Abstract

For the last decade there has been a growing interest in the interplay between mathematical practice and argumentation. The study of each of these areas promises to shed light on the other, as I and several other authors from a variety of disciplines have argued. I am particularly grateful to Begoña Carrascal for her careful critique of some central assumptions of this programme, as such challenges are vital for its long-term success. In this commentary, I wish to respond to two of her main points in a similar spirit. She writes: “From a review of many of the papers [of the programme] ... we can extract two main ideas. First, Johnson’s influential definition placed a burden on many of their authors to justify the claim that mathematical products are argumentative. Second, there is a manifest tension in these works between the examples of mathematical products considered as arguments and the process that leads to them” (Carrascal, 2013, p. 6). I will address each of these ideas in turn.