Can the issue of human (ir)rationality contribute to the scientific study of reasoning? A tempting line of argument seems to indicate that it can't. Here it is. (i) To discuss diagnoses of (ir)rationality arising from research in the psychology of reasoning one has to deal with arbitration, i.e., the assessment of competing theories of what a reasoner ought to do, if rational. But (ii), by the Humean divide between is and ought, arbitration is logically independent from the description of reasoning. And clearly (iii) the main goal of psychological inquiry is just such a description. It follows that normative concerns about diagnoses of (ir)rationality cannot serve the proper scientific purposes of the psychology of reasoning, and would better be left aside altogether in this area. A recent cornerstone for this debate is Elqayam and Evans (2011). Part of their discussion is devoted to voice precisely this criticism of “normativism,” thus favoring a purely “descriptivist” approach in the study of human thinking. In our view, the above argument is essentially valid, but unsound. Premise (i), in particular, may have seemed obvious but doesn't hold on closer inspection, as we mean to show. In reasoning experiments, participants are assumed to rely on some amount of information, or data, D. These include elements explicitly provided (e.g., a cover story), but possibly also further background assumptions. Note that, as a rule, D is not already framed in a technical language such as that of, say, probability theory: cover stories and experimental scenarios are predominantly verbal in nature, although they may embed more formal fragments (e.g., some statistical information). On the basis of D, participants then have to produce one among a set of possible responses R, for instance an item chosen in a set of options or an estimate in a range of values allowed (say, 0 to 100%). Here again, the possible responses do not belong to a particular formal jargon (although, again, some formal bits may occur in the elements of R). Suppose that some particular response r in R turns out to be widespread among human reasoners and is said to be irrational. Such a diagnosis, we submit, has to rely on four premises. (i) First, one has to identify a formal theory of reasoning T as having normative force1. (ii) Second, one has to map D onto a formalized counterpart D* belonging to the technical language employed in T. (iii) Third, one has to map R, too, onto a formalized counterpart R* belonging to the technical language of T. This step implies, in particular, that the target response r within R be translated into its appropriate counterpart r*. (iv) And finally, one has to show that, given D*, r* does contradict T. If either of (i)–(iv) is rejected, the charge of irrationality fails. We thus have a classification of the ways in which one can question diagnoses of irrationality that may be attached to the results of a reasoning experiment. Depending on whether (i), (ii), (iii), or (iv) is the main focus of controversy, we will talk about arbitration, data mismatch, response mismatch, and norm misapplication, respectively. Relying on this partition, let us now consider three prominent cases in which normative concerns have entered psychological research on reasoning.