe attemptto whitewashMach'spositionon atomismwill stand
up. It is understandablethat philosophersmay be reluctantto believe that
philosophicalviews, assumptions,or prejudicescan stand in the way of
scientificprogress,but sometimes the evidence is too strong to be easily
arguedor willed away.
PerhapsMach'soppositionto 'billiardball' atoms should have included
supportfor atoms as changing,perishable'corpuscles'such as Boltzmann
strongly advocated,but it never did. And perhaps Mach's opposition to
Boltzmann'skinetic theory should have been groundedon real technical
difficultiessuch as what Clarkcalls 'the problemof the anomalousspecific
heat ratios' or real defects in his use of idealisedmolecularmodels rather
thanseeminglyautomaticrejectionof anythingandeverythingbasedon the
atomictheory,but it neverdid. In principle Machwas remarkablytolerant.
He allowedthat the atomictheorymight have 'provisionalvalue'in science
and were there no need to reconcile the philosophical assumptions of
psychologywith those of physics, he would have no objectionto physicists
continuingto use the atomic theory. But in practice he was adamant.He
made no use of the atomic theory in his own scientific work during his
matureyears,not even concerningshockwaveswherethe theorymighthave
been useful.
In my [I972] book on Mach I failed to mention the many technical
objections to Boltzmann'skinetic theory which accompaniedthe many
philosophicalattacksby Mach,Ostwald,andtheirfollowers.My reasonwas
that virtuallyall of the technicalobjectionswere highly mathematicaland
most appearedin Englishjournals,and there was and is no evidencewhich
has been made availableto me that Mach had ever read the technical
objections or was even aware of them. His criticisms of Boltzmann's
statistical interpetationof the second law of thermodynamicswas quite
300
3fohnBlachmore
independentof scientificobjections,apartfrom the largely philosophical
reversibilityand recurrenceobjections of Loschmidt and Zermelo. To
partly comperusatefor my 'oversight' the forthcoming edition of
Boltzmann's correspondencewill include the technical objections by
Culverwell, Bryan, Burburry,Watson, and others including Boltzmann
himself which originallyappearedas lettersto the editor in Natureduring
the middle I890S.
PerhapsMach was too clever to be a 'simple-mindedpositivist' as Paul
Feyerabendsupposes.1Perhapsno philosopheris literallysimpleminded,
but his reductionof the physicalworld to sensationsand his belief that all
realknowledgeis scientificwas surelypositivisticas it wasunderstoodat the
time, and he did sharethe simplemindedoppositionto atomswhich many
positivists held. His reasons were -not primarly physical; they were
philosophical,if one maylabelthe opinionsof a posititivistas philosophical.
What were Mach's philosophicalobjections?Peter Clarksupposes that
his opposition to use of the atomic theory was based on his notion of
'Denkokonomie'as if one shouldalwayspick the simplesttheoryin science
and is if one could imagine a simpler approachthan atomism. Mach's
oppositionto the realityof 'billiardball' atoms (a very differentquestion)
was that as eternal and unchanging'substances'they were metaphysical
andincapableinprincipleof beingobserved.On the otherhand,it is not clear
why he seemed unable to appreciatethat by the late nineteenthcentury a
largenumberof physicistsand chemistswere alreadythinkingof atoms in
terms of divisible and transient corpuscles which were not necessarily
subject to Mach's philosophicalobjections.(His partialparalysisin I898
andwithdrawalfromuniversitylife in I 90 I naturallydid not help him keep
up with the latestopinionsin physics, but his fairlyrapidreturnto writing
andpublishingwouldsuggestthathe shouldhaveknownwhatwasgoingon.
His stronginterestin Einstein'sspecialtheoryof relativityduring I909 and
I9I0
would indicatehe was still capableof followingrecentdevelopments.)
There is a belatedly published story by Ludwig Boltzmann's last
assistant,StefanMeyer[I950] which I includein my biography([I972], pp.
3I9-23)
that Mach changedhis mind about atom-safterlookingthrougha
spinthariscopeand observingthe scintillations,but since Mach wrote and
published attackson the reality of atoms as late as I9I0, if there was a
conversionit presumablymust have been after that year, that is, between
I 9 I 0 andhis deathin I 9 I 6. The quotationagainstthe realityof atomsis to be
found in a 'Kampfschrift'againstMax Planckand assortedcritics ([I9I0]
& [I9I9],
pp.
I0-I
I)
The resultsof the atomictheorycan be just as manifoldand useful if one is not in
such a hurry to treat atoms as realities. Therefore all honor to the beliefs of
physicists! But I myself cannot make this particularbelief my own (trans.
Blackmore,[I972], p. 32I).
1 Note fromPaul Feyerabend,postmarked5 Januaryt984.
An HistoricalNote on ErnstMach
30I
The only evidence I have been able to find from Mach's published or
unpublishedwritings that he had begun to have second-thoughtsabout
atoms seems to surfacein his last 'Notizbuch'from I9I0 to I9I4. On page
37 he writes with a shakyleft hand, presumablyduring I9I I:
Atomebewegensich im Raumund Zeit. Was ist Raumund Zeit?Raumist von der
Materieabstrahiert,von der Ausdehnungder Materie.Zeit von der Veraenderung
der Materie.
And page I32, most likelyfrom I9I4 in an extremelyfaint and shakyleft
hand.(He was seventy-sixyearsold andhis paralysiswould still not let him
write with his right hand):
Atome nicht occult?1
II
Concerningkinetic theory, it may be well to keep in mind that there is a
differencebetweenatomistswho objectedto one or more technicalaspects
of Boltzmann'swork(such as virtuallyall of the contributorsto the kinetic
discussion in the British Isles) but who in general favouredthe kinetic
theoryandanti-atomistswho opposedthe kinetictheoryinprinciple(suchas
Mach, Ostwald,andtheirfollowers).Also, it might be helpfulto remember
that especially on the Continent physicists with a strong knowledge of
mathematicswere still rare birds. (Even the extensive interest in kinetic
theoryin Englandand Ireland,which presumablyhad been stimulatedby
Maxwell,was led primarilyby mathematicianswith an interestin physics
ratherthan by professionalphysicists, though Lord Kelvin would be an
exception.)Most Continentalphysicists(suchas Mach)wereexperimentalists who did not feel competentto handlecomplexmathematics.They could
carefully follow neither the technical arguments of Boltzmann nor his
critics. To justify this weaknessit was naturalto appealboth to a form of
thermodynamicreductionismand to positivistargumentsthat the purpose
of science was merely to discover relationsbetween physical appearances
and to remindeach otherthat atomsand moleculeswere still unobservable
(thoughLoschmidtand Kelvinhadcalculatedthe approximatesize of some
moleculesin a mannerconsistentwith Avogadro'slawas earlyas the middle
I 860s and by the I 8gos new elementsto fill in the periodicchartwerebeing
discoveredalmostevery year).
Mach's Notizbucherare locatedin the Ernst-Mach-Institut,Eckerstrasse4, Freiburgim
Breisgau.There aresixty-fivein numberfromthe I860S until I9I4. They includedraftsof
papers,diagrams,comments,addresses,lists of namesto send preprintsand booksto, but
afterMach'spartialparalysisin I898 the remarksareshorterandincreasinglymoredifficult
to read.Machtypedhis correspondence
afterI 898 andhe continuedto sendandreceivemany
lettersafterI 9 I4 untilhis deathtwo yearslater.None of his Notizbucherandveryfew of the
letterswrittenby him have been published,but FriedrichStadlerhas prepareda book of
essayswhich includesthe entiretyof the last Notizbuchas an appendix.The book will be
publishedin Viennaand shouldappearin I986.
302 ffohnBlackwore
Therecanbe little questionthatmorephysicistsat leastin CentralEurope
werefamiliarwith Mach'santi-atomisticbookssuch as ErhaltungderArbeit
[I 896] than
[I 872], Die Mechanik[ I 883], and Principiender Warmelehre
with technicalobjectionsto Boltzmann'skinetictheorypublishedabroadin
English. As alreadymentioned,semi-philosophicalobjections,which still
interest many people including Sir Karl Popper [I974], such as those of
Loschrnidton reversibilityof motion[I 876] andZermeloin his extensionof
Nietzsche's 'eternal recurrence'speculation [I896] were widely known.
It was Boltzmann's answers which were not sufficiently circulated or
comprehended (and even today his notorious 'H-theorem' can seem
mindboggling).
Mach's anti-atomismand opposition to a mechanical'explanation'of
thermodynamics,however,precededboth the argumentsof Boltzmannand
those of his criticsandat leaston the Continenthelpedto disposephysicists
and manychemistsagainstBoltzmann'sworkbeforethey had even readit.
Machstoppedusing the atomictheoryin his workin I 863 andattackedit in
I 872. Boltzmannbeganpublishingin the late I 860S, repliedto Loschmidt's
objections in the middle I870S, became well-known for his ideas in the
and was strongly criticized on mathematical,physical, and philoI880S,
sophicalgroundsduringthe I 8gos.
WilhelmOstwald,a co-founderof physicalchemistryand long the most
influential man in the discipline with his efficient laboratoryand vast
numbers of students, freely admitted that Mach among the living and
Robert Mayer among the dead had influenced his thinking the most
Ostwald's anti-atomismbecame conspicuous in I892
(Ostwald, [I90I]).
when he published a chemistrytextbookwith no referenceto atoms. His
attemptto substituteenergy equationsfor everythingatomisticprovoked
Boltzmannand the mathematicianFelix Klein into a devestatingreply at
Lubeckduringa scientificconferencein I 895, but the influenceof Machand
Ostwaldwas so great by then that most physicists and many chemists in
Germany, Austria, and France still seemed to oppose Boltzmann.
Continuumphysicsappearedto be the waveof the future,eitherOstwald's
'energeticism',Mach's 'physical phenomenology',or Lorentz's 'electromagneticworld-view'. Atomism seemed dead apartfrom the continuing
discoveriesof RamsayandRayleighandJ. J. Thomson'sapparentdiscovery
of somethingwhich was soon calledan 'electron'.
As for the technicalobjectionsto Boltzmann'swork which were much
discussedin I 895 and I 896 in England,while they seemedto fit in with the
generaloppositionto dis-continuityphysicsat the time andthe anticipation
that the triumph of continuum physics was at hand, should not be
overvalued,particularlyby us who have the benefit of hindsight.As John
Nyhof has pointed out in his still unpublisheddoctoraldissertation[I98I]
technicalobjectionssuch as those aboutanomalousspecificheat ratioswere
scarcelyfatal, as seems ratherevident from the fact that both Planckand
Einsteinfrom I900 on acceptedand used Boltzmann'smajorideas, that is,
An HistoricalNote orlErnstMach 303
well before such technical objections had been met. Had Continental
physicists been aware of Lakatos's theory of 'degenerating research
programmes'they might have labeledBoltzmann'skinetictheorywith the
expression,but they would havebeen as wrongthen as Peter Clarkappears
to be in his [I976] paper. When the continuumeuphoriahad died down
(largelyas a result of Planck'squantumtheory and Einstein's theory on
Brownianmotion)and it becameclearthat atomswerehereto stay, the tide
understandablybegan to turn againstthe anti-atomismof both Mach and
Ostwalduntil Ostwaldhimselfrecantedin I908 and perhapsMachin I9I4.
To be sure, not all of Boltzmann'sworkhas been retainedand there are
still occasionalcritics,but in terms of the largerpicturehe has contributed
so much of value to modern physics, and by no means least to the
understandingof Planck and Einstein themselves that to complainabout
difficultiesin retainingthe entirecorpusof his labourwouldbe likerejecting
Kepler's discoveriesor importancebecause of his occasionalmysticism,
technicaloversights,or his 'fourthlaw'.
As for Mach'sspecificobjectionsto Boltsmann'sstatisticalinterpretation
of the secondlaw, theredon't seem to be any exceptoppositionto anything
whichseems to presupposethe realityof atomsand a distrustof what Mach
termed 'Lottospiel' or in English bingo. In point of fact, Mach was not
persuadedthatthe secondlawwasessentiallydifferentfromthe first.He did
repeatLoschmidt'sobjectionthat if all mechanicalmotion was reversible
andentropywas not, then if the secondlaw was valid somethingwas wrong
with traditional mechanics. But he never seems to have replied to
Boltzmann'sstatistical interpretationof the second law as an answer to
Loschmidt,at leastnot in a mathematicalmanner.Indeed,apartfroma few
isolateddisparagingremarkshe did his best to ignorethe entire kineticor
mechanicaldevelopmentafterthe discoveryof the firstlaw. In fact,whenhe
in I896 (largelyto counterBoltzmann'sLubeck
publishedhis Warmelehre
triumphoverOstwaldthe previousyear)his bookwas severelycriticisedfor
just this failing.J. E. Trevor,who liked Mach'sotherbooks,could not help
mentioningin his review [I897]:
Mach's treatmentof the early history of the ltheoryof heat, say of the period
precedingGibbs arousesonly admiration,but the remainderof the bookhas by far
neither the same completenessnor the same finish. Horstmannsspracticalapplication of thermodynamicmethod to chemical action is neglected, Massieu's
characteristicfunctions,Helmholtz'stheory of free energyand its application,V.
Oettingen'santitheticdevelopmentsand the magnificentworkof Gibbs are all but
little more than cited. This is indefensible,especiallysince the authorbrings his
treatmentso far down into the presentas to touch upon the recentdiscussionon
'energetics'.Then again,the assemblageof both new and reprintedphilosophical
sketchesat the close, instructiveas they are,is verydisconnected;the bookas a whole
is neithera collectionof scientificpapersnor a well-roundedcriticaltreatiseon its
subject, we get the impressionthat a splendid work, partiallyfinishedhas been
dumpedupon the marketin companywith the materialsfor its completion.
In short, Mach's opposition to both the reality of atoms and to
3o4 3fohnBlackmore
Boltzmann'skinetic theory of gases was philosophicaland was not even
accompaniedby a serious scientificargumentagainst either one. On the
other hand, Mach's reputationas an experimentalphysicist and philosophical forerunner of logical positivism seems safe. Anel while his
contributions to theoretical physics such as his definition of mass
and what Einsteinwould call 'Mach'sprinciple'may still be controversial,
there can be little doubt that whether Einstein correctlyunderstoodhis
ideasor not thathe did considerablyinfluencethe younggenius,particularly
concerning absolute space, time, and motion. Mach's central role in
understandingmodern physics and philosophy of science is not about
to disappear, regardless of how misguided he may have been about
the realityof atomsor Boltzmann'skinetictheoryof gases.
Let me close with a passage from the British biographerMorris W.
Travers ([I9SI], pp. 25I-2) who rememberedfrom personalexperience
how anti-atomisticphilosophycould affect Britishthinkingabout science,
in this case chemistry:
. . . when in I9OI he (Ostwald)publishedhis Vorlesungen
uberNaturphilosophie,
in
whichhis anti-atomistictheorywas developed,respectfulattentionwasgiven to his
views.Most of the membersof Ramsay'sstaffboughta copyof the book,andreadit;
andthe subjectwaskeenlydiscussedat an eveningmeetingheld at his house,and,of
course, generallyin the laboratory.It must be admittedthat the atmosphereat
UniversityCollegebecamemomentarilystronglypro-Ostwald.It is difficultto say
how deeplychemistsgenerallywereimpressedby Ostwald,but physicistswerenot
impressedat all. Onemust saythatthe tendencyamongphysicistsat the time wasin
the directionof consideringnot onlymatterbut energyas particulate;and,indeed,it
was difficultto attachany meaningto Ostwald'sidea that heat energy, electrical
energyetc., were definitelydifferentiatedwithout adoptingsome such hypothesis.
Ostwaldwas reallytryingto swimagainstthe stream;but whilechemistswerenot at
first stronglyinfluencedagainsthis views by developmentsin the field of physics
generally,Rutherford'sdiscoveries,andthe enunciationof the disintegrationtheory
in I902, which demandedthe acceptanceof the atomic theory, dealt Ostwalda
deadlyblow. Rutherford'sviews quicklygained acceptanceby the youngermen.
Whilethe disintegrationtheorywascompletelyrevolutionary,it appearedto be very
simple,and at the sametime to coordinatea numberof verystrikingphenomena.It
involvedno particularstructureof the atom;andit violatedno principle,exceptthat
the atomwasthe ultimateandindivisibleparticleof matter,whichwasjust an article
of faith.While some stalwartsrefusedto acceptRutherford'sviews, these werenot
amongOstwald'sadherents,ratherthe reverse.
The writerhadthe privilegeof being a guest at a privatedinnergivento Madame
Curieand Lord Kelvinby LordReay,Presidentof UniversityCollege,London,in
June I 903. Madame Curie did her best to convert her dinner partner to the
disintegrationtheory,withoutsuccess,as a letterwrittenby Lord Kelvinto Ramsay
a little latershows (August22nd, I903):'Weareall at our "witsend" in respectto the emissionof heatby radium,andare
forced into thinking, if not actually harbouring very wild conjectures. The
interventionof etherwavesinto thermodynamicswasnot fully thoughtout 50 or 60
yearsago. It certainlydoesnot comeunder"reversiblereactions"contemplated,and
expresslydefinedby Carnotin his law. Wavesof ethermay conceivablysupplythe
enrgyradiatedout of radium;but I cannotat presentsee how they do it, if theydo it,
or whencethey get the energythey conjecturallysupply.
An HistoricalNote on ErnstMach 305
'The hypothesis of evolution in the atom or transformationof its substance,
coupledwith the suppositionthat energyemittedby the radiumis takenout of the
storein the atom seems to me to be utterlyimpossible. . .'
JOHN
BLACKMORE
Kirchbergam Wechsel,
LowerAustria
REFERENCES
BLACKMORE,
J. T. [I972]: ErnstMach-His Life, Work& Influence.University of California
Press.
CLARK,P. [ I 976]: 'Atomism versus Thermodynamics', in MethodandAppraisalin thePhysical
Science,ed. C. Howson, pp. 4I-I05.
Cambridge University Press.
CLARK,P. [I982]:
'Matter, Motion & Irreversibility' (Review of S. G. Brush The Kind of
MotionWeCall Heat)British3rournalfor
thePhilosophyof Science,33, pp. I65-86.
'Zahar on Mach, Einstein and Modern Science', British3tournalfor
the
Philosophyof S;cience,
3I, pp. 273-82.
GARDNER,M. [I979]: 'Realism and Instrumentalism in Igth Century Atomism', Philosophyof
Science,46, pp. I-34.
FEYERABEND,
P. [I980]:
LAUDAN,L. [I976]:
'The Methodological Foundation of Mach's Anti-Atomism and Their
Historical Roots', in Motionand TimeSpaceandMatter,ed. P. K. Machamer and R. G.
Turnbull, pp. 390-4I7.
Ohio State Universtiy Press.
MACH, E. [I896]:
Die Principiender Warmelehre-historisch-kritisch
entwickelt.4. Auflage
I923.
Verlag von Johann Ambrosius Barth.
MACH, E. [I9I0]:
'Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und
ihre Aufnahme durch die Zwitgenossen' Physikalische
Zeitschrift,II, pp. 599-606.
MACH, E. [I9I9]:
Die Leitgedankenmeinernaturwissenschaftlichen
Erkenntnislehre
und iAre
Aufnahmedurchdie Zeitgenossen.
SinnlicheElementeundnaturwissenschaftliche
Begriffe.
Verlag von Johann Ambrosius Barth.
MEYER,S. [ I 950]: 'Die Vorgeschichte der Grundung und das erste Jahrzehnt des Institutes fur
Radiumforschung' Sitzangsberichte
der &)sterreichischen
Akademieder Wissenschaft,
I59,
PP- 5o.
NYHOF,J. [I98I]:
Instrumentalism
and Beyond,Doctoral Dissertation, University of Otago,
Dunedin, New Zealand.
OSTWALD,W. [I90I]:
Vorlesungen
uberNaturphilosophie.
2. Auflage, I902,
p. 4. Verlag von
Johann Ambrosius Barth.
POPPER,
K. R. [I 974]: 'Autobiography of Karl Popper', in ThePhilosophy
ofKarlPopper,ed. P.
A. Schilpp, pp. I56-67.
Later published as UnendedQuest[I976].
Fifth Impression
[I980].
Fontana/Collins.
TRAVERS,M. [I9SI]: Sir WilliamRamsay,pp. Z5I-2. London.
TREVOR,J. E. [I897]: 3tournal
of PhysicalChemistry,I, p. 43I.
SOME RECENT
BAYESIAN
OBJECTIONS
THEORY
TO THE
OF SUPPORT
Bayesianism today makes a serious claim to be regarded as the logic of
scientific inference (one of its very obvious strengths is that it adjudicates
both statistical and non-statistical inference in a uniform way, for example).
My thanks to Stephen Brush for his acute comments which have contributed significantly to
the revision of this historical note.