Underdetermination

Numerical/Statistical Data

When data are strictly numerical, regression is an accepted means of curve-fitting that governs the derivation of mathematical expressions to explain the data. Strictly speaking, such expressions are valid only over the domain of the data used to derive them; additional data may result in a different explanatory expression. Regression introduces two ideas that affect our choice of theories. First, a theory that explains a lot is held to be better than one that explains small amounts of data. Second, one can discount as being somehow aberrant both data that seem to be extreme and predictions that are not satisfied.

Observational Data

In case study research data often consist of observations or events rather than numbers. Given an explanatory theory, the possibility that there is some other theory not yet considered or devised that will better explain the data cannot be discounted. Thus, despite the certainty with which a particular theory may be presented, it is considered strictly the best theory advanced to date and, as with the case of regression, additional data may demand a different theory or an ad hoc adjustment to an accepted theory.

Theory Choice

The sheep story that opened this entry illustrates three theories that explain the observation. How do we choose which one is “best?” The data will not help us. Because theories both explain and predict, we could argue that the sociologist's “all sheep” theory is preferable because it possesses greater predictive power than the alternatives, but this does not seem to be a good reason to accept it for its explanatory power; by this criterion, the philosopher's theory seems best. There is no obvious connection between explanation and prediction.

Other criteria used for theory acceptance are neither rigorously derived nor applied. The presentation of the preferred theory often takes the form of an inductive argument. The link between the premises (reasons to accept the theory) and the conclusion (that a particular theory best explains the data) is often inferential, a process not well understood.

Extratheoretical claims that govern theory choice (and are often not made explicitly) include the following. Although they are frequently used, it is (in a philosophical sense) difficult to justify any of them beyond the claim that “they work.”

...