ABSTRACT
Underdetermination is a misfit between theoretical ambitions, data, and methods of inference, where the ambition is to find kinds of truth about some system of interest, whether the cosmos or the brain or whatever is beneath or between. Underdetermination comes in different forms. Given a goal, say to identify the causal relations among a set S of variables in a system or class of similar systems, measurements of a set V of variables may be insufficient to distinguish any of the members of the possible collections of causal relations among the S variables no matter how large the sample sizes for values of variables in V. For brevity, we will call that “structural” underdetermination. Alternatively, the variables in V may suffice for correct estimation of S but only with samples that are larger than feasible. We will call that “sample” underdetermination. Again, aspects of the structure may be unidentifiable because of sheer computational complexity – we could not, for example, search exhaustively among the roughly 410,000,000,000 possible causal structures for the more than 100,000 or so time-series variables measured by contemporary functional magnetic resonance scans of the brain. We call this “computational” underdetermination. And, of course, depending on the estimation method used, the estimates of causal relations or other parameters may carry with them uncertainties expressed as probabilities. The difficulties are not mutually exclusive.
