IMG05

Ernst Much

arise whcrc a defcnsc might bc useful. Practical pcople and thosc men in acadcmic disciplincs such as history who thought their work was or could bc reliablc and who resented tliat such work was not gcncrally considercd “scientific,” howcvcr, had already begun to qucstion the rcstriction of science to abstract science.

As a good tcachcr and skillful writer Mach appreciated the valuc of historical or partieularistie understanding in arousing interest and en-thusiasm for learning, but as a physicist he denied it any place in “end science.” It was simply not cconomical cnough. Along this linę we should mention that when Mach spokc about a ‘‘complctc” understanding, he normally mcant a complete abstract or mathcmatical un-J derstanding. Similarly, his positivistic goal of “the unity of science” ' was understood mercly as a mathcmatical, or idealized unity.

Mach’s defcnsc of abstract science could scena strange to thosc rcad-crs who havc thought of him as an “empiricist.” But the cxplanation was simple. Mach held that a 11 science should bc grounded in observa-tion and expcrimcnt, but that all genuine science was ncccssarily matli-ematical in character. He did not oppose mathcmatical physics, but rather “uncconomical” use of formalism, mathcmatical theory, and mathcmatical eąuations whose physical meaning was not elear. It was truć that his interests wcrc morę empirical and cxperimcntal than mathcmatical, but that was another qucstion.

Mach was wcll awarc of the three major objections that could be raised against his theory of abstract, idealized description as the only legitimatc end science. Indeed, his frequcnt attacks on mathcmatical “dogmatism" and formalistic speeulation strongly suggested that he sympathized at least in part with these objections. Nonethelcss, as Mach's inereasing, Hume-like refercnces to common sense and partieularistie understanding as “vulgar” demonstrated, he had no intention of compromising on the matter. Only science could provide knowl-edge, and only mathcmatical science was true science.²¹

The three principal objections were: Abstract, idealized description was not reliablc cnough with respect to particular objeets and happen-ings. It was not informativc cnough for cithcr practical or curiosity purposes; and it was not interesting cnough to attract the numbers of students into the pursuit of understanding which could occur wcrc end science to inelude both abstract, idealized description and non-idcalizcd, partieularistie, historical understanding.

IV

Ernst Mach dcvclopcd a numbcr of mcthodological aids which hc hopcd would provc useful in actual scientific work. Many of thcsc suggestions wcrc first worked out in his lccturcs on the philosophy of science bctwcen 1895 ^anc^ 1898.²⁵ He rccognizcd the first nced as meth-odological freedom. Scicntists would bc handicappcd cither if they could not introducc promising aids or if they insisted upon using in-appropriatc aids. Freedom of choicc and fitting the right method to the right problem wcrc both ncccssary.

Mach's "theory of economy" was a major, cvcn if controvcrsial, eon-tribuTtoTi to the mcthodology of science. He, himsclf, emphasized ccon-omy of thought (DenĄpĄpnomie), but it was economy in logie and mathematies which has attractcd the most attention sińce his time. For the sake of clarity I have singlcd out a fcw of the different ways in which Mach employed his theory of economy.

1.    Economy of thought

No knowlcdgc worthy of the namc can be gathered up in a single human mind limited to the sp3n of a human lifc and gifted only with finitc powers, exccpt by the most cxquisitc economy of thought and by the carcful amassment of the economically ordered cxpcrience of thousands of co-workcrs.²⁶

2.    Economy of energy

This fundamcntal vicw . . . [epistcmological phcnomcnalism] is con-$cqucntly the one that accotnmodatcs itself with the least cxpcnditurc of energy, that is, morc economically ihan any other, to the present temporary collcctivc State of knowlcdgc.²⁷

3.    Economy of work and time

The scicntist sets himsclf the task of gaining the greatest possible amount of . . . trulh with the least possible labor, in the shortest possible time, and with the least possible thought.²⁸

4.    Methodological economv

The method* by which knowlcdgc is gained arc of an cconomical naturę.²⁰

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