Zur Deutung von Axiomensystemen bei Popper

In Was wir Karl R. Popper und seiner Philosophie verdanken. Zu seinem 100. Geburtstag. Academia Verlag. pp. 133-159 (2002)
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Abstract

In Popper's Logik der Forschung, a theoretical system is a set of sentences that describe a particular sub-area of science, in particular of empirical science. The goal of axiomatizing a theoretical system is to specify a small number of "axioms" describing all presuppositions of the sub-area under consideration, so that all other sentences of this system can be derived from them by means of logical or mathematical transformations. The paper discusses two philosophical interpretations of these proper axioms. First, proper axioms stipulate the use of the signs for the basic concepts of the system. Consequently, the proper axioms turn out to be analytic relative to a class of interpretations of the underlying logic. Hence, they cannot be falsified by refuting their logical consequences because these consequences are analytic as well. Secondly, proper axioms are synthetic, falsifiable and uncertain sentences. Hence, they are not immunized against falsification by refuting their logical consequences.

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Hans-Peter Leeb
University of Salzburg

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