What Have We Learned in the Path from Gödel and Turing to Artificial Intelligence?

  • Kumaraswamy Velupillai
Conference paper


The distant connection with that romantic and mythical figure of nights of splendour -Harun Al Rashid — that the term ALGORITHM evokes should not be dismissed lightly. From Arithmetic and Geometry to Analysis; then Al Khowarizmi’s Algebra; then again to Cartesian synthesis of Algebra and Geometry to the reign of SPACE, INTUITION and REASON; and finally the noble steps to the rehabilitation of logic in the analysis of reason and the founding of mathematics in the formalism of logic. It is as if we have traced a full circle from the analysis of number(s) to the number theoretic analysis of the reasoning processes of the mind — from the Pythagorean awe at the magic of numbers to the Gödelian numberings of our attempts to reason. Magic and Reason, the stuff that epics -be they Greek or Indian — are made of, have cause to be mediated by Decision. Economics, some say, is, partly at least, the science of optimal decision making under various constraints. And the making of decisions whether optimal or not, is almost life. The analysis of the making of decisions, the ubiquitous meta-level study, is where the confrontation between Magic and Reason must be resolved. That memorable resolution has been brought to the frontiers of pure and applied science by, first, Gödel introducing the notion of GENERAL RECURSIVENESS on the basic of a suggestion made by Herbrand; Turing making it fundamental with his codification by Turing Machines of Effective Computability and finally Putnam showing the equivalence of Rational Economic Man and the Universal Turing Machine. If this ‘rational reconstruction’ is even remotely plausible then the ‘Turing Test’, a turning point in Man’s endless quest to understand the embodiment of mind and his sometimes tragic but often heroic attempts to build ‘Artificially’ an ‘Intelligence’, deserves the public discussion that moral and ethical issues have always had in the body politic. It will not do, as Popper will have us do, to ignore the ‘Turing Test’:

“Turing said something like this: Specify the way in which you believe that a man is superior to a computer and I shall build a computer which refutes your belief. Turing’s challenge should not be taken up; for any sufficiently precise specification could be used in principle to programme a computer. Also the challenge was about behaviour — admittedly including verbal behaviour — rather than about subjective experience.”

(Popper and Eccles, 1977. p. 208; Italics added).


Turing Machine Initial Endowment Rational Reconstruction 13th Step Trade Cycle Theory 
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© Springer-Verlag Berlin · Heidelberg 1989

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  • Kumaraswamy Velupillai

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