This paper proposes an account of mathematical reasoning as parallel in structure: the arguments which mathematicians use to persuade each other of their results comprise the argumentational structure; the inferential structure is composed of derivations which offer a formal counterpart to these arguments. Some conflicts about the foundations of mathematics correspond to disagreements over which steps should be admissible in the inferential structure. Similarly, disagreements over the admissibility of steps in the argumentational structure correspond to different views about mathematical practice. (...) The latter steps may be analysed in terms of argumentation schemes. Three broad types of scheme are distinguished, a distinction which is then used to characterize and evaluate four contrasting approaches to mathematical practice. (shrink)

CHAMELEON is a computational melodic harmonization assistant. It can harmonize a given melody according to a number of independent harmonic idioms or blends between idioms based on principles of conceptual blending theory. Thus, the system is capable of offering a wealth of possible solutions and viewpoints for melodic harmonization. This study investigates how human creativity may be influenced by the use of CHAMELEON in a melodic harmonization task. Professional and novice music composers participated in an experiment where they were asked (...) to harmonize two similar melodies under two different conditions: one with and one without computational support. A control group harmonized both melodies without computational assistance. The influence of the system was examined both behaviorally, by comparing metrics of user-experience, and in terms of the properties of the artifacts that were created between the two experimental conditions. Results suggest that appreciation of the system was expertise-dependent. At the same time, users seemed to adopt more explorative strategies as a result of interaction with CHAMELEON based on the fact that the harmonizations created this way were more complex, diverse, and unexpected in comparison to the ones of the control group. (shrink)