Wheeler M (2011) In search of clarity about parity. Philosophical Studies, 152 (3), pp. 417-425. https://doi.org/10.1007/s11098-010-9601-5
First paragraph: Andy Clark's Supersizing the Mind: Embodiment, Action, and Cognitive Extension (Clark 2008) is, among other things, a characteristically bold and timely defence of the extended mind hypothesis (Clark and Chalmers 1998). According to this hypothesis, which Clark here calls EXTENDED, the physical mechanisms of mind (the material vehicles that realize cognition) sometimes extend beyond the traditional boundaries of skull and skin, such that "actions and loops through nonbiological structure [sometimes count] as genuine aspects of extended cognitive processes" (p. 85). In the brief treatment that follows I cannot hope to engage with everything that is worthy of discussion in Clark's rich and exciting text, so I shall content myself with exploring and assessing a central thread in his argument for EXTENDED. That thread revolves around what is called the parity principle. Here is how that principle is formulated in Supersizing the Mind (p. 77, drawing on Clark and Chalmers 1998, p. 8):
If, as we confront some task, a part of the world functions as a process which, were it to go on in the head, we would have no hesitation in accepting as part of the cognitive process, then that part of the world is (for that time) part of the cognitive process.
The general idea is this: if there is functional equality with respect to governing intelligent behaviour (for example, in the way stored information is poised to guide such behaviour), between the causal contribution of certain internal elements and the causal contribution of certain external elements, and if the internal elements concerned already qualify as the proper parts of a cognitive trait (system, state, process, mechanism, architecture...), then there is no good reason to deny equivalent status to the relevant external elements. Parity of causal contribution mandates parity of status with respect to the cognitive.
Philosophical Studies: Volume 152, Issue 3