Abstract. The philosophical case for extended cognition is often made with reference to 'extended-memory cases' (e.g. Clark & Chalmers 1998); though, unfortunately, proponents of the hypothesis of extended cognition (HEC) as well as their adversaries have failed to appreciate the kinds of epistemological problems extended-memory cases pose for mainstream thinking in the epistemology of memory. It is time to give these problems a closer look. Our plan is as follows: in §1, we argue that an epistemological theory remains compatible with HEC only if its epistemic assessments do not violate what we call 'the epistemic parity principle'. In §2, we show how the constraint of respecting the epistemic parity principle stands in what appears to be a prima facie intractable tension with mainstream thinking about cases of propositional memory. We then outline and evaluate in §3 several lines of response.Keywords: Extended cognition; propositional memory; knowledge; cognitive ability §1 Extended Cognition and Epistemic Parity Consider the following case, due to Clark & Chalmers (1998):Inga: Inga relies on her biological memory in a way that is perfectly normal; new information she learns is stored in her biological memory, which is also what she consults when she needs some old information.Two obvious observations are in order. First, Inga's biological memory is part of the cognitive process she employs in the ordinary course of storing and retrieving information. Secondly, Inga's biological memory is intracranial in that it is seated within her skin-and-skull.But now imagine that Inga's biological memory were instead somewhere outside her skull and skin, e.g., enclosed in a brain-in-a-vat that she carries around with her, playing the same role vis-à-vis stored and retrieved information as it usually does, intracranially, in the default case.While this would be a strange sight, we would surely not hesitate to include her portable biological brain as part of the cognitive process she employs in remembering the kinds of things she remembered before; her biological memory is after all playing the very same functional 2 role-viz., the role of being that which stores the new information she learns and the old information she retrieves. It would just be doing so in a way that goes beyond her bodily boundary. So, mere location can't be what matters. What then about implementation? Imagine that part of Inga's biological memory, say her dorsal premotor cortex, is replaced in the same location with a silicon-chip device which plays the same functional role in terms of storing and retrieving information. Again, we would not be reluctant to include that artificial implant as part of the cognitive process that she uses in remembering events that occurred before the surgery.So, actual constitution can't be what matters either. But now consider a combined case where part of a cognitive process is both constituted non-biologically and occurs outwith the skin-andskull. Here is Clark & Chalmers's (1998) case of 'Otto':Otto: Otto suffers from...