ABSTRACT: I examine some recent controversies involving the possibility of mechanical simulation of mathematical intuition. The first part is concerned with a presentation of the Lucas-Penrose ...

Computability theory establishes which problems can in principle be solved by mechanical procedures, formalised by the Turing machine model and its equivalents. It draws a firm boundary between ...

This algorithm is an example of Turing thinking. The algorithm ignores any issue of what resources are needed. It is assumed that pushes and pops will never fail for lack of resources. The algorithm ...

The solution to the difficulty of having to prove that you can implement every or any Turing machine is to notice that if a Turing machine can compute anything that is computable than there should be ...