Articles

Note from Michael Weisberg

In Discussion on March 3, 2010 by ariew

Michael asked me to post this.  Feel free to discuss.

Thanks to all for a very stimulating visit.
On the long trip home, I had some time for further reflection on a few of the issues that came up in Friday’s discussion.
1. André asked if I hadn’t changed the question because I no longer talked about the “model/world” relation, but now a three part relation: phenomenon to target target to mathematical representation of target and mathematical representation of target to model.
A better answer to his question is a simple “yes.” I think that what my analysis reveals is that the model is only related to the real-world through a series of intermediate steps. This is similar to a point Suppes made in the 1960s where he said that a theory is related to the world first through a series of isomorphisms of theoretical model to a model of the data and a model of the experiment, ultimately back to the world’s structure. I have dropped the isomorphism requirement, but the rest of the picture is similar. What I hope to show is that there isn’t a simple model/world relationship … it has at least these three parts.
2. Jake asked me several times about analogical reasoning and I note that his blog post tried to characterize analogical reasoning in terms of “number of isomorphisms shared.” I don’t have any major objection to Jake’s preferred way of analyzing the situation, just a Goodman-like reaction to it: analogical reasoning needs to be analyzed; it isn’t enough to just say that model’s are analogies of their targets. Maybe the account of feature matching that I am developing would be sufficient for both purposes?
3. Several people asked about whether “framing” plus isomorphism could do the same thing my account of feature matching is designed to do. Here I feel slightly less sure of my answer, but let me have a go:
Feature matching and isomorphism share something in common — they both involve literal matches of some element of the model with some element of the target. However, feature matching has some other properties:
1. Features can be weighed, isomorphisms (even element-by-element) can only be counted.
2. Isomorphism can only be between structural elements (properties and relations), but features can be anything at all. The kinds of features I was talking about like “amplitude” have to be identified — they are not simply structural elements.
3. My account allows for weighing the importance of absence of features as well as counting features that are present. This gives more flexibility.
So I don’t think it will be easy to recover the same kinds of subtleties with an isomorphism based account, but it isn’t impossible. And in the end of the day, my account depends on properties of set intersections and differences, which is obviously related to isomorphism.
Many thanks again for the simulating visit.
Michael
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