Danielle J. Williams

(FILE UPDATED 8.5.26) The simplest of all mapping views say that what is required for some physical system to implement a computational structure is that the state transitions of the physical system mirror the state transitions described by the computational description. This view, of course, is considered overly permissive as it allows systems such as pails of water and rocks baking in the sun to satisfy the implementation relation. Anderson and Piccinini's (2024) robust mapping account modifies the simple view by specifying a robust mapping requirement. If a robust mapping is made, then the physical system bears the physical signatures of computation. However, their account departs from standard mapping views in several ways, including its characterization of the relata at either end of the implementation relation. In this paper, I evaluate the robust mapping account and argue that the constraints it imposes on the descriptions of the respective relata prevent it from generalizing across contexts. Using physical descriptions in neuroscience, I demonstrate that the formulation of the physical description of the physical system in the robust mapping account leads to two problems: What I call the multiple descriptions problem and the granularity problem. Then, focusing on the computational description, I argue that the authors' mistaken Platonist assumption about standard mapping views leads to an additional problem: What I call the hybridization problem. Although this paper engages directly with the robust mapping account, it serves as a general overview of the scope and aims of standard computational implementation views by demonstrating how the metaphysical project of computational implementation relates to computational methodologies in cognitive science. This paper will be helpful for those who are interested in how a metaphysical project can contribute to explanation in the mind sciences.

The term “medium independence” has different meanings. One sense maps onto “abstract-as-abstracta” descriptions while the other maps onto “abstract-as-omission” descriptions. Both senses have been deployed when it comes to understanding the nature of physical computation. However, because medium independence is a polysemic term, the sense being used should be clearly stated. If the sense is not clearly stated, then those who wish to engage in debates regarding medium independence and physical computation run the risk of conflating different but related issues which can have consequences when it comes to thinking about physical computation across contexts.