Computers in Abstraction/Representation Theory

Abstract

Recently, 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 (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.

Physical computing: a category theoretic perspective on physical computation and system compositionality

“…This 'representational' view of concrete computation is contrary to the simple [49] and mechanistic [44] mapping accounts, and more in-line with the syntactic [23] and semantic [55]. What sets apart AR from syntactic [23] and semantic [55] accounts is that AR deviates from requiring the representational entity to be an aspect or product of mind or for the representations to be meaningful [22]. In fact, AR does not put any restrictions on the abstract (representational) mapping of the physical state [28].…”

Physics and Computation

“…Horsman, Stepney, Wagner, and Kendon (2014) introduced an account of computation, Abstraction/Representation (AR) theory, which has been subsequently developed (Fletcher, 2018, Horsman 2015, Horsman, Kendon, Stepney, and Young, 2017. The most important insight associated with AR theory is that our judgments about computation are mediated by the theories that describe the systems associated with computation.…”

“…One issue is how one should make determinations regarding the encoding and decoding operations. Fletcher (2018) calls this the objectivity problem for representational entities.…”

Why Do We Need a Theory of Implementation?

“…41 In fact matters are more complicated than this, since we can also use a physical system to model a mathematical computation. See(Fletcher [2018]) for some relevant discussion. Thanks to an anonymous referee for flagging this issue.…”