Towards an Informational Pragmatic Realism

Abstract

I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More specifically: (1) Probability theory is designed as the uniquely natural tool for representing states of incomplete information.(2) An epistemic notion of information is defined in terms of its relation to the Bayesian beliefs of ideally rational agents. (3) The method of updating from a prior to a posterior probability distribution is designed through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting framework includes as special cases both MaxEnt and Bayes' rule. It therefore unifies entropic and Bayesian methods into a single general inference scheme. I find that similar pragmatic elements are an integral part of Putnam's internal realism, of Floridi's informational structural realism, and also of van Fraasen's empiricist structuralism. I conclude with the conjecture that their valuable insights can be incorporated into a single coherent doctrine -an informational pragmatic realism.

Entropic Updating of Probabilities and Density Matrices

“…Being informationally stingy, that we should only update probability distributions when the information requires it, pushes inductive inference toward objectivity. Thus, using the PMU helps formulate a pragmatic (and objective) procedure for making inferences using (informationally) subjective probability distributions [41].…”

Entropic Updating of Probability and Density Matrices

“…Being informationally stingy, that we should only update probability distributions when the information requires it, pushes inductive inference toward objectivity. Thus using the PMU helps formulate a pragmatic (and objective) procedure for making inferences using (informationally) subjective probability distributions [28].…”

The Design of Global Correlation Quantifiers and Continuous Notions of Statistical Sufficiency

“…One is forced to address similar questions in the context of designing the relative entropy as a tool for updating probability distributions in the presence of new information (e.g., "What is information?") [1]. In the context of inference, correlations are broadly defined as being statistical relationships between propositions.…”

“…When one has incomplete information, the tools one must use for reasoning objectively are probabilities [1,2]. The relationships between different propositions x and y are quantified by a joint probability density, p(x, y) = p(x|y)p(y) = p(x)p(y|x), where the conditional distribution p(y|x) quantifies what one should believe about y given information about x, and vice-versa for p(x|y).…”