Computers in Abstraction/Representation Theory

Recently, Horsman et al. (Proc R Soc Lond A 470:20140182, 2014) have proposed a new framework, Abstraction/Representation (AR) theory, for understanding and evaluating claims about unconventional or non-standard computation. Among its attractive features, the theory in particular implies a novel account of what is means to be a computer. After expounding on this account, I compare it with other accounts of concrete computation, finding that it does not quite fit in the standard categorization: while it is most similar to some semantic accounts, it is not itself a semantic account. Then I evaluate it according to the six desiderata for accounts of concrete computation proposed by Piccinini (Physical computation: a mechanistic account, Oxford University Press, Oxford, 2015). Finding that it does not clearly satisfy some of them, I propose a modification, which I call Agential AR theory, that does, yielding an account that could be a serious competitor to other leading account of concrete computation.