Excerpt from Physical Idealization as Plausible Inference, Vol. 4
The analysis of physical systems almost always relies on idealized models of the objects involved. Any idealization, however, will be incorrect or insufficiently accurate some of the time. It seems reasonable, therefore, to view a physical idealization as a defeasible inference which can be withdrawn in the presence of contrary evidence. This talk discusses the consequences of such a view.
We focus on examples where a system may or may not go into a state where idealizations are violated, such as dropping a ball near an open switch connected across a battery. We show that:
1. Non-monotonic logics will try to enforce the idealization by supposing that the ball will miss the switch. This anomaly does not seem to be solvable by the kinds of techniques that have been applied to the Yale Shooting Problem, which it superficially resembles. We show that this problem is analogous to anomalies in non-monotonic logic that are time-independent.
2. A probabilistic analysis is possible, but it relies on independence assumptions that are hard to justify in general.
3. For completely specified systems, the rule "If the idealization gives solvable equations, then assumes that it holds" is, in fact, a monotonic system of inferences. It should therefore be possible to characterize this in a purely deductive theory. We show that this is, indeed, possible for simple cases, but can get messy in complex systems.
4. Programs that make physical predictions can avoid these problems by simply avoiding reasoning from the future to the past. Though most current programs observe this restriction, it seems likely that more powerful and general systems will have to violate it, and thus deal with this issue.
5. Finally, we look at dynamic systems where the idealization can be observed at any single instant, but it is inconsistent over extended intervals.
Reasoning about physical systems almost always relies on idealized models of the objects involved. Strings and pulleys are massless; springs obey Hooke slaw; solid objects are perfectly rigid, and so on [Addanki etal., 89]. Generally, analyses based on such idealizations are correct qualitatively and reasonably accurate quantitatively. (What constitutes reasonable accuracy depends both on the requirements of the task for which the analysis is being performed and on the availability of alternative models that are both more accurate and tractable. In practice, modellers often use idealizations that are known to be inaccurate, either because the next more accurate model is horribly complex, or because no more accurate model is known.)
Sometimes, however, simple idealizations give answers that are not adequate.
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