IMG06

Ernst Mach

5.    Economy as mathcmatical simplicity

7'hc rcquirement of simplicity is of course to thc cxpcrt a ditfcrent niattcr front what it is to a novicc. For thc first, dcscription by a system of dif fcrcmial cquations is sufficicnt; for thc sccond, a gradual construction out of clcmcntary laws is rcąuircd.³⁰

6.    Economy as abb,-cviation

In thc cconomica! schematization of science lies boih its strength and its weakness. Facts arc always represented at a sacrificc of complctcncss and ncvcr with greater prccision than fits thc nceds of thc moment.³¹

7.    Economy as nbstraction

Our reproductions fof facts into thoughts] arc invariably abstractions Herc again is an economical tendcncy.³-

8.    Logic as incomplctccconomy

The dcmands of economy go further than thosc of logie, which scrvcs so to speak, only as a negative role \Rcgulativ]³³

9.    Ontological economy

The main thing is thc abolition of an unncccssary doublcd existcncc fi.c., “appearancc” and “rcality”J.⁸⁴

10.    N9 economy in naturę

Therefore, in this sense thcrc can be nothing said about an economy in physical processcs, sińce between factuał occurrcnces thcrc can be no choice. Therefore in this field I h3vc not applied thc~concept of economy itTany way.³⁵

11.    Linguistic economy

Language, the instrument of this communication, is itsclf an economical contrivance.³⁶

Ernst Mach attempted to understand formal logie and mathematics in terms of sensory elcmcnts and an cvolutionary-historical approach.

¹ For his pains he rcćeived the charge of “psychologism” from Edmund Husserl.³⁷ No aspect of Mach’s philosophy has becn morę scverely eriticizcd than his refusal to excmpt logie and mathematics from a phenomenalistie rcduction. Mathematical “intuitionists,” “a priorists," and “Platonists” all fclt decply woundcd by Mach’s attemjit to relate purc, timcless verities to merę grubby expericnce. Herc arc iwo of Maeffs morc provocativc observations:

Philosophy of Science

Unlnascd psychological observation informs us, howcver, that thc forma-uon of thc conccpt of nutnber is just as much initiated by cxpcricncc as thc formation of geometrie conccpts.⁸⁸

The mathcmatician who pursues his siudics without elear vicws of this matter [Mach's theory of economy] must often havc thc uncomfortablc fecling that his paper and pencil surpass him in intclligcncc. Mathematics thus pursucd as an object of instruction is scarccly of morę cducational valuc than busying oneself with thc Cabala. On thc contrary, ii induccs a tendency toward mysticism, which is pretty surę to bear fruits.³⁹

Mach not only subordinated thc ttsc of formal logie to his phenom-enalism and theory of economy, but in a sense thc lattcr was his theory of logie. Wilhelm Jcrusalcm pointed this out:

If we should dccide to regard logie siinply as thc doctrinc of thc meth-ods of thought, and would consistcntly apply thc conccpt of thc “economy of thought" introduced by Ernst Mach. thc possibility of cxtcnsion in this dircction would become much greater. Logic would then be nothing morc than a univcrsal economy of thought, and its task would consist in dis-covcring how thought-instruments have always tendcd towards cconomic adjustment and how thcsc adjustments may be still further advanced.⁴⁰

Mach’s stand on logie and mathematics closcly rcscmblcd the ap- ( proach of William James, John Dcwcy, and other Pragmatistś uf dic period. To understand the plausibility in their point of view it may be ncccssary to emphasize thc elose relation bctwccn both their idcas on logie and mathematics and Mach’s theory of economy with what might best be callcd: common sense “means end" logie.

In everyday life an end or goal is ‘‘logical" to the extent it corre-sponds with morc important goals or with primary values, and a mcans or action is “logical” the morę it satisfies a particular purpose or purposes with a minimum of unfortunate side or after efTects. For-mal logie is “logical” only insofar as it scrvcs as an etheient mcans or aid to reach a dcsirable goal.

Pracdcal peoplc have long insisted on subordinating formal logie to common sense "mcans-end” logie, and many logicians, scientists, and philosophers just as adamantly havc insisted eiiher that such a subordi-nation can not or should not takc place. Mach was probnbly closer to common sense on this particular issuc than anywherc clsc in Itis phi losophy, and yet, it was precisely on this matter, thc relation of logie and mathematics to experience and practical lite, that Mach‘s views were most decisivcly rejected by thc morc prominent German and Austrian philosophers of his day. Historically, Husserl had morę in-

*75