Turing’s Computability

Abstract

This chapter focuses on Turing’s analysis, which reduces effective computability to Turing machine computability. The analysis consists of two steps. The first is the formulation of restrictive conditions on effective computations by idealized human computers. The second is an outline of a reduction theorem, from human computability to Turing machine computability. The chapter discusses in detail the claim that the Turing analysis targets human computers, and explicates some aspects of this notion. It then argues that while this analysis of human computability is of immense theoretical and practical importance, it cannot be taken as the basis of machine computation.