Thinking may be more than computing

Abstract

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.)

Philosophy of Computer Science

“…Further Reading: For more on Kugel's views, see Kugel 1986a. Wegner and Goldin 2006a is a response to Kugel 2005 clarifies how hypercomputation can show how some aspects of human cognition might not be Turing computable.…”

Logic and Complexity in Cognitive Science

“…In particular, some critics have argued that cognitive systems can do more than Turing machines. For example, learning understood as identifiability in the limit (Gold, 1967) is not computable (see Kugel, 1986, for an extensive discussion). Another strand of argumentation is motivated by Gödel's theorems.…”

Determining the Factors Influential in the Validation of Computer-based Problem Solving Systems

“…Platt (1964) has proposed how humans can be more effective in developing scientific theories. And Kugel (1986) is one of many writers comparing the human thought process to computing, an idea strongly ridiculed by Dreyfus (1972Dreyfus ( , 1988.…”