Der Apriorist - Blog 20. Oct. 2010

Mises Zitate - Was uns Euklids Logik über die reale Welt sagt

von Norbert Lennartz

Tags: Apriori, Wissenschaft, Zitate | Comments (0)

"The empiricist reaction against apriorism centers around a misleading interpretation of the non-Euclidean geometries, the nineteenth century's most important contribution to mathematics. It stresses the arbitrary character of axioms and premises and the tautological character of deductive reasoning. Deduction, it teaches, cannot add anything to our knowledge of reality. It merely makes explicit what was already implicit in the premises. As these premises are merely products of the mind and not derived from experience, what is deduced from them cannot assert anything about the state of the universe. [...] The axioms from which a deductive system departs are arbitrarily selected. They do not tell us anything about reality. There is no such thing as first principles a priori given to the human mind.[2] ...

In order to examine this philosophy, let us refer to the conflict between the Euclidian geometry and the non-Euclidian geometries which gave rise to these controversies. It is an undeniable fact that technological planning guided by the Euclidian system resulted in effects that had to be expected according to the inferences derived from this system. The buildings do not collapse, and the machines run in the expected way. The practical engineer cannot deny that this geometry aided him in his endeavors to divert events of the real external world from the course they would have taken in the absence of his intervention and to direct them towards goals that he wanted to attain. He must conclude that this geometry, although based upon definite a priori ideas, affirms something about reality and nature. The pragmatist cannot help admitting that Euclidian geometry works in the same way in which all a posteriori knowledge provided by the experimental natural sciences works. Aside from the fact that the arrangement of laboratory experiments already presupposes and implies the validity of the Euclidian scheme, we must not forget that the fact that the George Washington bridge over the Hudson River and many thousand other bridges tender the services the constructors wanted to get confirms the practical truth not only of the applied teachings of physics, chemistry, and metallurgy, but no less of those of the geometry of Euclid. This means that the axioms from which Euclid starts tell us something about the external world that to our mind must appear no less "true" than the teachings of the experimental natural sciences.

[...] The fortunate empirical fact [... is ...] that the human mind has the ability to develop theories which, although a priori, are instrumental in the endeavors to construct any a posteriori system of knowledge. Although logic, mathematics, and praxeology are not derived from experience, they are not arbitrarily made, but imposed upon us by the world in which we live and act and which we want to study.[4] They are not empty, not meaningless, and not merely verbal. They are—for man—the most general laws of the universe, and without them no knowledge would be accessible to man."

Quelle: Ludwig von Mises. The Ultimate Foundation of Economic Science. Chapter 1: 'The Human Mind'. 'Section 1: The Logical Structure of the Human Mind' LvMI., online edition. (First edition: Van Nostrand, 1962.)

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