Abstract
1936 was a watershed year for computability. Debates among Gödel, Church and others over the correct analysis of the intuitive concept “human effectively computable”, an analysis at the heart of the Incompleteness Theorems, the Entscheidungsproblem, the question of what a finite computation is, and most urgently—for Gödel—the generality of the Incompleteness Theorems, were definitively set to rest with the appearance, in that year, of the Turing Machine. The question I explore here is, do the mathematical facts exhaust what is to be said about the thinking behind the “confluence of ideas in 1936”? I will argue for a cultural role in Gödel’s, and, by extension, the larger logical community’s absorption of Turing’s 1936 model. As scaffolding I employ a conceptual framework due to the critic Leo Marx of the technological sublime; I also make use of the distinction within the technological sublime due to Caroline Jones, between its iconic and performative modes—a distinction operating within the conceptual art of the 1960s, but serving the history of computability equally well.
Subject
History and Philosophy of Science,Philosophy
Reference37 articles.
1. Review of Turing 1936;Church;J. Symb. Logi,1937
2. The theory of recursive functions, approaching its centennial;Kleene;Bull. Am. Math. Soc. (N. S.),1981
3. Origins of Recursive Function Theory;Kleene;Ann. Hist. Comput.,1981
4. Gandy, R. (1988). The Universal Turing Machine: A Half-Century Survey, Oxford University Press.
5. Marx, L. (1964). The Machine in the Garden: Technology and the Pastoral Ideal in America, Oxford University Press.