We elaborate on the approach to syllogistic reasoning based on "case identification" (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition (ecthesis), and that there are traces of this method in the strategies described by a number of psychologists, from Störring (1908) to the present day. It was hypothesised that by rendering individual cases explicit in the premises the chance that reasoners engage in a proof by exposition would be enhanced, and thus performance improved. To do so, we used syllogisms with singular premises (e. g., this X is Y). This resulted in a uniform increase in performance as compared to performance on the associated standard syllogisms. These results cannot be explained by the main theories of syllogistic reasoning in their current state
