Solving categorical syllogisms with singular premises

We elaborate on the approach to syllogistic reasoning based on “case identification” (Stenning & Oberlander, 1995 Stenning, K. and Oberlander, J. 1995. A cognitive theory of graphical and linguistic reasoning: Logic and implementation. Cognitive Science, 19: 97–140. [Crossref], [Web of Science ®] , [Google Scholar]; Stenning & Yule, 1997 Stenning, K. and Yule, P. 1997. Image and language in human reasoning: A syllogistic illustration. Cognitive Psychology, 34: 109–159. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). 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 Störring, G. 1908. Experimentelle Untersuchungen über einfache Schlussprozesse [Experimental research on simple inferential processes]. Archiv für die Gesamte Psychologie, 11: 1–127.  [Google Scholar]) to the present day. We hypothesised that by rendering individual cases explicit in the premises, the chance that reasoners would 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.