Probabilities over What?

Tourmen [this issue] gives an overview of a number of convergences and divergences between some contemporary probabilistic models of learning and development and Piaget’s model. Tourmen’s points are interesting and important, but so are also some caveats concerning the relationships between probabilistic models and Piaget’s model, which are given limited attention. I elaborate on some of those caveats. Models of learning focusing on the learning of probabilistic relationships have expanded over recent years. It is clear, and clear in Piaget’s work, that this is an important field of thought and development. There are at least two prominent species of such models in the current literature: one derived from Bayesian models of causality and causal inference, and another known roughly as “predictive brain” models. This article focuses exclusively on the first and so will also my commen ts. 1 Tourmen lays out very nicely multiple ways in which the Bayesian net causal model framework has some convergences with Piaget’s model; I will not rehearse those here. She also mentions in one or two sentences some differences which I argue are fundamental, and, therefore, at least partially undercut some of the more expansive claims made for the Bayesian net modeling approach. I first note that Bayes is a decision rule: it yields probabilistic information concerning the “best” selection to be made – the best decision among alternatives – in a specific Bayes’ rule sense. It is a powerful decision rule, but just one among many [e.g., Berger, 2010; Ferguson, 1967]. Decision rules involve varying kinds and degrees of power, with some, for example, being (under some circumstances) specific versions