From exchangeability to rational belief: a cognitive interpretation of de Finetti's theorem.

Probabilistic reasoning is central to many theories of human cognition, yet its foundations are often presented through abstract mathematical formalisms disconnected from the logic of belief and learning. In this article, we propose a reinterpretation of de Finetti's representation theorem as a principle of rational inference under uncertainty. Building on the framework developed by E. T. Jaynes-where probability is viewed as an extension of logic-we show that the structure of de Finetti's theorem mirrors the logic of belief updating constrained by symmetry. Exchangeable sequences, which treat observations as order-invariant, lead naturally to a representation in which probabilities are weighted averages over latent causes. This structure is formally analogous to the role of partition functions in statistical models, where uncertainty is distributed across hypotheses according to constraints and prior expectations. We argue that this correspondence is not merely mathematical but reveals a deeper cognitive interpretation: the mind, when faced with symmetry and incomplete information, may infer in ways that implicitly reflect maximum entropy principles. We illustrate this connection with a simple example and discuss how the underlying structure of de Finetti's theorem can inform our understanding of inductive learning, probabilistic belief, and the rational architecture of cognition.