Abstract: This article analyses the role of entropy in Bayesian Statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. ``Objects as eigen-solutions'' is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism. Keywords: Bayesian Statistics, Cognitive constructivism, Eigen-solutions, Maximum entropy, Objective-subjective complementarity, Objectice inference, Randomization, Subjective randomness.