Saturday, January 31, 2009

Models and Fiction

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 Honest Toil.)


  1. First of all, let me indulge in a bit of shameless self-advertising. Roman's paper will be appear in a special issue of Synthese on the ontology of scientific models that I have guest-edited, (the other contributors are Steven French, Ron Giere, Martin Thompson-Jones, Adam Toon and myself). Hopefully, the issue will be out sometimes in the near future. Check it out!

    I agree with you. I think that an abstract structure can represent (some aspect of) a concrete system without the mediation of a fictional model if one has what I call an interpretation of the structure in term of the system.

    I think the bridges example you use in your Nous paper illustrates the point quite well as there seem to be no need to invoke a fictional model there. (One may argue that our commonsense description of that real-world system (the one that carves it into bridges, islands, and canals) is itself the description of a fictional system for the real system is actually an enormous system of fundamental particles. But, as far as I can see, the fact that the latter descripiton is true does not make the former false.)

  2. "A weaker link is a relation of denotation between some parts of the abstract structure and features of the target systems. "

    I generally agree with the thrust of this criticism - however, I think the entire paranoia about not knowing, (with certainty?) the relation between some theoretical commitment and the world is just caused by an a priori assumption of representationalism. If we'll just admit that the digital camera view of human experience is a bad idea, and that it makes much more sense to believe that our notions of things in the world are just the world, formally, then there is no need to worry about whether our theories "actually" describe the world. Rather, they are either true or false - if they are the world, formally, then they are true. Furthermore, if form isn't mathematical, then we needn't even worry about certainty in order to say we have the world in our head, formally. There is nothing inherent in the notion of form (eidos, morphe, limit) which orders that we understand it as mathematical structure.