ANDREW D. WILSON”:

HERTZ, BOLTZMANN AND WITTGENSTEIN RECONSIDERED

I. Introduction

DLJKING THE past decade and a half, several scholars have tried to gain a

better understanding of Wittgenstein’s early thought by examining the

philosophical aspects of his scientific education. ’ Those taking this historical

approach have focused almost exclusively on the connection between

Wittgenstein’s picture theory of linguistic meaning and the epistemology of

mental pictures developed by the physicist Heinrich Hertz in the Introduction

to his Die Prinzipien der Mechanik, published in 1894. They have taken their

cue, quite naturally, from Wittgenstein. who refers twice to Hertz’s work in

the Tructutus Logico-Philosophicus. In addition to Hertz, but to a much

lesser extent, they have also discussed the role played by Ludwig Boltz-

mann’s philosophical writings in Wittgenstein’s intellectual development.

(Boltzmann, the great Viennese theoretical physicist, was the second natural

scientist Wittgenstein acknowledged as having a significant impact on his

philosophical outlook.) While analyzing and stressing the importance of

Hertz’s influence on Wittgenstein, however, they have misconstrued the

chronological and substantive relationship between Hertz’s philosophy and

the philosophical writings and ideas of Boltzmann. This, in turn, has

significantly affected the current understanding of the genesis and develop-

ment of Wittgenstein’s early thought. The purpose of this essay, therefore, is

to re-examine the historical and philosophical connection between Hertz and

Boltzmann as presented in the Wittgenstein literature, and to discuss an

Department of Historv, Cornell Univcrsitv. McGraw, Hall. Ithaca. NY 14X53-46Ol. U.S.A. Rec;ived 22 April 1YXx ‘Among those who have taken this approach are Allan Janik and Stephen Touhnin,

Wift,qensrein’s Viennu (New York: Touchstone Books. 1973): Peter Barker. “Hertz and Wittgenstein”. Studies in History and Philosophy ofScience I1 (It&W). 243-256; P. M. S. Hacker. Insight und Illusion (London: Oxford University Press. 1972); Brian F. McGuinness. “Wittgenstein’s ‘Intellectual Nursery-Training’“, Wirtgensrein Der Wiener Kreis und Der Kritische Rationali.~mus. Hal Berghel ef ~1. (ed.) (Vienna: Holder-Pichler-Tempsky, 1979). pp. 33-41; Friedrich Wallner. “Boltzmann, Hertz und Wittgenstein”, Ludwig Bol~zmann: Gesamtausgabe. 8. Band. Roman Sex1 and John Blackmore (eds) (Braunschweig: Fricdr. Vieweg, 1981). pp. 144-153: Robert Cavalier. Ludwig Wittgenstein’s Tractatus Logico-Philo- sophicus: A Transcendenral Cririyue of Ethics (Washington. D.C.: University Press of America, 1980). Earlier than these is James Griffin. Wirfgenstein’s Logical Atomism (Oxford: The Clarendon Press. 1964), esp. pp. Y%lO2. 109, and 149151.

Stud. Hist. Phil. Sci., Vol. 20. No. 2, pp. 245-263. 1989.

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245

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important consecfuencc a revised understanding 0U this connection has fat

understanding Wittgenstcin’s intellectual biography.

In works conccrnccl with the dcvclopmcnt of Wittgcnstein’s thought. it ha4

been standard to depict the philosophicxl relationship hctween flcrty.

Boftzmann. and Wittgenstein in the following manner. Hertz i\ ;tlu,ays

prescntcd ah the first and mot-c significant influence on the young Wittgen-

stein, with Wittgenstein adapting and tlcxeloping Hertz‘\ notion of mental

pictures. Boltzmann. in turn, is then f3rcsentcci 3% king important solel!,

because Wittgcnstein further encountered Hertz.4 ol-iginnl philosophical ideas

in his writings. Boltzmann’\ writings and thought arc therefore \kwcd as

being merely supplemental. not fundanicntal. to Wittgenstein’s intcllcctual

development. In this regard. too. scho1;11-s have helicved. or concluded. that

Boltmwnn was ;I philosophical devout follower of E-lcrtz. Thus. for example.

we rcxf in works hy P. M. S. I lxker. f’ctcr fJarker, and fiobert .f. C’avalier.

rcsfxxtivcly. that.

these are fundamental fiertzian themes which influenced the ywmg Wittgen-

stein and which. as we shall sec. continually reappear in his work. They were

reinforced by reading the works of L. Boltzmann, himself an admirer of Hertz. who

further emphasized the hypothetico-deductive structure of scientific explanation

and extcndcd klertz’s account of rcprescntation to all branches of phyics.

In both technical works and fxyxdar lccturcs he [ Boltzmannj defended and

elahoratecl the philosophy of science begun in flertz’x f’rir~ci/~lc\

From his [Wittgenstein’s] study of t lertl he had hoped to achieve the per\on;d

instruction of the IIertzian Ludwig Boltzmann.’

The belief that Boltzmann LV;IS :I philosophical f-fcrt/ian is. in fact. fairly

common and is not restricted to Wittgenstcin scholars. A. I. Miller. an

historian of modern physics. in an c\say OII Boltzmann‘\ mechanic\. has

written:

Like I IertL, Boltanann fmmulated ;I dcducti\ c account of mechanics that hogan

with mental picturch of point n~;~ssc>. Hrr~,i/~,q lctr~rc,t/ fko/~l Hertz tlrrrt /to /lt~or.\,

co~rltl bc cotttplctci~~ “ohjc7tiw“. the subjecti\ ity of Boltrmann’s mechanic\ is the

replacement of Hertz’s concealed nlasscs and constraints \bith the notion of point

I~;ISSC’S interacting through unspecified central forces: [empha\ix mine]

clear by taking a brief look at: ( I) Boltzmann’s criticisms of Hertz’s system of

mechanics; (2) Boltzmann’s familiarity with the epistemology of mental

pictures; and, finally, (3) what Hertz and Boltzmann understood the essence

of mental pictures to be. 1 shall begin with a few details associntcd with the

development of Hertz’s Principles.

Hertz began to study the fundamental principle of mechanics on 19 March

1X91, after becoming discouraged and worn out by unsuccessful experiments

on semipolar induction.J Hc had stopped his experimental work on 23

January, being both “powerless to work” and feeling just plain disgusted with

experimenting in general. He subsequently spent the month of February

searching for a starting point for fresh work.5 Hc found a new start while

reading the scientific papers of William Rowan Hamilton. the great Irish

mathematician and physical theorist. Inspired by his reading of Hamilton,

Hertz worked sporadically from March 1891, to the middle of January 1892

on mechanical problems. Beginning on 17 January 1X92, he committed his full

energy to writing a monograph on theoretical mechanics. This was his first

real entry into theoretical physics. By the second week in June, he had

reached a stage in his work where he “rewrote the paper on mechanics

completely”.” It was not until 10 October 1893. though. that his book was

completed. Until then, he continued to make corrections and additions to his

newly developed system of mechanics. But he still was not completely

satisfied with the finished product. Even after sending the manuscript to the

publisher, he remained unsure about his theoretical ideas and the manner in

which he presented them. In a letter to his parents dated 19 November 1x93,

hc wrote:

Naturally I want to XC the book brought out. but not at the cost of poor form.

Moreover. now that it is being set, I have much the feeling of “God protect the

house”. The book would easily reduce my by and large good repute to rack and

ruin. “if the casting fail”. Even ;I minor fault can flaw the whole. It frightens mc to

come out with something that I have never talked over with any human being. At

least I find comfort in knowing myself to be 21 member of several academies; where

else to obtain confidence in oneself?’

‘Heinrich Hertz. Mrmoirs-Letrc,~.s-L)icrrie~. arranged by Johnnna Hertz. translated by Lisa Brinner et al. (San Francisco: San Francisco Press. IY75). p. 313.

‘Ibrd. “Ibid.. p. 323. ‘“Mir ist natiirlich erwiinscht. das Buch heraus zu haben. aher doch nicht auf Kosten sciner

Form. Jetzt. wo es an den Druck geht, habc ich iibrigenb schr das Gefiihl: ‘Gott bewahr das Haus’. Das Buch ist sehr geeignet. meincn im ganzen guten Ruf griindlich zu vcrderbcn und zu verbrcnnen, ‘wcnn der Cuss misslang’. Ein kleiner Fehler kann schon das Ganze missklingend machen. Und es ist doch ein etwas bingliches Gefiihl. mit ciner Sache herauszutretcn, die man niemals mit keinem Menschen besprochen oder heraten hat. Da empfinde ich es doch ganz angenehm, Mitglied einiger Akademien zu sein. woher sollte man sonst das Vertraucn zu sich selber nehmen?” Ibid.. pp. 312 and 343.

Whether it was because of his lack of confidence. or not. tlertz v,illfully did

not discuss the contents of the I’rirtciplcs with anyone hcforc it w;14 published:

he had no such choice after it app~~a~-cd in print. On New Yeal-‘s Day. 1894.

he succumbed to scpticeniia. the result of a malignant tumor that had hcen

plaguing him for almost three years. Hc was 37 years old. liis Principles of

A4erAmic.s Prestwteti irt tlew Form appeared posthumously that spring.

Hertz‘s concern over his rcprcscntation of mechanics was not unfounded; it

was indeed far from being orthodox. In fact. it appeared to hc undermining

the foundations of traditional classical mechanics by eliminating the central

concept of force. lHert/ replaced force in hi4 system with Hermann van

Helmholtz‘s notion of hidden m;1ssc4 in motion. But. as Martin Klein has

observed.

There w;t’r one real trouble with Hertz’s systenl. tie gave no es;~mplc~ to show hou

one could account for particular mechanical plleno~net~~~ hy tllc;~~ls of ;I particulx

arrangement of hidden iiiasses in motion. Wow than that - it ~1 as apparently not

possible to construct such txplanations for cvcii wry simple mechanical problcni\.

Boltzniann. whose mechanical ingenuity had already been amply demonstrated.

was utiahle to find ;I incchanism. of the general type allowed in t lertzian

mechanics. which wo~~lcl give ;I kinematic reduction for wch ;I simple and basic

problem as the elastic collision of two xphcres. f lc c~uestiotwd, therefore. whether

the theory would hc of much value t’ol- physics. “in spite ot’ aII itx philosophical

beauty and cotllpletetless”. and tie did not follow t Iertz’s appt-oath iii his own

lectul-es on lllechalllcs.”

In fact, five years after the release of the I~rittc~iplr~s. Boltzmann rcmnrkcd in

an address at the Naturforschcrvers~lmmlung in Munich that it LV;IS indeed

unfortunate that at the same moment Hertz had constructed “a strikingly

simple system of mechanics. his lips became forever scaled to the

thousand requests for clarification that are certainly not on the tip of my

[Boltzmann’s] tongue alone.“” Boltzmann’s &sire to have Hertz‘s ideas

clarified was deeply rooted in his staunch defense of traditional classical

mechanics and atomiam (the -‘older mechanics”. as hc called it). Since around

ltzX6, he had considcrcd it his intellectual duty and mission to defend the

foundations of traditional mechanics against the threat of Ernst Mach’s

Hertz. Boltzrnmt~ and Wittgrnstcit~ 249

positivistic psycho-phenomenalism, Wilhelm Ostwald and Georg Helm’s

energeticism, and. to a lesser extent. Gustav Kirchhoff’s mathematical

phenomenalism. all of which rejected explanations of natural phenomena

that relied on theories grounded in visualizable physical hypotheses and

models of reality. Such theories were believed to be too metaphysical and

misleading since. according to Mach ef al., physics could really only provide

us with descriptions of nature. not explanations of its inner workings. In

Hertz’s system, force was eliminated because it was thought to be one of these

metaphysical concepts. Upon reading Hertz’s book. Boltzmann realized that.

in addition to eliminating the concept of force, Hertz had incorporated many

of Kirchhoff’s mathematico-physical ideas and methods, especially in

developing the physics of monocyclical systems. Following this realization, he

could not accept Hertz’s understanding of the nature and value of physical

theories.

As far as Hertz’s system as a whole was concerned, Boltzmann commented:

Hertz’s mechanics is more a programme for the distant future. Should people one day succeed in explaining without artificiality all natural phenomena by means of

hidden motions. then the old mechanics would be superseded by the Hertzian.

Until then, the former alone can represent all phenomena in a really clear manner

without adding things that are not only hidden but of which we have not the

slightest idea of how we are to conceive of them.“’

Two years before this, in 1897. Boltzmann published the first part of his

Lectures otz the Principles of Mechlics. partly in response to Hertz, and

partly as an extension to his Lectures m Gas Theory. In the book on

mechanics, Boltzmann “merely tried. by means of as consistent an account as

possible, to secure mechanics against any objections and in particular against

the reservations that Hertz makes with regard to the older mechanics in the

Preface to his book”. ” Boltzmann’s method in his treatise differed markedly,

indeed. fundamentally from Hertz’s, and his tone was such as to have the

“‘Ibid. “Die Hertzsche Mechanik scheint mir daher mehr ein Programm fur eine ferne Zukunft zu sein. Wenn es einst gelingen sollte. alle Naturvogange durch solchc verborgene Bewegungen im Hertzschen Sinne in ungektinsteltcr Weisc zu erklaren. dann wiirde die alte Mechanik durch die Hertzsche tiherwunden sein. Bis dahin ist die erstere die einzige, welche alle Erscheinungen wirklich in klarer Weise darzustellen vermag, ohne Dinge beizuziehen. die nicht nur verborgen sind. sondern von denen man such gar keinc Ahnung hat, wie man sie denken soll.” (Populuerr Schriften. p. 215).

“Ludwig Boltzmann, Vorlcsungen ueher die Principe der Mechanik, 1. Theil (Leipzig: J. A. Barth, 1897). Boltzmann made this remark concerning his book on mechanics in his, “On the Fundamental Principles and Equations of Mechanics”, delivered at Clark University in 1899. and published in his Populaere Schrifien. The address is reprinted in McGuinness. op. cit., note 9. p. 113. “Ich bemiihte mich nur. diese durch eine moglichst konsequente Darstellung gegen etwaige Einwtirfe. bcsonders gegen die Bedenken zu sichern. welche Hertz in der Vorrede seines Buches gegen die Bltere Mechanik erhcbt.” (Populaere Schrifrm. p. 270).

work called by one reviewer “a polemic against Hertz”.” Boltzmann’5 deep

misgivings about the physical and methodological lx~ses of Hertz’s mechanics

should preclude considering him ;I Hertzian in physics. as C’avalicr would

maintain: and. contrary to Hacker‘s claim, thi$ indicates that Boltzmann in no

way “extended Hertz‘s account of rcprescntation to all branches of physics.”

II

Contrary. as well, to the statements by Cavalier and Barker. Boltzmann

did not defend and elaborate the philosophy of science begun in Hertz’s

f’ritrciplrs. Nor, contra Miller, did he learn “from Hertz that no theory could

be completely ‘objective”‘. since he already bclievcd this to be the cast. To

begin with, Hertz’s philosophy was not completely original to the I’rittc~if~lcs.

and Boltzmann knew it. He hinted at this in his Lrctrrws oti (hc l’r-it7ciplc.s o,/‘

Mcchunics, where. along side his rcscrvations concerning Hertz‘s mechanics.

he stated:

Nobody surely ever doubted what I lertz emphakxx in his hook. namely that our

thoughts arc mere pictures of objects (or better. Ggns of them). which at most hacc

some sort of affinity with them but never coincide with them but are related to them

as letters to spoken wunds or written note5 to musical souncl5.”

Elsewhere. Boltzmann expressed similar thoughts by asserting.

Iiertz makes physicists properly aware of something philosophers had no dout>t

long since stated. namely that no theory can he ohjcctive. actually coinciding with

nature. hut rather each theory is only a mental picture of phenomena. rrlatcd to

them 3s sign is to designatum.”

In the first passage Boltzmann begins by pointing out that “nobody surely ever

doubted what Hertz emphasizes in his book”. indicating that the general

““Es wurdc wohl nicmalh hezwcilelt und wird van 1 lertr In dcm angcluhrtcn Buchc hcsondcr\ hcrvorpehohen. dass un\crc Gcdankcn hlossc Bildcr cler Ohjecte (hesscr Zcichcn l’ur dvxvlhcn) \ind. wclchc mit dicscn htichstcns cinc gcwissc Vcrwandt\chaft hahcn. \ich aher mit ihncn nicmals deckcn kiinncn. aondern sich 111 ihncn verhaltcn. wit die Buchdahen LU den Lautcn trdcr dlc Notcn zu den l‘Onen.” Boltzmann. Vor/c~rr~~,q:cvr rrdw die f’rirrcipc~ t/c~r Md~trrriX. I. Thcil. zwcitcr unvcrandcrtcr Ahdruck (Lcip/ig: Vcl-la 5 Johar,n AmhroGus Barth. 1010). l-2. ‘lhls passage is rcprintcd in McGumncss. o,‘. CII.. note V. p. 275.

“Lop. cit.. note 9. p. 00. “Hertz [hringt] den Physikern so recht klar 7um Bewusstsem, was wohl die Philosophen schon Itingst ausgcsprochen hatten. dass keinc Thcoric ctwas Objwtivcs. mit der Natur wirklich sich Deckcndcs sin kann. class vielmchr jcde nur ein geistiges Bild der Erschcinungen ist. dns sich zu diesen verhiilt. wit dns Zeichen zum Bezeichnetcn.” (Poptdnr~ Sdl~~fi<W. pp. 115-2 lb).

Hrrrz, Boltznmm and Wittgrttsteitr 251

epistemology of mental pictures was not unique to Hertz, but had been widely

accepted for some time. That Boltzmann did not consider Hertz’s epistemo-

logical beliefs concerning mental pictures to be new is further supported in

the second passage when he remarks that philosophers had long since stated

that theories are no more than mental pictures of phenomena. Moreover.

Boltzmann knew that, in addition to following Kirchhoff’s methodology of

mathematical phenomenalism, Hertz drew on James Clerk Maxwell’s

epistemological ideas concerning the construction of mental pictures. He

made this perfectly clear by stating in an essay from 1899:

In his book of mechanics Hertz has given a certain completion not only to Kirchhoff’s mathematico-physical ideas but also to Maxwell’s epistemological ones. Maxwell had called Weber’s hypothesis a real physical theory, by which he meant that its author claimed objective truth for it, whereas his own account he called mere pictures of phenomena. ”

Maxwell. in fact, who was in many ways the guiding star for both Hertz’s and

Boltzmann’s scientific research, had at various times expressed an episte-

mology emphasizing the construction of mental pictures of phenomena. He

had done this, in practice, as early as 1867 in his first paper on Faraday’s lines

of force. And. in an address on the relationship between mathematical and

physical thought delivered to the British Association in 1870. he remarked,

“the human mind, in order to conceive of difficult kinds of quantities. must

have them presented to it by Nature”. According to Maxwell. this entailed

forming ;1 “mental image of the concrete reality” existing behind the

mathematical abstractions.‘” It should be remembered too, that Maxwell

concluded his great Treatise m Electricity and Mugnestisnz (1873) with the

following:

Hence all these theories lead to the conception of a medium in which the propagation takes place, and if we admit this medium as an hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavor to construct a mental representation of all the details of its action. and this has been my constant aim in this treatise.”

“Ibid. “Hertz hat in seinem Buche iiber Mcchanik. ebcnso wie die mathcmatisch - physikalischen ldeen Kirchhoffs. such die erkenntnistheoretischen Maxwells zu einer gewissen Vollendung gchracht. Maxwell hatte die Hypotheae Webers eine rcale physikalishc Theoric gcnannt. womit c‘r sagen wollte. das ihr Autor ohjcctive Wahrhcit daflir in Anspruch nahm. seine eigencn Ausfiihrungcn dagcgen bezcichncte cr als hlosse Bilder der Ervzheinungen.‘. (fo/~&rrr Schrifir77. p. 21.5).

“‘James Clerk Muwell. “Address to the Mathematical and Physical Sections of the British Association”. The .S&nt(/i’c~ 1’qx~r.s of Jntws Clrrk Ma.rwd. 2 vols. W. D. Nivcn (cd.) (Cambridge: Cambridge University Press, 1890). vol. 2. pp. 21~220.

“James Clerk Maxwell. A Trrcdtr OH Ekrricir_v rrttd Mqtwtkttt. 2 vols (Oxford: The Clarcndon Press. 1X73). vol. 2, p. 438.

Thus, according to Maxwell. the method he had followed in developing

Faraday’s field theory of electromagnetic action was founded on constructing

a mental representation of the action of an hypothetical entity. namely the

ether. For Maxwell, this mental representation was at first ;I visualizable.

physical model from which he was able to work out the necessary

mathematical equations. Only gradually did hc abandon the physical model.

in all its mech:mical intricacy, leaving nothing more than the bare field

equations.

Furthermore. none of this talk about mental pictures and representations

by either Hertz or Maxwell would have been new to Boltzmann. He had

encountered such epistemological notions from the very beginning of his

formal philosophical education at the Akaclemisches Gymnasium in Linz.

Upper Austria. during the IXSOs and lX6Os. Is There he studied philosophy

from Robert Zimmermann’s textbook. l’ltilo.soplti.sc~Itc f’rOi)ftC~irtltik. In the

second edition (1X60) of this book, the edition Boltzmann used, Zimmer-

mann divided the course into three sections. The first outlined the basics 01

formal logic, following the system developed by Zimmcrmann’s teacher.

Bernhard Bolzano, in his Wi.sscrt.sc.hr~fi.slt/tr~~. The second trentcd empirical

psychology. following the example of Johannes Hcrbart’s philosophy and

psychology. The third section. entitled “Zur Einleitung in die Philosophic”,

introduced students to general issues in epistemology and metaphysics. In this

section of the I’ropclctlctrtili, Zimmcrmann makes several explicit stntemcnts

concerning the construction of mental pictures as the means by which we

obtain knowledge of the external world. To take ,just one cxamplc. he stated

the following:

Hertz, Boltzrnum and Wittgensteirl 253

Zimmermann qualified this view, however, by asserting that ultimately our

impressions remain nothing but impressions, namely that our ideas are at best

only subjective pictures of the world: “I see the quality of blueness, but not

blue itself, feel the quality of hardness. but not hard itself. 1 indeed cannot go

beyond my own sensations. . [We] indeed can never go out of the circle of

our sensations, but the diversity and certainty of our sensations become

apparent to us as an intelligible picture of the diversity and certainty of

external qualities, whose actual nature. or essence remains withheld from

us. “‘(’ Boltzmann not only studied from Zimmermann’s textbook, but with

Zimmermann himself at the University of Vienna. He took nine philosophy

courses from Zimmermann, several of them seminars. while a university

student. There is thus no doubt that he was very familiar with Zimmermann’s

thought.

Finally. in this regard. Boltzmann expressed his own epistemological ideas.

which were based on the construction of mental pictures, four years before

Hertz’s book was printed, and two years before Hertz had even committed his

ideas to paper. From the fact that Hertz’s work was something he had never

discussed with any human being, and that the explicit picture aspect of his

epistemology does not appear in any of his published papers before the

Principles, Boltzmann could not have been privy to Hertz’s ideas prior to

1894. Thus, it is impossible for him to be echoing Hertz in IX90 when, in front

of the faculty of the University of Graz, he declared, “I am of the opinion that

the task of theory consists in constructing a picture of the external world that

exists purely internally and must be our guiding star in all thought and

experiment”.” Indeed, this sounds much more like Maxwell at the end of his

treatise on electricity and magnetism than Hertz in his book on mechanics. In

any case, there is no doubt that Boltzmann was exposed to and aware of

epistemological picture theories before reading Hertz, and had his own

understanding of this epistemology before encountering Hertz’s book.

III

Not only did Boltzmann apparently espouse a scientific epistemology based

on the construction of mental pictures before he read Hertz, he disagreed

with Hertz as regards the essence of mental pictures qua scientific theories.

“‘“So kommen wir zwar nie aus dcm Krcise unserer Empfindungen hinaus. abcr die Mannigfaltigkeit und Bestimmtheit dieser letztern gewahrt uns ein unds versttindliches Bild van der Mannigfaltigkeit und Bestimmtheit iiusserer QualiCiten. deren eigentliches Wesen unds entzogen blcibt.” Ibid., p, 373. My translation.

“Ludwig Boltzmann. “On the Significance of Theories’. (1891)). reprinted in McGuinnesa, 0~. ci/. . note 9. p. 33. “Ich bin der Mcinung. dass die Aufgabe der Theorie in der Konstruktion eines rein in uns cxistierenden Abbildes der Aussenwelt besteht, das uns in allen unsercn Gedanken und Experimenten als Lcitstern zu dicnen hat. .” (Pop&err Schrifrm. p. 77).

Their respective understanding and evaluation of the method Maxwell used in

developing electromagnetic field thcsry provide us with an excellent example

of their disagreement.

In the introduction to the volume of his collected papers on electric waves.

Hertz provided an overview of the experimental and theoretical development

of Faraday and Maxwell’s field theory of electricity and magnetism. In the

theoretical section, he set out to arrive at ;I precise definition of what “we call

the Faraday-Maxwell theory”. He was not satisfied to say that “Maxwell’s

theory is the one which is propounded in [the treatise on electricity and

magnetism]“. for the reason that.

Many ;L ma11 has thrown himself with zeal into the study of Maxwell’\ work. and.

even when hc has not stumbled upon unwonted mathematical difficulties. ha

nevertheless been compelled to ;~ha~ldon the hope of forming for himself ai

altogether consistent conception of Maxwell’s i&as. I have t’~~i no better myself.

Notwithstanding the greatr\t admiration for Maxwell’s mathematical concelJtions,

I have not always felt quite certain of having graspcd the physical significance of his

statelllellt\.~~

In&cd. it was Maxwell’s physical models that acted LIS stumbling blocks for

Hertz. and. according to him. for others as well. The inability to follow

Maxwell’s physical reasoning prompted some theorists to recast Maxwell’s

work into more intclligiblc physical forms, while retaining the mathematical

structure of his theory. For Hertz, especially. “this common significance of

the different modes of rcprescntation appears to bc the underlying

part of Maxwell’s work. This. and not Maxwell’s peculiar conceptions or

methods. would 1 designate as “Maxwell’s theory”. To the question, “What

is Maxwell’s theory?” I know of no shorter or more definite answer than the

following: - Maxwell’s theory is Maxwell‘s system of equations”.” Thus. for

tHertz. only the mathematical, logical form of ;I theoretical representation was

important, not the physical vision of nature it portrayd. Indeed. the

equations wcrc the heart and swl. the c’ss~ncc. of ;I reprcscntation. A

scientific mental picture. I/UU theory, to HeI-tL was a logical (m~lthem~ttic~ll)

structure that could bc compared with reality hy cxperimcntation. In short. :I

physical theory is really no more than mathematical equations (Kirchhoff’s

mathematical phenomenalism). They are the essence of theory.

Boltzmann. on the other hand. had an opposite view from Hertz. To him. ;I

mental picture, or theory. was not really considercd to be a formal, logical

structure or representation. For Boltzmann. a physical picture was quite

literally ;I visunlizablc image of reality. something hc could picture in his mind

Hertz, Boltzmann and Wittgenstein 255

that had both physical content and form. Boltzmann had to be able to see

physical reality in his mind’s eye. This is one reason why he rejected Hertz’s

use of hidden masses in motion as one of the principles of mechanics. As he

pointed out in one of the passages above, “we have not the slightest idea of

how we are to conceive of them.” This is also one reason why he had so much

faith in atomistic explanations for thermodynamic phenomena. Atoms, or

discrete quantities in general (that are not hidden), can easily be conceived

of, even when one does not attribute any real physical qualities to them.

This, too, is why he frequently referred to Christopher Columbus and

Michael Faraday as true theoreticians. They were guided in their discoveries

by pictures, or visions, of what the physical world is like. And, finally, this is

what attracted him to Maxwell. It was Maxwell’s keen ability to visualize the

workings of nature, his ability to construct physical pictures of nature that

Boltzmann admired. Thus, according to Boltzmann, “Maxwell’s formulae

were merely consequences of his mechanical models, so that Hertz’s

enthusiastic praise is due in the first place not to Maxwell’s analysis, but to his

ingenuity in discovering mechanical analogies.““’ For Boltzmann, physic-

ally visualizable (anschaulich) representations come first, followed by math-

ematical formalism. This is the exact opposite of Hertz’s understanding.

Due to Boltzmann’s rejection of Hertz’s system of mechanics, his

familiarity with and early expression of epistemological ideas based on the

construction of mental pictures, and his different understanding of the nature

of mental pictures, I think it is fair to say, contrary to the currently accepted

view, that Boltzmann was in no way a Hertzian.

IV

At this point, I would like to turn to a second issue concerning the

intellectual connection between Hertz, Boltzmann, and Wittgenstein,

namely, the probable order in which Wittgenstein encountered Hertz’s and

Boltzmann’s works. It is usually assumed by Wittgenstein scholars that

Wittgenstein encountered Boltzmann’s writings after Hertz’s, and this served

to supplement what he had previously learned from Hertz. We have seen this

expressed in the passages from Hacker and Cavalier at the beginning of the

essay. They, however, are not the only ones who believe Wittgenstein

received his first philosophical exposure to mechanics and theoretical physics

in general from Hertz’s Principles. Janik and Toulmin, in their Wittgerzstein’s

Vienrza assert that,

“Ludwig Boltzmann, “On the Methods of Theoretical Physics” (1892) in McGuinness. op. cir.. note 9. p. 10. ** dass Maxwells Formeln lcdiglich Konsequeozen seiner mechanischen Modelle waren und Hertz’ begeistertes Lob in erster Linie nicht dcr Analyse Maxwell. sondern dessen Scharfsinn in der Auffindung mechanischer Analogicn gebtihrt.” (Populncre Schrifien.

P.8).

Hcinrich Hertz’s book T/if f’rittc,iplcs of‘ M~~~~/tctttic:s will have come into Wittgcn-

stein’s hands in the ordinary course of h’is education. And it will have done so, not just as one textbook among others, hut a:, the authoritative and magisterial analysis

of fundamental ideas about the physical world.2”

Cavalier, in this regard, follows Janik and Toulmin closely by stating:

The study of engineering as ;I formation profexGonale would have included. by the

standards of his day. ;I thorough intellectual grasp of theoretical physics. This, in

turn. would have brought Wittgenstein into contact with the Kantian Heinrich

Hertz whose Pritrcipks of A4cdtctttic.s (IS%) 1. ] w were [Gc] ;I matter of course.“’

Janik and Toulmin add further, “in this respect. Ludwig Wittgenstein had the

same formutiot~ profrssiotuile as a Swiss ‘engineer’ only a few years older

than he. Albert Einstein”.” Finally, Janik and Toulmin. and Cavalier seem to

assume that Wittgenstein absorbed Hertz’s Pritlciplcs while he attended the

Obcrrealschule in Linz. For they assert, respectively, “If the late lamented

Heinrich Hertz gave Wittgcnstein his first magisterial example of physics,

Boltzmann was the man he hoped to learn from directly.” And. “From his

study of Hertz, he had hoped to achieve the personal instruction of the

Hertzian Ludwig Boltzmann.“‘”

From what I have already presented concerning Hertz’s system ot

mechanics, it should be clear that most of what Janik and Toulmin. and

Cavalier say is untenable. Moreover, that Wittgcnstein would have en-

countered Hertz’s book "as ;I matter of course” before entering the

Technische Hochschulc in Berlin-Charlottcnburg. is not at all certain. One

should not expect :I secondary school. even in Austria or Germany, to have

utilized ;I wlork that was at once unorthodox. and. ;IS HcrtL himself wrote.

“not well suit4 for use as ;I first introduction”, but intended for students

“who have already ;I fair mastery of mechanics as usually taught”.“’ The

theoretical treatment of monocyclical systems. as well, which figured

prominently in Hertz’s book. had fallen into rclativc obscurity after the turn

of the century. Therefore, the odds of finding a physicist who would teach

such an unorthodox. difficult. advanced. and problematic text to secondary

Hertz, Boltztmnn rrncl Wittgensteirz 257

schoolers are certainly very low, to say the least. Also, Albert Einstein. the

so-called Swiss “engineer”, actually took his degree in mathematics and

physics, not engineering, at the Zurich Polytechnic; and even there, Einstein

only came across Hertz’s Principles in the course of his studies from his own

initiative. It was not the standard authoritative text, or part of the ordinary

course of his formal education. And finally. Boltzmann once remarked that

he had often “heard Hertz’s mechanics praised yet never seen anybody

pursue the path he indicated”. Most physicists found Hertz’s theory “only of

purely academic interest”?’ Thus, if Wittgenstein used Hertz’s Principles as a

formal textbook at all. it is only reasonable that this would have been when he

was in Berlin. and not before.

Wittgenstein, however, had read Boltzmann before leaving Vienna for

Berlin; he bought and read Boltzmann’s Pophere Schriftm soon after it was

published in IYOS? Wittgenstein originally intended, as well, to study under

Boltzmann at the University of Vienna. beginning in the fall of 1906 - only

to have his plans brought to an end by Boltzmann’s suicide that September. 1

therefore suggest that Wittgenstein actually read Boltzmann’s philosophical

writings first. which are filled with references and analyses of Hertz’s thought,

and then read and digested Hertz’s book. And there, like Boltzmann before

him. he found a clear and complete exposition of a picture theory of scientific

explanation that stressed the logical, formal structure of scientific pictures of

reality. That Wittgenstein encountered Boltzmann’s works before Hertz’s

may also be supported by a statement written by Wittgenstein himself in 1931.

At that time. Wittgenstein described his philosophy as unoriginal and derived

from other people’s works. In a fashion uncommon to him. he then listed the

names of the men whose ideas figured directly and significantly in his

philosophical outlook. Here is what he wrote:

I believe it is in truth if I think in my thought I actually have only been

reproductive. I think I have never invented a line of thinking. Rather, I have always

taken it from someone else. I have only picked it up with passion for my work of

“‘Op cil., note Y, pp. 8X. YO. I’. so hahc ich Hertzs Mechanik zwar schr oft preiscn gchort. aher noch niemanden sah ich auf dem wn Hertz gewiesenen Wege weitcr wandeln.” (Poprdtrcw Schriften. p. 213). .I_ das Problem im Sinne der Hertzschen Theorie ist der Wert der letzteren doch nur rein akademischer.” (Pophere Schriftrr1. p. 2 13).

“Michael Neho an Michelr Ranchetti (eds), L~ctlwaiq Wit/pw.stc+r~: Seirz L&n i/r Bildrnr ~frrtl Textrn (Frankfurt am Main: Suhrkamp. IYS3). p. 61. See also John Blackmore. “Introduction”. op. cit.. note 1. p. 5.

clarification. This is how Boltzmann. Hertz. Schopenhaurr. Fregc. tiussell. Krauh.

Weininger, Spenglcr. and Sraffa have influcnccd nit.”

Brian McGuinness has pointed out that Wittgcnstein presumably listed these

names “in the order in which their influence was exercised.“‘-’ Now.

following McGuinness. this can mean one or both of two things. Either

Wittgenstcin put Boltzmann at the head of the list hecause hc was

chronologically the first important influcncc on his thought. or hccausc

Boltzmann simply had the greatest influence on his thought. or both. I wo~dd

not go so far to say that Boltzmann had the grcatcst impact on Wittgenstein.

at least not at the present time. I tlicreforc interpret Wittgenstcin’s list and

McGuinncss’s commentary to mean that Boltzmann’s writings got the

philosophical hall rolling for the young Wittgenstein. This passage by

Wittgenstcin may also indicate that Wittgenstein did not consider Bolts-

mann to he ;I Hcrtzian, and that Boltzmann’~ philosophic~~l ideas were not

merely supplemental to Hertz’s, By listing both Boltzmann‘s and Hertz’s

names, Wittgenstein may have heen indicating that both men wcrc’ signifi-

cant, but for different reasons. After all. Wittgcnstein was not one to waste

words or credit. This brings us to what may be the most important

consequences of all this: Boltzmann’s real influence on Wittgcnstein.

In the Ttucfrrf~r.s. Wittgcnstcin seems to have developed Hertz‘s notion of

mental pictures, i.c. his emphasis on logical (mathematical) form, and the

logical structure of scientific theories. I think there can be no doubt ahout

this. But now. it’ Boltzmann was not ;I scientific or philosophical follower of

Hertz, and it’ Boltzmann’s understanding of the nature of mental pictures was

diametrically opposite from Hert;l’s. and therefore not redly developed by

Wittgenstein. what was Boltzmann’s importance in Wittgcnstein’s intellectual

development? I suggest that Holtzmann was at least as cc~ually important as

Hertz to Wittgenstein, not hccause of his picture theory, but lxxause of the

Hertz. Boltzrmtln md Wittgetntein 2.59

rudimentary philosophy of language presented in several essays in his

Populuere Schriften.

From the time he was a Gymnasium student, to the end of his life,

Boltzmann was sensitive to the value and use of language. Even as a teenager

he dreamed of “a philosophy that clearly defined each concept at the time of

introducing it”? As an adult. though, he realized that “we cannot define

everything but merely need to use known signs to indicate rules for

simplifying our ways of denoting and adapting them to experience”?’ In

other words, according to Boltzmann, “we must adopt the objective point of

view”?” What mattered to Boltzmann most was that ‘*the sense of words be

ever more appropriately fixed, which in the case of the simplest concepts

cannot occur through definition but only by reference to familar experi-

ence”.37 Thus, in statements about physical reality, “contradictions . . can

lie only in ways of denoting and are thus a sign that these have been chosen

inappropriately. Experience cannot contradict itself, for even if its laws were

to change completely, ways of denoting would have to adapt to the new

I~ws”.~” Consequently, Boltzmann believed that “often a problem is half

solved as soon as the right way of asking the question has been found”?’

Boltzmann provided the most complete outline of his philosophy of

language in 1904, two years before his death. at the International Congress of

Arts and Sciences in St. Louis, Missouri. There he made the following

remarks, which I will quote at length because of their importance. He

maintained that. in judging the utility of physical hypotheses and the value of

scientific theories.

“Ludwig Boltzmann, “On the Question of the Objective Existence of Processes in Inanimate Nature” (1807). in McGuinness. q~. ci/.. note 9. p. 57. “Es war noch zur Zeit meiner Gymnasialstudien. als mich mein nun lange verstorbener Bruder oft vergeblich von der Widersinnigkeit meines Ideals einer Philosophie zu uherzcugen suchte. welche jedcn Bcgriff hei seiner Einfiihrung klar definiert”. (Populuerr Sc/~i@~z. p. 162).

251hid. “Mann kann kaum drastischer zeigen. welche Mcnge von Erfahrungen. sowic von Worten und Gedanken. womit sie bezeichnet werden. als bekannt vorausgesetzt wcrden miissen. wenn wir uns uberhaupt verstehen sollen. und dass wir nicht alles definieren k6nnen. sanders bless mittels ebenfalls hekannter Zcichen Kegeln anzugeben hahcn. wit unsere Bezeichnungen vcreinfacht und den bekannten Erfahrungen angepasst werden k&men”. (Pop&eve Schr~frrw, p. 162).

‘“Ibid., p. 64. “Wir miissen uns. wit man sagt. auf den objcctlven Standpunkt stcllcn”. ( Populorre Schr~jier2, p. 173)

“Ibid.. p. 67. “Man muss den Sinn der WOrtcr immcr zweckmitsaiger fixieren. was hei den cinfachsten Begriffen nicht durch Definition. aondern hlosa durch den Hinwcis auf bekannte Erfahrungcn geschehen kann”. (foprtlrrc,rcj .Sc/~ri/io~. p. 176).

‘Xlhid., p. 75, note 1. “Widerspruche kiinnen nur in den Bezeichnungen liegen. sind also ein Fingerzeig. dass diese unzweckmassig gewahlt sind. Die Erfahrung kann sich nicht widersprechen; denn selbst wen ihre Gesetze ganz wechseln wurdcn, hattc sich die Bezeichnung den veranderten Gesetzen anzupassen”. (Populurre Schrifrm, pp. 162-163 note 2).

“‘Ludwig Boltzmann, “On the Fundamental Principles and Equations of Mechantcs” (IXYY). in McGuinness. q~. cit.. note 9. p. 10-I. “Oft ist ein Problem schon halh gel&t. wenn die richtigc Mcthode der Frageatcllung gel’unden ist”. (Popdacw .Schr[fie/r. p. 257).

Hc went on to sav.

My present theory is totally differcnt from the c.iw that ccrt;iin questions fall

outside the lwundarics of human cognition. For according to that theory this ih ;I

defect or impert’cction of I~;III’\ cognitive capacity, whereas I regard the existence

of these qucstiom and protdems them5clves as an illusion. On 5uperficiat ~reftection

it may of courw he surprising that after Ireco~nition of the itluxion the dri\,e tmvarct5

answering these questions does not ct’xsc’. I‘hc mcntat habit is much too powcrfut

to toos~n its hold on us.

Only wry slowly and qxlu;dly wilt all these iltu\ion\ recdc and I regard it ;I\ ;I

ccntrat task of phitosophg to give ;I clear account of the in~ll’l”‘(~l”i;lt~ll~~~ of this

overshooting the mark on the part of our thinking habit\: and further, in choosing

and linking concepts and woi-ds. to aim onlv iit the most appropri;itc expi-cssion ot

the given. irrcspectivc of our inherited hahits. If thcrcfore philosophy ~CI-c to

succwd in creating ;i swtcm such that in all cases mentioned it stood out clcart\

when ;I r~ucstion is not judfiect so that the ciri\c towrd askin, (r it \~otittl gradualI\

die abvay. wc ~tloutd at one stroke have resolved the most ohscut-e riddles and

ptiitowph~ \voiitd bccomc worthy of the nxiic of qwcn of the sciences.“’

For Boltzmann. the limits of our knowledge are defined both by the

intrinsic nature of language, and by the relation and connection between

language and physical reality. In fact. our language should mirror reality so

“that the connections we create between words are everywhere as adequate

as possible to the connection in reality.” He maintains further, in regard to

the limitations of knowledge. that there arc no questions that lie beyond our

cognition: whatever can legitimately be asked can be answered. The existence

of questions whose answers lie beyond our ken is an illusion. and it is only by

habit of thought that we continue to answer questions which prove in reality

to be meaningless. In the end, the perennial philosophical riddles about the

world would be resolved. if only there existed a system wherein “it stood out

clearly when a question is not justified.”

To anyone familiar with the Trwrafus. the parallels between Boltzmann’s

and Wittgenstein’s thought are indeed striking. I refer the reader especially to

propositions 2-2.223. 3.1. 3.21. 4.06, 4.116. 6.5, 6.53 and 7. In much the same

manner as Boltzmann, Wittgenstcin asserts in the Tractatlrs, “for an answer

which cannot be expressed the question too cannot be expressed. The riddle

does not exist. If a question can be put at all. then it also can be answered.”

(prop. 6.5) Earlier in the work, he statcd:

4.003 Most proposition5 and questions, that have been written about philosophical

matters. are not fulse. but senseless. We cannot. therefore. answer qucstiona

of this kind at all. but only state their scnselessncss. Most questions and

propositions of the philosophers result from the fact that we do not

understand the logic of our hnguagc. And so it is not to he wondered at

that the deepest problems are really no problems.”

Following Boltzmann. the right method of philosophy for Wittgenstcin would

therefore be this:

6.53 To say nothing except what can be said, i.e. the propositions of natural

science. i.e. something that has nothing to do with philosophy: and then

always, when someone else wished to say something metaphysical, to

demonstrate to him that he had given no meaning to certain signs in his

propositions.”

As we have seen. Boltzmann was also) concerned with philosophical

prohlcms surrounding the habit of asking mcaninglcss qucstiona. ltc had

suggested that their scnsc’lcssncss might be rootccl in our tendency to combine

words that together cxprcss no clear thought. I‘hi5. of course. implied that the

solution to these problems is to he found in csamining and unclcrs~anding the

logic of language. i.e. understanding how ;III~ when ;I pet-son is ahlc to

combine words in ;I meaningful way. Boltzmann. however. did not undcrtakc

such an examination. Icavins the task undone. In the ‘1‘twlrrl~r.v. Wittgcn-

stein appears to have picked up whcrc Holtdiiann stopped. Whet-c Bolt~mann

c~illcd for an end to meaninglcs~ quc\tions. Wittgcnstein con~tritctcd ;I

philosophical system to do ,just that. ;I sytem that attempts to define the

limits of meaningful questions and proposilions. >I sy\tetn that cotlcllldes,

“Whereof one cannot speak. thereof one must lx! silent”.“: (prop. 7) It could

\‘ery well he the cast that Wittgenstein was introcluced to the importance ot

linguistic analysts (or solving philosophical prol~lems from reading Bolts-

111a1111’s I’opltrcw Sclr~i/icvl, and. in turn. w;i\ thus started along the path ot

his philosophical program. In this xxnsc. l3oltzm~tnn’s importance to

Wittgenstein’s dcvclopment may esceetl I Ict-ty/‘s.

VI. Conclusion

In this essay I have prcsentcd evidcncc indicating that a few important

historical points concerning Wittgcnstcin’s early intellectual developtncnt

have hccn misltnclcrstood. From this evidence. I think the following revisions

should hc included in future historical accounts of Wittgenstein‘s thought:

first. that Wittgcnstcin received his first philosophical introduction to

theoretical mechanics. and to problems in the philosophy of Ianguagc from

Boltzmann’s I’oplrlrww Sdrrific~tr, not Hertz‘s I’r~itwiplcs: second. the reading

of 13oltzmann’s work ccmcnted Wittgcnstcin‘s desire to study under Boltz-

mann at Vienna. as well as dir-cctecl Wittgcnstcin to Hertz’s /‘rir~c~i~~/c.s: third.

that Boltzmann should no longer lx clescribccl as. and considerucl to he ;I

xicntific or philosophical “I lertc.ian”: and. tinally. that llert;l should no

longer he autot~iatically considcrcd ;I more important influcncc on Wittgen-

stein than was Boltzmann. To be sut-c. more work ncccls to bc done before

Wittgenstcin‘s intcllectu~il biography can lx 1‘uIIy uncicrstood. and txfore he

can he pl;~ced in the hro~rdcr xicntific and technological contest of his time.

For instance. his studies and interes;ts at the Ohcrrealschule in Lin/. anti at

the Tcchnischc I iochschule in Bet-lin~(‘h~rr1ottcnhul-g need to lx unaminecl.

For the moment. thou$l. getting rhc detail\ straight of the general

chronology and relationship hetwecn HertL. IJoltzmann. and Wittgenstein i\

II step toward a more complete understanding of Wittgenstein’s biography, as

well as toward providing new insight to the background. purpose. and value

of the philosophy presented in the Trmtrctus.

A~~t?ot~l~,tlgc,r,lcnr - I would like to thank L. Pearce Williams and llelge Kragh for

reading, and commenting on. the manuscript draft of this paper.