Mathematical and formalized epistemologies

Robert Vallée

pp. 309-324

in: Mioara Mugur Schchter (ed), Quantum mechanics, mathematics, cognition and action, Berlin, Springer, 2002

Abstract

A mathematical epistemology at the macroscopic level is proposed, based on the process of perception represented by an observation operator. The linear case introduces a Volterra composition with the two extreme cases of multiplication and convolution. Presented in terms of observation operators, are introduced the concepts of epistemological indiscernibility and of epistemological inverse transfer. The case of perception of duration is considered, as well as time-space selection and time-space filtering, which give rise to rather general modelings of familiar observation devices. If the observing system also has the ability to decide, a pragmatic operator, the product of observation and decision operators, may be introduced. It generates pragmatic indiscernibility and pragmatic inverse transfers. The resulting actions modify the evolution of the supersystem composed of the system and its environment, thereby creating a feedback loop allowing the construction of a mathematical epistemo-praxiology, which may be seen as a step toward other formal epistemologies not restricted to the macroscopic domain.