Economic Science and the Austrian Method_3

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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
Economic Science and the Austrian Methodas units by a procedure of"do it again, construct or identifyanother unit by repeating the previous operation."S9 Again,one can say, of course, that 2 plus 2 is sometimes 4 butsometimes 2 or 5 units, and in observational reality; for lionsplus lambs or for rabbits, this may even be true,60 but in thereality of action, in identifying or constructing those unitsin repetitive operations, the truth that 2 plus 2 is neveranything but 4 could not possibly be undone.Further, the old rationalist claims that geometry; that is,Euclidean geometry is a priori and yet incorporates empiricalknowledge about space becomes supported, too, in viewof our insight into the praxeological constraints on knowledge.Since the discovery of non-Euclidean geometries and590n a rationalist interpretation of arithmetic see Blanshard, Rcason andAnalysis~ pp. 427-31; on the constructivist foundation ofarithmetic, in particular,see Lorenzen, EinfUhrung in die operative Logik und Mathematik; idem, MethodischesDenken, chapters 6, 7; idem, Normative Logic and Ethics~ chapter 4; on theconstructivist foundation of classical analysis see P. Lorenzen, Differential undIntegral: Eine konstruktive EinfUhrung in die klassische Analysis (Frankfurt/M.:Akademische Verlagsgesellschaft, 1965); for a brilliant general critique ofmathematical formalism see Kambartel, Erfahrung und Struktur, chapter 6,esp. pp. 236-42; on the irrelevance ofthe famous Godel-theorem for a constructivelyfounded arithmetic see P. Lorenzen,Metamathematik (Mannheim: BibliographischesInstitut, 1962); also Ch. Thiel, "Das Begrlindungsproblem derMathematik und die Philosophie," in E Kambartel and J. Mittelstrass, eds.,Zum normativen Fundament der Wissenschaft, esp. pp. 99-101. K. Godel'sproof-which, as a proof, incidentally supports rather than undermines therationalist claim ofthe possibility ofapriori knowledge-only demonstrates thatthe early formalist Hilbert program cannot be successfully carried through,because in order to demonstrate the consistency of certain axiomatic theoriesone must have a metatheory with even stronger means than those formalizedin the object-theory itself. Interestingly enough, the difficulties ofthe formalistprogram had led the old Hilbert already several years before Godel's proof of1931 to recognize the necessity ofreintroducing a substantive interpretation ofmathematics ala Kant, which would give its axioms a foundation and justificationthat was entirely independent of any formal consistency proofs. SeeKambartel, Erfahrung und Struktu1j pp. 185-87.60Examples of this kind are used by Karl Popper in order to "refute" therationalist idea of rules of arithmetic being laws of reality. See Karl Popper,Conjectures and Refutations (London: Routledge and Kegan Paul, 1969), p. 211.74 • The Ludwig von Mises Institute
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ECONOMIC SCIENCEAND THEAUSTRIAN MET
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PREFACEIt was a tragic day when eco
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Economic Science and the Austrian M
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Page 92: ABOUT THE AUTHORHans..Hermann Hoppe
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Economic Science and the Austrian Method_3

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