Difficult problems are often made easier to approach and solve through the use of external aids such as diagrams, physical/mathematical models, or computer simulations 1. Within the social, natural, and applied sciences, these objects may be thought of collectively as “scientific representations”. While the ubiquity of these representations can be taken as prima facie evidence of their utility, their heterogeneity has made philosophical engagement with them a challenge. A minimalist explanation might attempt to reduce the class to a dyadic “representational function”: content-bearing vehicles stand in for a target in virtue of some relationship that holds between features of the vehicle’s content and features of the target 2. These dyadic relations have traditionally been conceived of in structuralist terms, such as similarity ($A$ represents $B$ if and only if $A$ and $B$ have any relevantly similar contents) or isomorphism ($A$ represents $B$ if and only if $A$ contains structures that can one-for-one map onto structures in $B$). Unfortunately, structuralist accounts of this sort run into a challenges involving directionality and misrepresentation.
Barwise1995.
Vorms2013a.