spencer-brown vs. probability and statistics entropy’s testimony on subjective and objective randomnessspencer-brown与概率和统计熵对主观和客观随机性的证词.pdf

Information 2011, 2, 277-301; doi:10.3390/info2020277 OPEN ACCESS information ISSN 2078-2489 /journal/information Article Spencer-Brown vs. Probability and Statistics: Entropy’s Testimony on Subjective and Objective Randomness Julio Michael Stern Department of Applied Mathematics, Institute of Mathematics and Statistics, University of Sao Paulo, Rua do Matao 1010, Cidade Universitaria, 05508-090, Sao Paulo, Brazil; E-Mail: jmstern@; Fax: +55-11-3819-3922 Received: 08 February 2011; in revised form: 22 March 2011 / Accepted: 23 March 2011 / Published: 4 April 2011 Abstract: This article analyzes 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; randomization; subjective randomness 1. Introduction In several already published articles, I defend the use of Bayesian Statistics in the epistemological framework of cognitive constructivism. In particular, I show how