David E. Dunning

My current book project, Writing the Rules of Reason, is a history of two fundamental transformations in the practice of logic, as it was first reconstructed as a mathematical science and later as a theoretical basis for computing. The idea of logic as a science of reasoning itself—not of human minds but of the abstract laws those minds supposedly follow, or ought to follow—has deep roots in European intellectual history. But between the mid nineteenth century and the Second World War, mathematicians and philosophers across Europe and North America fundamentally reimagined that ancient science. They replaced the prose-based formal logic of Aristotle, a pillar of Mediterranean and Western higher learning for two millennia, with a variety of novel methods for manipulating equations and symbolic systems. This mathematical remaking was shortly followed by a second transformation. With the advent of the digital computer, some experts fought to position the recently reimagined science of logic as crucial to the nascent field of programming. In less than a century, the ancient practice of using words to reason about human reasoning had mutated into a mathematics of machines purportedly capable of reasoning themselves.

I tell these intertwined stories by focusing on the inscriptive techniques through which logicians gave physical form to abstractions; before any theory of reasoning could be embodied in a machine, it was first embodied on paper. Attending to symbolic practice grounds theorizing in the material and social layers of logic as a human activity. By centering notations and communities of users, I show how the most abstract of sciences was rooted in local milieus around a transnational network of practitioners, intertwined with their commitments ranging from religious piety and masculinity to nationalism and anti-Semitism. New methods of writing, always bearing traces of human writers, constrained shifting ideas of what reason is and how it can be materialized. The diversity of symbolic techniques eventually shaped not only the presentation but also the content of logic. In the first instance, to make logic mathematical meant very different things to different nineteenth-century European writers. Rather than uniting around any one way of writing logic mathematically, these practitioners almost invariably introduced idiosyncratic new systems of their own. As notations proliferated, the study of logic demanded ever closer attention to differing affordances of various symbolic systems; readers learned to see competing symbolisms as contingent, and to see potential in that contingency. By the 1930s, mathematical notations had so thoroughly remade logic that many logicians saw symbolic systems not just as useful tools but as objects of study in their own right. This inscriptive reflexivity in turn underlay logic’s appeal to practitioners in computing. Mathematical logic was not intrinsically relevant to programming a computer; rather, as a difficult new way of writing, programming was centrally concerned with notation. Through this practical, even mundane affinity, computer scientists clothed their discipline in a particular set of prestigious conceptual trappings originating in the histories of philosophy and of mathematics. Thus disparate inscriptive cultures, in the service of different agendas in different times and places, provided the contingent raw material for a usable intellectual lineage of the digital era.

See Publications for my articles on the German mathematician Gottlob Frege, the Warsaw School of Logic, and the role of notation in the history of computing, all of which draw on this research.

Two competing ways of writing the same syllogism:

Attending to performances of rigor in mathematical logic led me to broader investigations into the imbrication of gender and mathematics. I am currently co-editing (with Brigitte Stenhouse) a special issue of Endeavour that explores the role of marriage and other domestic partnerships in the lived practice and constructed memory of mathematics. The issue grows out of a conference we co-organized in 2021, in which contributors used cases of marital and familial collaboration to analyze the unstable boundaries dividing labour into the intellectual and the domestic, the masculinized and the feminized, the credited and the unacknowledged. We also published a piece in the London Mathematical Society’s Newsletter arguing that these histories, by revealing gendered categories to be contingent, can promote more equitable visions of math today. In the special issue I will contribute a paper showing how Victorian pedagogue Mary Everest Boole (1832–1916) framed her husband George Boole’s posthumous legacy, implicitly presenting that legacy as a product of both their writings. I argue that she filtered everything—science, religion, morality and home life—through a pedagogical lens. She used an expansive conception of teaching to span the gulf between professional and domestic spheres, constructing the domestic perspective as a privileged view of her husband’s work. Together, the papers in the issue surface the diverse ways mathematical practice has been a resource in constructing particular versions of domesticity, and vice versa.