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 It's Only a Theory.)

2 comments:

Bryan said...

On Frigg: "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"

Frigg's presupposition of a target system here is in danger of making his claim trivially true (does target system mean concrete description?). But, if what Frigg means is something more general (e.g., target system = physical reality) then I agree with you Chris -- there seem to be plenty of ways to 'make the link' to an abstract model.

Here's an example.

In quantum theory, one often takes a model (of the commutation relations) to be an algebra of observables. The measurable quantities (the things we have empirical access to) are the possible eigenvalues of these observables.

Now, if one takes a 'target system' to be a particular space of states (of something like an atom), then a 'concrete description' of the system has trivially already been assumed. But this assumption is not necessary. It seems to me that the model (the algebra of observables) provides a perfectly coherent description of physical reality, even without the presupposition of a concrete Hilbert space.

徐若瑄Vivian said...
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