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Ernst Mach

thcy mean by thc word "cmpirical” ncccssarily shifts according to thcir cpistcmological and ontological assumptions. Pcoplc assuming difTcrcnt thcorics of knowlcdgc and rcality cannot mcan thc Siimc thing by thc words they uśc.

For Mach, physical objccts containcd both primary and sccondary qualitics, but for Newton thcy possessed ncither, but mcrcly had qual-itics closcly resembling thc cxpcricnccablc primary qualitics of sizc, shapc, cxtcnsion, density, number. and wcight. Since it was possiblc, howcvcr, to imagine objccts with indistinguishably similar qualitics, say two rubber balls, cxccpt one bouneed higher or responded to pres-surc difTerently, then clcarly an additional quality had to be attributed to physical objccts.²³ Newton callcd this quality vis insita, i.c., “resident forcc,” which might best be translated as a combination of tcxtural and structural rcsistancc or what we now cali ‘‘incrtial mass.”²⁴ Newton was vcry rcluctant to speeulate on thc naturę of this “resident foreć." In terms of his philosophy hc would havc had to framc^-an "hypothcsis,” that is, make an infcrcncc that he could not propcrly support with cmpirical data. Most of thc other qualitics of physical objccts hc presumed wcrc quite similar to c.\perienccablc primary qualitics, but resident forcc seemed to havc no empirical analogue at all. Our “feeling" of forcc might historically havc first suggested thc physical notion of force to prehistorie man, but in a reliable fashion such an “analogy” could hardly morę than mercly symbolizc what Newton was driving at without in any sense bcing dcscriptivcly ac-curate.

The problem was not thc rcality of “resident forcc" but thc obscurity of its naturę. If an objcct had all of thc other qualilics similar to ob-scrvable primary ones but lacked resident forcc, then prcsumably any-thing could pcnctratc it without opposition and it could not afTcct any-thing else. In other words, from a common sense point of vicw it would remain a merę gcometrical configuration, a spadał phantom, a referent without causal significance, and hcncc, in cfTcct, nothing. In ontological terms, resident forcc transformed a merę gcometrical particie into a physical causc and hcncc into a physical reality. In dynamie terms,

! Newton anticipated thc qualitative aspeets of Einstein’s mass-energy law.

Newton, besides wanting to be cmpirical, was also a mathcmatician. Hc distinguished betwccn “mathcmatical causcs," which could be .rcliably mcasured by an analogous cmpirical measurement of sclcctcd

sensalions, and "physical causes'’ such as resident forcc which di. sccm to be mcasurablc cvcn by analogous or other iń* " ^ ⁰⁰¹ \ The Closest hc could comc to mcasuring resident (orce waTto hopelhl ¹ measurcment of d,e s.zc and density of particles would give a rclilw iodication of thc relauve strength of that forcc, as if thaT forcc v ,eH dircctly with sizc and density. Needlcss to say, this was whiul' ^d thc dark, but it did give a kind o£ justification for hi, mathemaficTl dcfinition of mass.    ' ^LJl

NewtonV‘empiricism” meant that hc thought that thc mathematical aspects of objccts which lay outsidc of cypcricnce, that is, physical objccts, but Which were rcl.ably rcprcscntcd i„ consciousncss by the nri" mary qualmcs of scnsauons, could bc understood in a scicntific wav Thesc mathematical aspects, that is, in thc physical objcct outsidc of cxpcricncc, he called ''mathematical causes." The nonmathcmatical (and nongeomctrical) aspects of physical objccts such as rcsidcntlórce hc called ''physical causes,” and apparently, hc did not bclicsc that thcy ^! could bc understood in a scicntific way bccause thcy did not cven sccm to havc expcrienccable analogucs of any kind.

Newton defined ''mass” as quantity of maitcr. This was a mathe-maucal dcfinition, and mass was supposed to bc a mathematical cause If his hope that resident forcc varied dircctly with the size and density of particles were truć, then for practical purposes thcrc should bc no harm in treating mass as though it were not only a mathematical but also a physical causc, in Nc\vton’s usc of those two terms.

The advantagc of Newton*s definition of “mass*’ was that it madę particular masses measurablc. The formal disadvantage was the one that threatened all mathematical definitions, especially when thc author was not cxtremcly careful, namely, that someone would discovcr a cir-cularity. And of course in this particular casc that somconc was Mach. The factual disadvantagc was that by formulating a mathematical in-stead of a physical dcfinition (nonontological us. ontological, kinematie vs. dynamie) Newton avoided thc wholc issue as to the rcal cfficient causc or causes of physical motion and changc. In his laws of motion Newton presupposed mass as resident forcc, but in his explicit definition hc retreated to mass as quantity of matter.

Bcforc studying Mach’s criticisms in detali it is neccssary to present and clarify some of Newton’s other definitions that Mach opposed. This is not an casy task, and it requires making distinctions that Newton mcrcly assumed, but did not clearly express.

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