We present a sketch of a computational account of the relationship between certain aspects of introspection with aspects of third-person ascription of mental states (mindreading). The theory we propose is developed in large part as a reaction to what we perceive to be a lack of precision in the literature and a lack of experimental techniques to properly inform the debate on the relationship between 1st and 3rd-person ascription. We first discuss the set of phenomenology associated with self-ascriptions and other- ascriptions before briefly mentioning patterns of deficits associated with each. We sketch the very beginnings of a theory of mindreading in both the 1st and 3rd person within a computational cognitive architecture having mental simulation as one of its core operations. The theory we develop provides computationally-grounded explanations that are compatible with both clinical data and the phenomenology of 1st-person attribution.