Pat, (01) There are two independent questions here: (02) 1. The historical or hermeneutic question of what exactly Tarski, Quine, or Montague intended. (03) 2. The question of whether it is useful to make a distinction between models and what they are intended to model. (04) I'm sorry that I raised question #1 in my previous note, because the important issue, in my opinion, is #2. (05) The diagram I use to illustrate the distinction is the attached mthworl2.gif. On the left is a representation of the world in a picture that suggests its complexity. On the right are some formulas of some theory. In the middle is a Tarski-style model represented as a graph. (06) The point I emphasize is that model theory evaluates the formulas of a theory in terms of a model to determine a value T or F for each formula. But the question of degree of approximation is best considered in terms of how accurately the model corresponds to that aspect of reality it is intended to characterize. (07) When I show that diagram to various people who know logic and model theory, I get two sharply polarized reactions. Some immediately say "Of course, that's obvious." But others get angry and say that I am misrepresenting logic, or model theory, or analytic philosophy. (08) The point I make is that the right side of the diagram involves logic, which by itself is independent of any application until we try to apply it. The left side involves an application, which gets into an enormous number of issues that are outside the realm of pure logic and address philosophy of science, engineering, experimental error, and practical problems of all kinds. (09) I believe it's important to make that distinction, and this diagram (or something else along those lines) helps to clarify the issues. (010) John (011)
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