Sensor arrays are often proposed as powerful, relatively low-cost approaches for characterization of complex chemical mixtures. However, such arrays routinely underperform as general-purpose analytical devices in more complex applications. Although these difficulties can be colloquially interpreted as a deficiency in selectivity, the reality is that there is a surprising lack of consensus around a quantitative definition of selectivity for multivariate analytical measurements, and little discussion about the analytical implications of partial selectivity, which is a salient feature of most sensor arrays. This work discusses the current qualitative criteria for selectivity as determined by IUPAC and proposes a general-purpose selectivity figure of merit based on Fisher information. The connection between this figure of merit and contemporary chemometric expressions of selectivity based on net analyte signal is demonstrated. The figure of merit is applied to chemical sensor array design via simulation and the limitations of so-designed sensor arrays in addressing arbitrary chemical sensing tasks are explored. Finally, the role of selectivity in sensor array design is reevaluated and discussed.