Monday, March 30, 2009
SVT: Original and Continuing Motivation
At the recent MS3 meeting, I gave a brief presentation on Pat Suppes contributions to thinking about models. One point is relevant to Contessa’s question about the original arguments in favor of the SVT over the statement view. At least two of the three founders of the SVT, Suppes and Beth (the third was Arthur Burks), were much concerned with the foundations of physics, Suppes with classical mechanics and Beth with quantum theory. They found attempting reconstructions in first (or even second) order logic to be impossibly cumbersome. The physics gets lost in the logic. To be convinced of this, one need only look at Richard Montague’s 1962 first order reconstruction of classical mechanics. [Deterministic Theories. In Formal Philosophy and Selected Papers of Richard Montague, ed. R. H. Thomason, 303-59. New Haven, Yale University Press, 1974.] As I remember, one can barely make out F= ma in something like Axiom 24. Set Theory and State Spaces are far more perspicuous than first order formulae. van Fraassen, who was inspired by Beth, had a similar motivation. The general idea of getting the philosophy of science closer to the science has been for me, and I think many others, a major attraction of the SVT, even though the primary interest has been understanding the actual practice of science rather than the foundations of theories.
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Especially the last sentence sounds a bit as if the semantic view had not been developed as a competitor to the syntactic view at all, but rather as a different means of analysis for a different purpose (understanding scientific practice and describing theories easily and without much change from the original formulation). If that is the case, then there does not have to be anything wrong with the syntactic view at all given its purpose (analyzing developed theories, their relation to observations etc).
ReplyDeleteJust focusing on syntactic and semantic approaches in general (rather than specific versions like constructive empiricism or the received view), I am not convinced that either description has to be more cumbersome than the other. In semantic descriptions, few or none of the axioms of set theory or the subsequently introduced definitions of mathematical concepts are mentioned, and I don't see why those couldn't also be omitted in a syntactic description. In the case of F=ma, one could write that out somewhat more perspicuously as
F(p,t)=m(p)·a(p,t),
at which point one can choose whether one understands this as a restriction on a tuple of sets F, m, a, P, and T or one takes the universal closure of this as a formula of a sorted first or higher order logic.
Hi Ron,
ReplyDeleteThanks for the interesting post. To my mind, though, this is another example of saddling the view that theories are sets of sentences/propositions with unnecessary (and dubious) assumptions and then throwing the baby away with the bath water. I don't see any reason to think that, if theories are collections of sentences/propositions, then they must be formalizable in some first or second order language. In other words, the fact that most scientific theories cannot be translated in a first-order language, at most, seems to reveal the expressive limits of such a language not the limits of the view that theories are collections of sentences. Isn't it?
One can distinguish between a strict syntactic view of theories and a more general statement view which keeps theories as sets of statements in ordinary scientific language. So this is really a kind of semantic view also since the statement are interpreted. But then one omits models. The objection to this is that all the statements are strictly speaking false of the world. Here one has the option of somehow making the statements vague enough to be true of the world or making them exactly true of models, with the vagueness then relegated to the application of models to the world. I prefer the latter option, with similarity being the appropriate relationship between models and the world. I think this provides an overall better account of scientific practice.
ReplyDeleteRon,
ReplyDeleteI agree and probably I should have put my original question in a less loaded terminology. The idea that I'm toying with lately is that there is no good reason to think that the one between the two options in your comment is an exclusive 'or'--i.e. that we cannot take theories to be sets of sentences/propositions that are true of some models and, in some cases, approximately true of the world.