The idea is that logical formalisms — boolean algebras, relations, functions, or frames and the like — are good at describing complex structure and relations for small sets of things. But if you have lots of things, you need to introduce abstractions involving counting — averages, covariance, correlations, and the like. The even more vague idea is that, given a nice axiomatic formalism, perhaps there is a way in which statistical notions result from having to consider learning/inference over large quantities of things. <br/><br/>There are approaches to probability theory (Cox/Jaynes as I understand it) that demonstrate it as a consequence of adding induction/uncertainty to boolean logic… I was wondering if there might be something analogous for statistics.