Economic Science and the Austrian Method_3

Hans-Hennann Hoppealways understood it, now also becomes discernible. The prevailingempiricist-formalist orthodoxy conceives of arithmeticas the manipulation ofarbitrarily defined signs according toarbitrarily stipulated transformation rules, and thus as entirelyvoid of any empirical meaning. For this view; whichevidently makes arithmetic nothing but pIa); however skillfulit might be, the successful applicability of arithmetic inphysics is an intellectual embarrassment. Indeed, empiricistformalistswould have to explain away this fact as simplybeing a miraculous event. That it is no miracle, however,becomes apparent once the praxeological or-to use here theterminology ofthe most notable rationalist philosopher-mathematicianPaul Lorenzen and his school-the operative or constructivistcharacter of arithmetic is understood. Arithmeticand its character as an a priori-synthetic intellectual disciplineis rooted in our understanding of repetition, therepetition of action. More precisel); it rests on our understandingthe meaning of"do this-and do this again, startingfrom the present result." And arithmetic then deals withreal things: with constructed or constructively identifiedunits of something. It demonstrates what relations are tohold between such units because of the fact that they areconstructed according to the rule of repetition. As PaulLorenzen has demonstrated in detail, not all of what presentlyposes as mathematics can be constructivelyfounded-and those parts, then, should ofcourse be recognizedfor what they are: epistemologically worthless symbolicgames. But all of the mathematical tools that are actuallyemployed in physics, i.e., the tools ofclassical analysis, can beconstructively derived. They are not empirically void symbolisms,but true propositions about reali~ They apply toeverything insofar as it consists of one or more distinctunits, and insofar as these units are constructed or identifiedThe Ludwig von Mises Institute • 73