Comparative Historical Studies (0): Introduction

Despite the paramount importance of the \(\lambda \) -calculus as a formal system, historical studies provide an alternative way to uncover and explicitly analyze diverse logico-philosophical aspects of Church’s work and the \(\lambda \) -calculus in general. Moreover, the naturalness and intuitiveness of the \(\lambda \) -calculus can also be appreciated by means of the historical approach. Comparative historico-philosophical analyses show similarities and differences between the \(\lambda \) -calculus and great figures from the past; such analyses, suggested by Church in The Calculi of Lambda-Conversion, illuminate diverse aspects of the \(\lambda \) -calculus that are relevant for \(\lambda \) -philosophy. In particular, the following three chapters of this part of the book offer three comparative historical studies between the \(\lambda \) -calculus and Viète’s The Analytic Art (or New Algebra), Descartes’ analytic geometry, and Wittgenstein’s Tractatus. These three studies are preliminary components of a projected multidisciplinary history of the \(\lambda \) -calculus to be carried out in a future publication.