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Thinking May Be More Than Computing
 Cognition
, 1986
"... 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 machin ..."
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Cited by 18 (3 self)
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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.) 1.
Effectivizing Inseparability
, 1991
"... Smullyan's notion of effectively inseparable pairs of sets is not the best effective /constructive analog of Kleene's notion of pairs of sets inseparable by a recursive set. We present a corrected notion of effectively inseparable pairs of sets, prove a characterization of our notion, and show that ..."
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Cited by 2 (0 self)
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Smullyan's notion of effectively inseparable pairs of sets is not the best effective /constructive analog of Kleene's notion of pairs of sets inseparable by a recursive set. We present a corrected notion of effectively inseparable pairs of sets, prove a characterization of our notion, and show that the pairs of index sets effectively inseparable in Smullyan's sense are the same as those effectively inseparable in ours. In fact we characterize the pairs of index sets effectively inseparable in either sense thereby generalizing Rice's Theorem. For subrecursive index sets we have sufficient conditions for various inseparabilities to hold. For inseparability by sets in the same subrecursive class we have a characterization. The latter essentially generalizes Kozen's (and Royer's later) Subrecursive Rice Theorem, and the proof of each result about subrecursive index sets is presented "Rogers style" with care to observe subrecursive restrictions. There are pairs of sets effectively inseparab...