A series of hypotheses is proposed, connecting neural structures and dynamics with the formal structures and processes of probabilistic logic. First, a hypothetical connection is proposed between Hebbian learning in the brain and the operation of probabilistic term logic deduction. It is argued that neural assemblies could serve the role of logical terms; synapse-bundles joining neural assemblies could serve the role of first-order term-logic statements; and in this framework, Hebbian learning at the synaptic level would be expected to have the implicit consequence of probabilistic deduction at the logical statement level. A conceptual problem arises with this idea, pertaining to the brain's lack of a mechanism of “inference trails” as used to avoid circular reasoning in AI term logic inference systems; but it is explained how this problem may be circumvented if one posits an appropriate inference control mechanism. Finally, a brief discussion is given regarding the potential extension of this approach to handle more complex logical expressions involving variables – via the hypothesis of special neural structures mapping neural weights into neural inputs, hence implementing “higher order functions.”