Theories of Extended Mind have evolved in waves to reach the present state of disagreement with regard to whether or not external artefacts become part of the mind when used for memory purposes. A four-step approach has been used to address and resolve this disagreement. First, a new component for models of mind which provides a saliency function is provided. This saliency function corresponds to computational elements found necessary in large mainframe computer systems for handling rich data environments. Second, there is introduced a Computational Model of Memory containing the new component which models the operation of human memory. The Computational Model of Memory contains four interoperative elements including the new component, short-term memory, long-term memory, and a cross-reference associator. Third, the work of Marcin Milkowski is drawn upon to obtain a general method of assessing a computational model’s well-formedness, and the method is applied to prove the adequacy of the Computational Model of Memory. According to Milkowski’s schema, the model satisfies most criteria for a well-formed computational model, including in particular a separation between conceptual elements of the model, and constitutive elements of the model, which while explicitly related, are required to subsist at separate logical conceptual levels. Fourth, the Computational Model of Memory is applied to outstanding arguments in Extended Mind to clarify and resolve several of these arguments. The model serves to highlight where the nature of the disagreement depends upon a category error of reference, and further resolves a key disagreement by demonstrating that the mind may treat external artefacts as an alternative realizable constitutive element of short-term and long-term memory.