Thinking may be more than computing

The uncomputable parts of thinking (if there are any) can be studied in much the same spirit that Turing (1950) suggested for the study of its computable parts. We can develop precise accounts of cognitive processes that, although they involve more than computing, can still be modelled on the machines we call ‘computers’. In this paper, I want to suggest some ways that this might be done, using ideas from the mathematical theory of uncomputability (or Recursion Theory). And I want to suggest some uses to which the resulting models might be put. (The reader more interested in the models and their uses than the mathematics and its theorems, might want to skim or skip the mathematical parts.)