In this second part of our genealogy, we move not forward in time, but look back to an encounter that took place between two foundational figures in logic and mathematics, in an attempt to identify the conflicting role of contradiction, misunderstanding, failure, and disagreement in the queer history of computation. While again these figures are well known, the encounter between them is often dismissed as a missed connection and a failed opportunity. As such, it is often relegated to an uninteresting footnote in the history of mathematics. By reengaging this encounter I hope to blur the lines between computing, philosophy, and mathematics, and to disrupt the narrative trajectory that would see Turing as the single foundational figure within this history.
In the spring of 1939, Ludwig Wittgenstein taught a course at the University of Cambridge on the foundations of mathematics, a topic that occupied much of his work from 1922 through to the end of the Second World War. That same semester Wittgenstein was finally elected chair of philosophy at the university, acquiring British citizenship soon thereafter. At fifty years old, he was an established figure in analytic philosophy, having published his groundbreaking Tractatus Logico-Philosophicus almost twenty years prior, and having written extensively on the work of Gödel, Russell, and Whitehead. While Wittgenstein is considered by many to be the most important philosopher of the 20th century, he published very little in his lifetime, and much of his thought and character can only be derived from what survives of his lectures, notes, and seminars. Still less is known of his sexuality, and until the 1980s it was a subject rarely discussed among colleagues or in the many biographies written about his life and work.[i] Even now that Wittgenstein's homosexuality has been largely acknowledged, most scholars are hesitant to imply a connection between his philosophy and his sexuality – that is, between his work and his inner state, emotions, or personality. If, however, in a contemporary light we understand queerness as a structuring mode of desiring, we might view Wittgenstein's thought not as emerging from his sexuality, but as structured by the way in which it shaped his mode of being in the world.
Wittgenstein with Francis Skinner in Cambridge ca. 1933
Wittgenstein is widely regarded to have fallen in love with three men; David Pinset[ii] in 1912, Francis Skinner in 1930, and Ben Richards in the late 1940s.[iii] While it is clear these were relationships of love and affection, the extent to which they were physical is often contested. What seems to make many Wittgenstein scholars uncomfortable in confronting his homosexuality is that it conflicts with the ascetic, almost priestly view of a man so revered by contemporary philosophy. As Bruce Duffy suggests in a 1988 New York Times article on the life of Wittgenstein, "In their effort to put forth a plain, unvarnished record of what Wittgenstein did and said, some of these memoirs have almost the feeling of gospels – hushed, reverential, proprietary."[iv] The philosopher – or indeed, the mathematician – as a carnal, sexual being produces a seemingly irresolvable contradiction. Even those accounts that do concede his affection for other men often suggest that those feelings were purely aesthetic or emotional, and were never acted upon. That said, in perhaps the most controversial section of his 1973 biography of Wittgenstein, W. W. Bartley suggests that the philosopher frequently engaged in a kind of anonymous cross-class sexual contact facilitated by public cruising spaces such as parks and high streets.
By walking for ten minutes to the east . . . he could quickly reach the parkland meadows of the Prater, where rough young men were ready to cater to him sexually. Once he had discovered this place, Wittgenstein found to his horror that he could scarcely keep away from it . . . Wittgenstein found he much preferred the sort of rough blunt homosexual youth that he could find strolling in the paths and alleys of the Prater to those ostensibly more refined young men who frequented the Sirk Ecke in the Kärntnerstrasse and the neighboring bars at the edge of the inner city.[v]
These kinds of exceptional spaces as sites for anonymous sexual encounters continue well into the 20th century, and are instrumental in the structure of being and interaction that the author Samuel Delany identifies as contact:
[C]ontact is also the intercourse—physical and conversational—that blooms in and as “casual sex” in public rest rooms, sex movies, public parks, singles bars, and sex clubs, on street corners with heavy hustling traffic, and in the adjoining motels or the apartments of one or another participant, from which nonsexual friendships and/or acquaintances lasting for decades or a lifetime may spring . . . a relation that, a decade later, has devolved into a smile or a nod, even when (to quote Swinburne) 'You have forgotten my kisses, / And I have forgotten your name.'[vi]
Bartley's sources have been called into question by many historians, but it is less the detail of his description than the acknowledgement of an embodied sexuality that is significant to this history; it is the difficulty we often have in finding the sexual in the everyday, in the lived work of a person beyond these exceptional moments of contact. While such effects may be invisible or to a degree, unknowable, that does not mean they aren't real and do not have a direct effect on the world.
The Prater park in Vienna
In the Tractatus, Wittgenstein defines truth as a tautology, that is, a result achieved through the mere repetition of the same meaning. While he insists that there exist religious or ethical truths, he argues that they cannot be put into words, that they are unknowable through language, and that claims to express ethical truths through philosophy must fail. Wittgenstein summarizes the Tractatus with the maxim: “What can be said at all can be said clearly; and what we cannot talk about we must pass over in silence.”[vii] What does it mean that for Wittgenstein truth is something that can be known but not discussed, that is indescribable? And how does he apply this critique to truths we understand to be beyond language – the truth of the body, or the truth of mathematics?
Back at Cambridge in 1939, another young scholar and philosopher was also beginning his research at the university. After two years working under Alonso Church at the Institute for Advanced Study in Princeton, New Jersey, Alan Turing took up a position as an untenured research fellow at Cambridge, having failed to acquire a full lectureship. Turing and Wittgenstein had been introduced the summer of 1937, but it was not until two years later in 1939 that they would have any meaningful interaction. That spring Turing was also teaching a course on the foundations of mathematics that shared the same name as Wittgenstein's lecture.[viii] Perhaps intrigued, Turing enrolled. Over the course of the semester, Turing engaged in a lengthy dialogue with Wittgenstein, challenging and outright refusing much of Wittgenstein's thoughts on logic and mathematics.[ix] Despite their disagreement, this seems a pivotal moment in the history of computing, in which two queer figures engage with the limits of knowledge and computability, questioning that which exists outside of or beyond.
As a young man, Wittgenstein had thought logic could provide a solid foundation for a philosophy of mathematics. Now in his fifties, he denied outright there were any mathematical facts to be discovered. For Wittgenstein, a proof in mathematics does not establish the truth of a conclusion, but rather fixes the meaning of certain signs. That is, the "inexorability" of mathematics does not consist of certain knowledge of mathematical truths, but in the fact that mathematical propositions are grammatical, a kind of language game through which meaning becomes fixed. One the first day of class, Wittgenstein begins by stating, "I shall try and try again to show that what is called a mathematical discovery had much better be called a mathematical invention."[x]
The Erkenntnis from the Königsberg Congress of 1930