Hans-Hernt-ann Hoppein particular since Einstein's relativistic <strong>the</strong>ory of gravitation,<strong>the</strong> prevailing position regarding geometry is onceagain empiricist <strong>and</strong> formalist. It conceives of geometry asei<strong>the</strong>r being part of empirical, aposteriori physics, or asbeing empirically meaningless formalisms. Yet thatgeometryis ei<strong>the</strong>r mere pIa)', or forever subject to empirical testingseems to be irreconcilable with <strong>the</strong> fact that Euclideangeometry is <strong>the</strong> foundation of engineering <strong>and</strong> construction,<strong>and</strong> that nobody <strong>the</strong>re ever thinks ofsuch propositionsas only hypo<strong>the</strong>tically true. 61 Recognizing knowledge aspraxeologically constrained explains why <strong>the</strong> empiricist-formalistview is incorrect <strong>and</strong> why <strong>the</strong> empirical success ofEuclidean geometry is no mere accident. Spatial knowledgeis also included in <strong>the</strong> meaning of action. Action is <strong>the</strong>employment of a physical body in space. Without acting<strong>the</strong>re could be no knowledge of spatial relations, <strong>and</strong> nomeasurement. Measuring is relating something to a st<strong>and</strong>ard.Without st<strong>and</strong>ards, <strong>the</strong>re is no measurement; <strong>and</strong> <strong>the</strong>reis no measurement, <strong>the</strong>n, which could ever falsify <strong>the</strong> st<strong>and</strong>ard.Evidentl)', <strong>the</strong> ultimate st<strong>and</strong>ard must be provided by<strong>the</strong> norms underlying <strong>the</strong> construction ofbodily movementsin space <strong>and</strong> <strong>the</strong> construction of measurement instrumentsby means of one's body <strong>and</strong> in accordance with <strong>the</strong> principlesof spatial constructions embodied in it. Euclidean geometr)',as again Paul Lorenzen in particular has explained,is no more <strong>and</strong> no less than <strong>the</strong> reconstruction of <strong>the</strong> idealnorms underlying our construction of such homogeneousbasic forms as points, lines, planes <strong>and</strong> distances, which arein a more or less perfect but always perfectible way incorporatedor realized in even our most primitive instrumentsofspatial measurements such as a measuring rod. Naturall)',61SeeonthisalsoMises, The Ultimate Foundation of<strong>Economic</strong> <strong>Science</strong>) pp.12-14.The Ludwig von Mises Institute • 75
<strong>Economic</strong> <strong>Science</strong> <strong>and</strong> <strong>the</strong> <strong>Austrian</strong> <strong>Method</strong><strong>the</strong>se norms <strong>and</strong> normative implications cannot be falsifiedby <strong>the</strong> result ofany empirical measurement. On <strong>the</strong> contrar~<strong>the</strong>ir cognitive validity is substantiated by <strong>the</strong> fact that it is<strong>the</strong>y which make physical measurements in space possible.Any actual measurement must already presuppose <strong>the</strong> validityof<strong>the</strong> norms leading to <strong>the</strong> construction ofone's measurementst<strong>and</strong>ards. Itis in this sense thatgeometry is an a priori science;<strong>and</strong> that itmust simultaneously be regarded as an empiricallymeaningful discipline, because it is not only <strong>the</strong> very preconditionfor any empirical spatial description, it is also <strong>the</strong>precondition for any active orientation in space. 62In view of<strong>the</strong> recognition of<strong>the</strong> praxeological characterof knowledge, <strong>the</strong>se insights regarding <strong>the</strong> nature of logic,arithmetic <strong>and</strong> geometry become integrated <strong>and</strong> embeddedinto a system of epistemological dualism. 63 The ultimate620n <strong>the</strong> aprioristic character ofEuclidean geometry see Lorenzen,<strong>Method</strong>ischesDenken, chapters 8 <strong>and</strong> 9; idem, Normatipe Logic <strong>and</strong> Ethics, chapter 5; H.Dingler, Die Grundlagen der Geometrie (Stuttgart: Enke, 1933); on Euclideangeometry as a necessary presupposition of objective, i.e., intersubjectively communicable,measurements <strong>and</strong> in particular of any empirical verification of nonEuclidean geometries (after all, <strong>the</strong> lenses of <strong>the</strong> telescopes which one uses toconfirm Einstein's <strong>the</strong>ory regarding <strong>the</strong> non-Euclidean structure ofphysical spacemust <strong>the</strong>mselves be constructed according to Euclidean principles) see Kambartel,Erfahrung und Struktur, pp. 132-33; ~ Janich, Die Protophysik der Zeit(Mannheim: Bibliographisches Institut, 1969), pp. 45-50; idem, "Eindeutigkeit,Konsistenz und methodische Ordnung," in E Kambartel <strong>and</strong> J. Mittelstrass, eds.,Zum normatipen Fundament der Wissenschaft.Following <strong>the</strong> lead ofHugo Dingler, Paul Lorenzen <strong>and</strong> o<strong>the</strong>r members of<strong>the</strong> so-called Erlangen school have worked out a system of protophysics, whichcontains all aprioristic presuppositions ofempirical physics, including, apart fromgeometry, also chronometry <strong>and</strong> hylometry (i.e., classical mechanics withoutgravitation, or "rational" mechanics). "Geometry, chronometry <strong>and</strong> hylometry area-priori <strong>the</strong>ories which make empirical measurements ofspace, time <strong>and</strong> materia'possible'. They have to be established before physics in <strong>the</strong> modern sense of anempirical science, with hypo<strong>the</strong>tical fields offorces, can begin. Therefore, I shouldlike to call <strong>the</strong>se disciplines by a common name: protophysics." Lorenzen, NormatiTJeLogic <strong>and</strong> Ethics, p. 60.630n <strong>the</strong> fundamental nature of epistemological dualism see also Mises,Theory <strong>and</strong> History, pp. 1-2.76 • The Ludwig von Mises Institute