Abstract

Each formalism implies a specific distinction between objects and the system of their combination. Thereby, the concept of function has a peculiar role: it governs how objects interact, and is also an object of computation. Over more than a century, this intermediary status has broached the problem of how exactly a formalism should admit functions as first-class citizens. In this text, I demonstrate how traces of this problem can be found across disciplinary boundaries, from the early foundational crisis to the advent of contemporary programming languages. As it turns out, the problem carries with it a shift in the understanding of the unsaturated function argument: while originally conceived of as a mere placeholder that awaits a guaranteed fulfilment, it is given the status of an object without guaranteed properties, sans-papier. This citizenship of sans-papiers is not without an impact on the laws of their mutual combination, however. Through a number of examples, I touch upon a number of philosophical, political, and technological implications and discuss what practical consequences this problem has for logic and computing.