One of the most central issues in epistemology concerns the nature of scientific theorizing. Across the sciences, theorizing is frequently aided by quantitative methods for data analysis and for the drawing of inferences. In other situations, though, scientific theorizing is performed without the guidance of mathematical methods. This talk explores certain non-quantitative methods through the lens of some well-established quantitative methods. On the one hand, some non-quantitative methods have been subjected to criticism, even though they are structurally identical to a large body of quantitative methods. The centrality to ordinary scientific inquiry of the latter methods thus supports the legitimacy of the non-quantitative ones. On the other hand, certain other non-quantitative methods are frequently used, even defended, in some areas of cognitive science. However, research on judgment and decision-making strongly suggests that these methods are highly susceptible to numerous distorting influences. Thus, in this case, there is reason to look for new, most probably quantitative, methods that can be shown to be more reliable. Both types of cases are illustrated with examples from contemporary linguistics.