
CHAPTER 2 / COMPLEXITY MEASURES 37
that are true, but cannot be proved true--this is in fact very closely related to non-computability
results, where the algorithmic language corresponds to the logical system, and the true statements
that can be defined but not proved correspond to functions which can be defined but not computed.
In reading this chapter, keep in mind that when we refer to non-computable functions, we are
not talking about simply a lack of power or speed of current machines, nor are we talking about a
function which we simply have not been clever enough to invent an algorithm for. We are talking
about a fundamental incomputability ...