The text shows a historical approach to the concept of logic in relation with mathematics. Therefore it exposes the contributions of ancient and medieval logic, and problematizes the approaches of logicism and intuitionism with the idea of providing aesthetic reasonableness based upon the theory of abduction of Charles Sanders Peirce. Later on, it demonstrates the fundamentals of a hermeneutic–approach qualitative research. Finally, it advances the development of aesthetic reasonableness based on the design and staging of a didactic strategy, supported on the analysis of fictional stories and research articles. The first results of the strategy show teachers in training, both in literature and mathematics, at the University of Antioquia, are unaware of the logical and creative possibilities that can be experienced and identified through literary and scientific texts. This difficulty suggests the importance of further progress in the teaching strategy design and experience.