Jessica Carter

This chapter presents aspects of the work of Charles Sanders Peirce showing that he adhered to a number of pre-structuralist themes. Further, it indicates that Peirce’s position is similar in spirit to the category theoretical structuralist view of Steve Awodey (2004). The first part documents Peirce’s extensive knowledge of, and contribution to, the mathematics of his time, illustrating that relations played a fundamental role. The second part addresses Peirce’s characterization of mathematical reasoning as diagrammatic reasoning, that is, as reasoning done by constructing and observing rational relations in diagrams.

According to one prominent view of exercising abilities (e.g., Millar 2010), a subject, S, counts as exercising an ability to ϕ if and only if S successfully ϕs. Such an ‘exercise-success’ thesis looks initially very plausible for abilities, perhaps even obviously or analytically true. In this paper, however, I will be defending the position that one can in fact exercise an ability to do one thing by doing some entirely distinct thing, and in doing so I’ll highlight various reasons (epistemological, metaphysical and linguistic) that favor the alternative approach I develop over views that hold that the exercise of an ability is a success notion in the sense Millar maintains.