The concept of periodic equivalence introduced by Rudolf Carnap serves to form classes within the large number of periodic processes. Two processes are called periodically equivalent if the ratio of their frequencies is constant.
In fact, there are periodically equivalent processes in all biological organisms, which, however, do not run in step with the physical periodic processes.
The introduction of the concept of periodic equivalence became necessary when the analysis of the rules for the operationalization of the concept of time showed that time can only be metrized with the help of periodic processes and that there is no way of proving that any periodic process is always exact are the same length. The same problem arose with the introduction of the metric concept of length , as it also turned out that no length scale can be said to be of any length whether or not its length changes when it is moved from one place to another or also over time. The only solution to this dilemma is the introduction of equivalence relations , which divide the set of objects to be metrized into classes, in which an object can be selected that can be defined as a standard for measuring within this class .
The concept of periodic equivalence is such a class-forming equivalence relation that divides the set of processes into non-element classes, which are referred to as PEP classes. PEP abbreviates the English term p eriodic e equivalent p rocess .
Carnap was of the opinion that fortunately there is only one - overwhelmingly large - class of physical processes, so that the introduction of a physical measure of time does not cause any problems as soon as a periodic process from the PEP class of the physical world is selected as the unit of time.
This view has been criticized by pointing to the existence of circadian rhythms , which other large PEP classes suggesting the existence, with the help of which a different tempo than let determine the physical time, the concept of defined within a system system time lead.
- On this, see Rudolf Carnap, Introduction to the Philosophy of Natural Science , Nymphenburger Verlagshandlung, Munich 1969, p. 88 ff. (Translated from Philosophical Foundations of Physics , ed. M. Gardner, New York-London 1966, p. 82 there ff.) or W. Deppert, Zeit. The foundation of the concept of time, its necessary division and the holistic character of its parts , Steiner Verlag, Stuttgart 1989, ISBN 3-515-05219-4 , p. 212.
- For the introduction of this term cf. Hans Jörg Fahr, time and cosmic order. The never-ending story of becoming and returning , Carl Hanser Verlag, Munich / Vienna 1995, ISBN 3-446-18055-9 or Janke Jörn Dittmer, The system time concept as an example for general system variables, in: Fundamental problems of our time, Volume I, p. 181 –253, Leipziger Universitätsverlag, Leipzig 2002, ISBN 3-935693-73-7 .
- Rudolf Carnap, Introduction to the Philosophy of Natural Science , Nymphenburger Verlagshandlung, Munich 1969, p. 88ff.
- W. Deppert, time. The foundation of the concept of time, its necessary division and the holistic character of its parts , Steiner Verlag, Stuttgart 1989, ISBN 3-515-05219-4 , p. 212.
- W. Deppert: The sole rule of physical time is to be abolished in order to gain space for new scientific research , in: Hans Michael Baumgartner (Ed.): Das Rätsel der Zeit . Philosophical analyzes, Karl Alber Verlag, Freiburg / Munich 1993, pp. 111–148, there p. 121 ff.
- Wolfgang Stegmüller , Problems and Results of the Philosophy of Science and Analytical Philosophy , Volume II / 1 Theory and Experience , Springer Verlag 1970 (1st edition)., P. 75 and context.