ABSTRACT
The five large volumes that make up the New Elements of Mathematics amply illustrate both the breadth of Peirce’s mathematical concerns and the proportion of his time that was devoted to mathematical topics. Alongside studies in mathematical logic and foundational issues, we find discussions of a wide range of topics: drafts of textbooks employing novel ideas of how the subject should be taught; mathematical studies of map projection deriving from his work for the United States Coastal Survey; discussions of linear algebra, probability, the four-colour problem, the theory of measurement, non-Euclidean geometry. Since he grew up in a family of mathematicians, and had so much close knowledge of the subject, his views on the nature of mathematics could hardly fail to be important for an overall assessment of his philosophical achievement. But, if that were the only reason for examining them the need to be selective in a volume that is to be of manageable and moderate length might lead us to mention these views in passing or discuss them in a cursory fashion. In fact, for at least two reasons, Peirce’s writings about mathematics are closely integrated with his work on the issues that concern us directly here; his doctrines about how mathematical knowledge is possible are presupposed by his accounts of knowledge and reality, and by his accounts of philosophical method.1
