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Can Machines Think? An Old Question Reformulated

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Abstract

This paper revisits the often debated question Can machines think? It is argued that the usual identification of machines with the notion of algorithm has been both counter-intuitive and counter-productive. This is based on the fact that the notion of algorithm just requires an algorithm to contain a finite but arbitrary number of rules. It is argued that intuitively people tend to think of an algorithm to have a rather limited number of rules. The paper will further propose a modification of the above mentioned explication of the notion of machines by quantifying the length of an algorithm. Based on that it appears possible to reconcile the opposing views on the topic, which people have been arguing about for more than half a century.

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Notes

  1. Around the same time other approaches like Church’s λ-calculus (Church 1936) or Post’s production systems (Post 1943) had been developed. Subsequently, however, it had been proven that all these different formalisms are equivalent with respect to the set of functions which they describe.

  2. Input can be simulated by a subprogram which prints the required input onto the tape.

  3. Of course, the exact complexity depends on the considered universal Turing machine U and may be different for a ‘nonstandard’ universal Turing machine.

  4. To add another technicality to the considerations, we may assume that the considered universal Turing machine has less than say 1,000 lines in its Turing table. An example of such a universal Turing machine can be found, e.g., in Minsky (1962). This would result in the fact that the Kolmogorov complexity depends only to a very limited extent on the respectively considered universal Turing machine.

  5. This holds at least for the engineering approach of AI.

  6. that can be accomplished by an intelligent human.

  7. For some particular k and some given universal Turing machine U.

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  1. School of Computer Science and Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    Achim Hoffmann

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  1. Achim Hoffmann
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Hoffmann, A. Can Machines Think? An Old Question Reformulated. Minds & Machines 20, 203–212 (2010). https://doi.org/10.1007/s11023-010-9193-z

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