On the Possibility of a Formalized Epistemology

Abstract

We present an attempt to a mathematical epistemology valid at the macroscopic level. Do similar perceptions correspond to similar objects? How can we recompose two perception processes? The use of mathematical observation operators provides an answer. Identical perceptions may correspond to different objects perceived, due to the lack of an inverse of an observation operator. Consequently, there is a process of inverse transfer of structures inherent to the observing system on the observed world. Moreover, multiplication of observation operators gives a representation of the composition of perception processes. So we have at hand an algebra opening the way to a mathematical and thus formal epistemology. Also, the intervention of decision, composed with perception, allows the introduction of considerations analogous to those valid in the purely epistemological case, giving rise to a formal epistemo-praxiology. The possibility of a formal epistemology, even completed by praxiology, at the macroscopic level provides arguments in favor of a general formal epistemology acceptable at all levels.

See “Important Note” on p. xviii.