In a forthcoming paper "Models and Fiction", Roman Frigg gives an argument for the view that scientific models are best understood as fictional entities whose metaphysical commitments are “none” (17). I think this argument is a new and important one, but I don’t agree with it. Frigg first considers the view that models are abstract structures. He points out that an abstract mathematical structure, by itself, is not a model because there is nothing about it that ties it to any purported target system. But "in order for it to be true that a target system possesses a particular structure, a more concrete description must be true of the system as well" (5). The problem is that this more concrete description is not a true description of the abstract structure and it is not a true description of the target system either in the case if idealization. So, for these descriptions to do their job of linking the abstract structure to their targets, they must be descriptions of "hypothetical systems", and it is these systems that Frigg argues are the models after all.
My objection to this argument is that there are things besides Frigg’s descriptions that can do the job of linking abstract structures to target systems. A weaker link is a relation of denotation between some parts of the abstract structure and features of the target systems. This, of course, requires some explanation, but a denotation or reference relation, emphasized, e.g. by Hughes, need not involve a concrete description of any hypothetical system.
(Cross-posted with It's Only a Theory.)