 In its original context, Turing’s identification between the computable numbers and Turing machines was aimed at proving that the Entscheidungsproblem is not a computable problem and so not a so-called “general process” problem (Turing 1936–7: 248). The basic assumption to be made for this result is that our “intuitive” notion of computability can be formally defined as Turing computability and so that there are no “computable” problems that are not Turing computable. But what was Turing’s “intuitive” notion of computability and how can we be sure that it really covers all computable problems, and, more generally, all kinds of computations? This is a very basic question in the  philosophy of computer science.