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Ernst Mach

betwcen the idcas of Berkeley and Mach probably dcserve to _pur. sucd morc than they have becn.³⁰ Berkeley s opposition to many ₀f Newton’s idcas and definitions can be found in his An Essay Towards a Netu Theory of Vision (1709) and in Dc Mota (1721).

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If Mach had understood Ncwton's philosophy in terms o£ what it actually was, that is, an ontological dualism that identified physical rcality with what Iay cntirely outside expcrience, Mach logically would havc had to rcjcct all of Ncwton’s idcas on physics as “mctaphysical” and “unscicntific.” Mach, however, did not so understand ir, and a blankct rejcction of Ncwton’s contributions to physics would not havc bccn likcly to influence his collcagucs or young students in a favornhlc way. Instcad, hc tried to understand and accept Newton’s idcas in terms of his own phenomenalism, and when he was simply unablc to do this, hc accuscd Newton of being “unfaithful" to Ncwtons own “empirical” idcals as cxprcssed in the scholia to his Principia Mathe-matica.⁴⁰ It is within this curious context of misunderstanding that Mach launched his cpoch-changing criticisms.

Mach praiscd Newton for his resolution to deal only with “actual facts” and for his rejcction of “hypothescs."⁴¹ But for Mach, only sensations were facts. whilc Newton mcant all happenings, both “men-tal” cxpericnccable ones and “physical" noncxpcrienceable ones. Sim-ilarly, Mach used the word “hypothcsis” in a different way than Newton. For Mach all infercnces beyond thc appearances were “hypo-thctical,” and at best provisional, but for Newton sińce thc entirc physical world was outside the appearances carcful inference heyond , sensations was not only legitimatc, but was requircd by science.⁴² Only rhosc infercnces beyond thc appearances which were not supported by relcvant empirical analogiies dcscrved to be considercd “hypothescs" and hence from Newton’s point of vicw, “illegitimatc."⁴¹ In other words, Mach’s praisc of Nevvton’s attitudc toward “facts" and “hy-potheses" was misleading sińce Mach misunderstood what Newton mcant by the terms.

Mach’s basie opposition ro Newton’s understanding of mass was that it only madę sense if we assumed thc rcality of physical qualities outside expcricnce, that is, resident force. Marhs best known opposition rcfcrrcrl to a logical flaw in the written form of Ncwton’s definition.

I„ his .868 and .872 cr.t.cism Mach sull allowed for an alternatiye to circularicy. ''[Newton* definition] . . . _ls cnhcr a vcry ~Z* clc, or it IS ncccssary for one to conccWc of forcc as ‘pressure ¹ But pressure loaks very strange at thc head of thc quitc phoronJmiwl [kinemattej mcchamcs of tcday.”“ Mach’$ 1883 Science of Mechamcs howcvcr, Icft room for no altcrnatwc. Herc is a quotation from a Ller cdition (1912): “With regard to the conccpt of ‘mass*, it is to be ob-scrvcd that thc formulation of Newton, which defines mass to be thc quantity of niatter of a body as measured by thc product of its volumc and density, is unfortunate. As we can only dcfinc density as the mass of unit of volumc, thc circlc is manifest.”⁴⁵

The advantage of this logical criticism was that it seemed to be valid even when understood within thc contcxt of widcly ditfcring phiTo*>-phieś and points of view. Evcn philosophical opponents likc Boltzmann were impressed by it.^<0 Opcnly phenomenalistie obfectionsTo Ńewton’s ^} definition of “mass" would have had a much morę limitcd appcal. But oncc pointed out, the circularity in Newtons definition was simply too manifest to be casily argued away. What form could or should be used to replacc it?

Two Solutions were evident; first "mass” could be redefined as resi- • dent force, that is, as a nonmathematical quality best in accord with Newton’s cpistemological and ontological philosophy, and quitc con-sistent with common sense; or second. “mass” could be redefined in strictly phenomenalistie terms, but in a way less consistcnt with common sense. Mach chosc the lattcr alternative. We do not know to what cxtcnt Mach dcvelopcd his own preferred definition of "mass” himself or to what cxtcnt it was suggested by his reading of Berkeley or by an analysis of Newton’s third law of motion. To thc extent that it seemed to follow from the third law Mach could argue that he was merely correcting Newton in accordancc with Newtons own inten-tion to be “empirical." On the other hand, as alrcady mentioncd, Newton did not rnean the same thing as Mach by the term “empirical." and hc surcly did not intend his laws of motion to be understood in a phenomenalistie way. Newton’* physical definition of mass as “resident forcc" treated mass as a quality of an object. Mach, following Humc, defined mass as merely a relation.

Mach first introduccd his own definition of "mass," a phenomenalistie deser iption of thc etfects of mass in an 186S ar licie. Hc repcated his kinematic—but dynamie scemmg—definition in his 1872 book On

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